Generalizable long short-term memory models for beef cattle DMI under grazing

Abstract

Estimating individual dry matter intake (DMI) on pasture remains costly, labor-intensive, and episodic. We developed a deployable sequence model to predict daily, per-animal DMI using walk-on scale weights, metered water intake, animal metadata, and publicly available weather. A 3-layer long short-term memory (LSTM) network (hidden size = 256, dropout = 0.20) ingested 7-d windows of engineered covariates, including rolling statistics, first- and second-order differences, short lags, thermal ranges, and temperature–humidity index (THI), scaled with a RobustScaler; categorical variables were encoded with learned embeddings. The prediction head was a compact multilayer perceptron, and outputs were inverse Box–Cox transformed to kilograms per day. Training used animal-identity–grouped splits, Huber loss, Adam optimization with gradient clipping, learning-rate scheduling, early stopping, and Optuna hyperparameter tuning. A single feature–scaler bundle was evaluated against National Academies of Sciences, Engineering, and Medicine (NASEM) equations and three strictly held-out external validations: regional drylot (Morgantown, WV), non-regional drylot (Hyplains, KS), and grazing (2023 Wardensville, WV). Using identical evaluation masks, the LSTM improved accuracy relative to NASEM (pooled RMSE 1.329 vs. 1.858 kg/d; R² 0.655 vs. 0.326), with the largest gains in grazing (LSTM RMSE 1.180, R² 0.507; NASEM RMSE 3.883, R² −4.337). Iterative fine-tuning with a frozen encoder showed stable behavior under bias-only head updates across production systems. These results demonstrate that accurate, generalizable DMI prediction can be achieved from pragmatic inputs, enabling scalable evaluation of intake phenotypes and feed-efficiency traits directly in grazing systems.

We show that week-scale trajectories of weight, water use, and weather—collected passively—are enough to predict individual cattle intake on pasture with a compact, calibratable LSTM, enabling pasture-based DMI prediction at scale.

Introduction

Grassland agriculture is a cornerstone of global food production, underpinning both rural economies and ecological stability. Properly managed grazed grasslands enhance soil health, sequester carbon, increase microbial biodiversity, and transform low-quality forages into nutrient-dense animal protein (Barnes et al. 2007). These systems are particularly valuable in landscapes unsuitable for cropping and in communities dependent on livestock for food security and income. However, ruminant livestock production is also a major contributor to anthropogenic greenhouse gas (GHG) emissions, with livestock accounting for ∼14.5% of global emissions and beef and dairy cattle responsible for the majority through enteric methane (CH₄) production (Gerber et al. 2013). Dry matter intake (DMI) is a fundamental driver of cattle productivity, feed efficiency, and environmental impact. It is the single strongest predictor of CH₄ emissions in grazing cattle (Min et al. 2022; Ruden et al. 2023) and is essential for calculating residual feed intake (RFI) and other efficiency metrics that can be leveraged for genetic selection to reduce emissions (Lahart et al. 2024). While nutritional interventions such as lipid supplementation, nitrate feeding, or plant secondary compounds can reduce methane output (Civiero et al. 2021; Santander et al. 2023; Costigan et al. 2024; Dwan et al. 2025), selecting for inherently feed-efficient cattle remains one of the most cost-effective and durable strategies for CH₄ mitigation in grazing herds (Lahart et al. 2024).

Accurate measurement of DMI in grazing systems remains challenging. Gold-standard approaches—marker dilution, direct forage sampling, or specialized feeding facilities—are labor-intensive, costly, and impractical for routine use (Williams et al. 2019; Fowler et al. 2022). Predictive equations, such as those in the National Academies of Sciences, Engineering, and Medicine beef cattle requirements (NASEM 2016), offer a low-cost alternative but suffer from reduced accuracy when applied outside the conditions for which they were developed (Williams et al. 2019). Moreover, many recent modeling and machine learning (ML) studies in cattle have relied on NASEM-predicted DMI as a proxy for measured intake, rather than using ground truth intake data (Davison et al. 2021; Salleh et al. 2023; Koşkan et al. 2025). While this approach facilitates modeling in data-limited contexts, it constrains biological validity and risks compounding equation-based biases in subsequent analyses.

ML approaches offer a powerful alternative, capable of integrating nonlinear relationships among heterogeneous data sources in ways that traditional regression equations cannot. Across agriculture, ML adoption has accelerated (Liakos et al. 2018; Benos et al. 2021), integrating remote sensing, sensor networks, and climate data for predictive modeling. However, uptake in livestock production has lagged, with most applications confined to dairy or feedlot cattle (Salleh et al. 2023; Koşkan et al. 2025). Early successes in DMI prediction from feeding behavior data (Davison et al. 2021) and mid-infrared milk spectra (Salleh et al. 2023; Koşkan et al. 2025) demonstrate the potential but highlight the scarcity of models developed for grazing systems using measured DMI data.

Recent advances have shown that engineered incremental and time-series features can substantially improve DMI prediction performance (Blake et al. 2023b; Walker et al. 2024). These features capture within-animal changes in behavior, physiology, and environment over time, offering a dynamic representation that static, single-day variables cannot provide. In beef cattle, incorporating such incremental features from multiple days—rolling averages, deltas, and other temporal derivatives—has been shown to improve predictive accuracy and model generalizability across environments (Blake et al. 2023b; Walker et al. 2024). This temporal complexity makes recurrent neural network architectures, such as the long short-term memory (LSTM) network, particularly well-suited for DMI prediction in cattle. LSTM models are designed to capture dependencies across sequential data and to retain information over varying time lags, making them ideal for integrating multi-source, multi-scale time-series variables (Ellis et al. 2020; Hubbart et al. 2023). They can simultaneously account for animal, environmental, and management variables, learning patterns in how these change incrementally over time. Yet, despite their suitability, no published studies have tested LSTM models for DMI prediction in grazing cattle or explored how much system-specific grazing DMI data is required to achieve reliable predictions.

The objective of this study was to develop and evaluate an LSTM-based DMI prediction model for beef cattle in both drylot and grazing systems, using engineered incremental and time-series features within an iterative training framework. The central hypothesis was that adding ground truth grazing DMI data incrementally to the training set would improve prediction accuracy for grazing cattle, with performance gains plateauing after a threshold amount of grazing-specific data. The model was validated on three independent datasets: 1) an unseen similar drylot system, 2) an unseen dissimilar drylot system, and 3) an unseen grazing herd to assess generalizability across production systems.

Materials and methods

Animal care and use statement

The animal work described below was approved by the West Virginia University Animal Care and Use Committee as protocols no. 2206054350, 2204052569 and 2108046615. The West Virginia University Animal Care and Use Committee uses the Guide for the Care and Use of Agricultural Animals for its Agricultural Animal Program. The Agricultural Animal Program is AAALAC-accredited no. 1957.

Animal sourcing

All animal data were collected at three locations: the West Virginia University (WVU) Reymann Memorial Farm Research, Education, and Outreach Center (REOC) in Wardensville, WV; the WVU Animal Science Farm REOC in Morgantown, WV; and the Hy-Plains Feedyard in Montezuma, KS. The data from the Reymann Memorial Farm REOC were either collected from the drylot facility or the grazing complex during grazing tests in 2021, 2022, or 2023. The data from the Animal Science Farm REOC were all collected in the drylot facility. Locations differed in elevation and climate (Table 1).

Table 1.

Climate summaries for Wardensville, WV (elevation = 307 m), Montezuma, KS (elevation = 847 m), and Morgantown (elevation = 354 m), WV, from 2021 to 2024.

Location	Avg temp (C)	Temp range (C)
2021
Wardensville, WV	11.8	−10.0 to 37.2
Morgantown, WV	NA	NA
2022
Wardensville, WV	11.0	−16.1 to 32.8
Morgantown, WV	13.0	−5.6 to 28.3
2023
Wardensville, WV	11.8	−13.3 to 35.0
Morgantown, WV	10.0	−13.3 to 32.2
2024
Wardensville, WV	11.7	−12.7 to 36.0
Morgantown, WV	10.8	−14.4 to 36.1
Montezuma, KS	14.2	−33.3 to 45.5

Animals at the Reymann Memorial Farm REOC were sourced from the West Virginia Department of Agriculture herd, the West Virginia University herd, or were privately consigned to either the West Virginia Young Sire Performance Test or the Summer Performance Test conducted at Reymann Memorial Farm REOC. Upon arrival at WVU facilities (Wardensville and Morgantown), animals underwent standardized receiving procedures under veterinary supervision. For bull cohorts, this included physical examination, chute weighing, radio frequency identification (RFID) tag confirmation or application, administration of a dewormer (Safe-Guard®, Merck Animal Health, Madison, NJ, USA), metaphylactic treatment for bovine respiratory disease prevention (Draxxin®, Zoetis, Parsippany-Troy Hills, NJ, USA), and intranasal vaccination for Pasteurella spp. (Bovilis® Once PMH, Merck Animal Health, Omaha, NE, USA), consistent with station performance-test guidelines. Comparable health-management protocols were applied within each cohort according to veterinary recommendations. All procedures followed approved institutional animal care and use protocols. Cattle included in the Hy-Plains Feedyard validation cohort were processed according to standard commercial feedyard veterinary receiving protocols prior to intake monitoring. All animals were tagged with half duplex (HDX) RFID ear tags either prior to arrival or during initial processing at the station. Animals at the Animal Science Farm REOC were sourced from the West Virginia Department of Agriculture herd or the West Virginia University herd. During a period from 2019-07-08 to 2024-07-25, robust individual intake data were collected on 2,084 animals of 12 breeds (Angus, Charolais, Limousin, Braunvieh, Crossbreed, SimAngus, Hereford, Simmental, Charolais Cross, Black Hereford, Red Angus, Akaushi) and three sex classes (bull, steer, heifer: Table 2). All animals in this study were Bos taurus breeds or Bos taurus–derived crossbreds typical of U.S. finishing-stage beef production systems; Bos indicus or indicus-influenced genetics were not represented.

Table 2.

Summary of test groups, production systems, and animal characteristics across study years (2019–2024).

Start date	End date	Location	System	Animal number	Animal class	Breed(s)	Avg start weight (kg)	Avg start age (days)
2019
2019-07-08	2019-08-30	Wardensville	Drylot	65	Bull	Angus (n = 62) Braunvieh (n = 2) Limousin (n = 1)	314	293
2019-07-22	2019-09-09	Wardensville	Drylot	41	Heifer	Angus (n = 41)	366	498
2019-11-25	2020-02-20	Wardensville	Drylot	136	Bull	Angus (n = 110) Hereford (n = 10) SimAngus (n = 10) Charolais (n = 3) Simmental (n = 3)	305	283
2020
2020-03-20	2020-05-08	Wardensville	Drylot	53	Steer	Cross Breed	261	442
2020-06-29	2020-08-19	Wardensville	Drylot	36	Heifer	Angus (n = 26) Charolais (n = 9) Limousin (n = 1)	304	269
2020-06-29	2020-08-25	Wardensville	Drylot	99	Bull	Angus (n = 63) Cross Breed (n = 18) Charolais (n = 17) Limousin (n = 1)	309	269
2020-11-23	2021-02-15	Wardensville	Drylot	68	Bull	Angus (n = 61) SimAngus (n = 5) Charolais (n = 2)	404	268
2021
2021-03-22a	2021-05-12	Wardensville	Drylot	56	Steer	Cross breed	261	335
2021-04-13	2021-06-01	Wardensville	Drylot	70	Heifer	Cross breed	299	371
2021-05-12a	2021-11-05	Wardensville	Grazing	36	Steer	Cross breed	286	390
2021-06-29	2021-08-17	Wardensville	Drylot	37	Heifer	Angus (n = 22) Charolais (n = 15)	286	263
2021-06-29	2021-09-02	Wardensville	Drylot	151	Bull	Cross breed (n = 68) Angus (n = 62) Charolais (n = 19) Charolais Cross (n = 1) Limousin (n = 1)	320	290
2021-12-01	2022-02-18	Wardensville	Drylot	153	Bull	Angus (n = 110) SimAngus (n = 16) Simmental (n = 14) Hereford (n = 13)	356	287
2022
2022-03-10b	2022-04-28	Wardensville	Drylot	108	Steer	Cross breed	281	339
2022-04-28b	2022-10-30	Wardensville	Grazing	36	Steer	Cross breed	335	397
2022-07-05	2022-09-02	Wardensville	Drylot	56	Heifer	Angus (n = 32) Charolais (n = 24)	301	289
2022-07-05	2022-09-20	Wardensville	Drylot	114	Bull	Angus (n = 79) Charolais (n = 32) Black Hereford (n = 3)	344	287
2022-09-12	2022-11-01	Morgantown	Drylot	37	Steer	Cross breed	488	527
2022-11-30	2023-02-15	Wardensville	Drylot	151	Bull	Angus (n = 106) SimAngus (n = 16) Hereford (n = 13) Simmental (n = 13) Charolais (n = 3)	356	287
2022-12-28	2023-03-07	Morgantown	Drylot	43	Heifer	Cross breed	314	297
2023
2023-03-17c	2023-05-08	Wardensville	Drylot	80	Steer	Cross breed	249	361
2023-04-19	2023-06-13	Wardensville	Drylot	59	Steer	Akaushi Wagyu	228	216
2023-04-25	2023-06-14	Morgantown	Drylot	39	Steer	Cross breed	233	210
2023-05-08c	2023-10-19	Wardensville	Grazing	36	Steer	Cross breed	322	419
2023-07-05	2023-08-24	Morgantown	Drylot	40	Steer	Cross breed	365	476
2023-07-06	2023-09-04	Wardensville	Drylot	79	Bull	Angus (n = 47) Charolais (n = 30) Red Angus (n = 2)	404	292
2023-07-14	2023-09-04	Wardensville	Drylot	54	Heifer	Angus (n = 28) Charolais (n = 25) Red Angus (n = 1)	339	299
2023-11-30	2024-02-16	Wardensville	Drylot	173	Bull	Angus (n = 122) Hereford (n = 23) SimAngus (n = 13) Simmental (n = 11) Charolais (n = 4)	378	288
2024
2024-01-22	2024-03-18	Morgantown	Drylot	37	Heifer	Hereford (n = 21) Angus (n = 18)	257	335
2024-12-23	2025-03-06	Hyplains	Drylot	98	Steer	Crossbreed (n = 98)	622	629

Trials were conducted at Wardensville and Morgantown, West Virginia, in drylot or grazing systems. Reported values include number of animals, sex class, breed composition, mean starting body weight, and mean starting age. a–d Starting dates with shared superscripts indicate sequential cohorts within the same production cycle and indicate which drylot cohorts have been evaluated under grazing conditions. Cross Breed = animals of mixed or unrecorded parentage. Avg = average.

Collection of drylot animal data

Water intake and body weight data were collected using Vytelle In-Pen-Weighing (IPW) Positions and attached, metered Ritchie Ecofount waterers (Vytelle, LLC, Lenexa, KS, USA; Ritchie Industries, Inc, Conrad, IA, USA; JLC International, Inc, New Britain, PA, USA; Blake 2023a; ArunKumar et al. 2025). Body weight is recorded when an animal, typically enticed by an attractant, steps onto the unit platform. The platform, which is held on load cells, records the animal’s front-end weight and imputes a verified full bodyweight. There is an RFID antenna array attached to the platform that captures the animal’s RFID number (MacNeil et al. 2021; Wells et al. 2021). Incoming weight data from the load cells is sampled every 0.97 milliseconds at a resolution of 30 grams. In our studies, water was used as the attractant to initiate voluntary weighing via the IPW units. Ritchie Ecofount waterers were used in tandem with custom flow meters to generate WI data. To access the water, an animal passes its head through an RFID-reading array, thereby verifying the animal present. The volume of water to refill the waterer during and immediately after a drinking event as measured by the flow meter is assigned as WI. Accuracy of the water intake measurement approach has been validated (VanGilder et al. 2025). By combining metered WI and IPW units, body weight and WI are recorded each time an animal drink. Due to the high granularity of the data, bodyweight, total WI, drinking event duration, and average drinking event water consumption were calculated as daily summaries. Water via the IPW units was continuously available to all cattle during every test. The Reymann Memorial Farm REOC drylot consists of five pens measuring 29 m × 51 m, each including at least six Feed Intake Nodes and two IPW units. The Morgantown drylot consists of four pens measuring 9 m × 12 m, each including three Feed Intake Nodes and one IPW unit.

Individual DMI were collected in the drylot settings using Vytelle Feed Intake Nodes (GrowSafe 8000; Blake 2023a; ArunKumar 2025). Briefly, the Feed Intake Nodes collect feed intake data via a feed bunk on load cells, with feed disappearance, as measured by difference in feed weight, being assigned as feed intake. Adjustable gates allow for limitation of only a single animal access to a single feed bunk, ensuring that only one animal can use a bunk at a time and a RFID antenna is embedded in the lip of the bunk. DMI is calculated from the recorded feed intake by multiplying the feed intake by the dry matter (DM) percentage of the offered ration. Ration DM, energy, and nutrient content varied by test and were assessed via grab samples collected from the feed truck after mixing and prior to dispensing into the feed bunks as per Cumberland Valley Analytical sample submission guidelines. Collected samples were refrigerated and overnight shipped to Cumberland Valley Analytical Services (Waynesboro, PA, USA). Near Infrared Reflectance Spectroscopy was used to estimate ration nutrient content (Table 3). Drylot animals were offered a total mixed ration ad-libitum. As with the WI data, feed intake data were calculated as daily summaries.

Table 3.

Ration nutrient analyses for experimental groups by test period and site (W = Wardensville and M = Morgantown).

Site	Start	End	Dry Matter	CP	ADF	NDF	NEm	NEg	TDN	ASH	Ca	P	Mg	K	Na	Fe	Mn	Zn	Cu
	Date		(%)	(%DM)			(Mcal/kg)		(%)	(% DM)						(ppm)
W	2019-07-08	2019-08-30	60.0	11.4	22.5	37.9	1.72	1.10	73	5.8	0.7	0.40	0.21	1.0	0.11	240	57	71	17
W	2019-07-22	2019-09-09	71.5	7.7	22.2	37.7	1.74	1.20	74	3.5	0.2	0.32	0.14	1.1	0.15	260	50	31	6
W	2019-11-25	2020-02-20	52.0	13.2	31.9	41.4	1.47	0.88	66	6.9	0.9	0.44	0.22	1.4	0.16	240	93	88	21
W	2020-03-20	2020-05-08	43.4	13.2	31.9	41.4	1.47	0.88	66	6.9	0.9	0.44	0.22	1.4	0.16	240	93	88	21
W	2020-06-29	2020-08-19	43.5	11.4	30.2	46.9	1.56	0.97	65	6.0	0.4	0.35	0.17	1.4	0.16	226	70	62	17
W	2020-06-29	2020-08-25	43.8	12.8	27.2	42.8	1.67	1.06	68	6.0	0.5	0.39	0.17	1.4	0.17	367	72	71	20
W	2020-11-23	2021-02-15	50.6	12.9	26.5	42.8	1.67	1.06	68	6.8	0.8	0.31	0.16	0.9	0.15	172	88	57	14
Wa	2021-03-22	2021-05-12	41.6	10.7	39.0	61.7	1.28	0.70	58	7.0	0.7	0.30	0.18	1.8	0.15	348	96	45	12
W	2021-04-13	2021-06-01	38.0	10.7	39.0	61.7	1.28	0.70	58	7.0	0.7	0.30	0.18	1.8	0.15	348	96	45	12
W	2021-05-12	2021-11-05	88.9	7.5	43.3	71.0	1.14	0.57	55	5.6	0.5	0.25	0.15	1.8	0.01	207	63	23	6
W	2021-06-29	2021-08-17	44.7	11.4	30.2	46.9	3.43	2.13	65	6.0	0.4	0.35	0.17	1.4	0.16	226	70	62	17
W	2021-06-29	2021-09-02	42.3	12.8	27.2	42.8	3.68	2.36	68	6.1	0.5	0.39	0.17	1.4	0.17	367	72	71	20
W	2021-12-01	2022-02-18	51.3	11.7	25.3	39.8	1.70	1.08	69	5.8	0.5	0.33	0.7	1.2	0.16	253	80	62	15
Wb	2022-03-10	2022-04-28	45.4	10.6	38.4	62.8	1.23	0.66	57	8.6	0.5	0.33	0.17	1.6	0.17	349	125	53	12
W	2022-07-05	2022-09-02	39.7	14.3	28.4	43.9	1.52	0.95	63	7.6	0.9	0.34	0.17	1.6	0.28	234	127	96	26
W	2022-07-05	2022-09-20	39.8	13.3	24.4	38.4	1.67	1.06	67	6.7	0.8	0.32	0.17	1.4	0.23	244	131	87	25
M	2022-09-12	2022-11-01	55.7	13.5	37.6	55.1	1.81	0.71	58	9.0	0.9	0.37	0.19	2.0	0.13	167	112	54	10
W	2022-11-30	2023-02-15	49.6	14.9	24.2	40.8	1.76	1.14	70	6.0	0.7	0.36	0.16	1.3	0.17	369	76	80	16
M	2022-12-28	2023-03-07	41.7	13.5	37.6	55.1	1.24	0.71	58	9.0	0.9	0.37	0.19	1.9	0.13	178	112	54	10
Wc	2023-03-17	2023-05-08	41.5	12.9	19.6	28.6	1.87	1.24	73	6.0	0.9	0.33	0.21	1.0	0.41	329	63	75	21
W	2023-04-19	2023-06-13	46.9	12.5	20.7	33.5	1.85	1.21	73	5.5	0.7	0.40	0.19	1.3	0.2	271	82	69	17
M	2023-04-25	2023-06-14	43.2	13.7	17.8	29.2	2.02	1.22	74	5.2	1.0	0.38	0.15	1.0	0.23	294	63	71	22
M	2023-07-05	2023-08-24	48.6	13.1	19.5	32.1	1.56	1.15	74	5.7	0.9	0.33	0.16	1.4	0.16	784	77	55	19
W	2023-07-06	2023-09-04	48.3	11.6	23.5	38.5	1.74	1.12	70	5.8	0.6	0.37	0.15	1.3	0.16	228	90	110	29
W	2023-07-14	2023-09-04	48.3	11.7	26.7	42.8	1.65	1.06	68	6.0	0.8	0.36	0.16	1.3	0.17	325	91	129	33
W	2023-11-30	2024-02-16	49.0	13.3	38.6	23.3	1.76	1.12	70	5.4	0.9	0.30	0.15	1.1	0.23	433	109	81	22
M	2024-01-22	2024-03-18	37.6	13.1	33.0	51.9	1.48	0.90	63	6.0	0.9	0.35	0.16	1.4	0.18	437	79	89	20

Diets are reported on a dry matter (DM) basis unless otherwise noted. Nutrient concentrations include crude protein (CP), acid detergent fiber (ADF), neutral detergent fiber (aNDF), net energy for maintenance (NEm), net energy for gain (NEg), total digestible nutrients (TDN), and mineral content. Starting dates with shared superscripts indicate sequential cohorts within the same production cycle. DM = dry matter; CP = crude protein; ADF = acid detergent fiber; aNDF = neutral detergent fiber; NEm = net energy for maintenance; NEg = net energy for gain; TDN = total digestible nutrients. Entries labeled GRAZING indicate periods without a TMR (small-plot rotational grazing with marker-based DMI estimation); no bunk ration was offered during those windows. Site names are Wardensville, WV; Morgantown, WV; and Hyplains (Montezuma, KS). Superscripts a–c denote cohorts phenotyped in drylot immediately prior to the corresponding 2021–2023 grazing cycles (as cross-referenced in Table 6). “NA” indicates not analyzed for that window. Minor discrepancies between DM and moisture totals reflect rounding and the use of composite samples.

Collection of grazing animal data

To collect individual DMI of grazing cattle, a grazing complex was constructed at the Reymann Memorial Farm REOC site. Four, 0.4 ha Test Plots were established, and each was subset into seven, 0.05 ha Subplots (Figure 1; Table 4). In addition to the Test Plots, 10, 0.8–1.8 ha Reservoir Plots were established. Both Test and Reservoir plots were predominantly tall fescue, orchardgrass, and white clover. Each Test Plot—and all subplots within—had access to an IPW unit for the collection of body weight and WI data. Sorted animal groups were assigned to each Test Plot and would be rotated through each of the seven subplots every 24 h for 7 d. Prior to animals entering a subplot, 25 forage height measurements were collected using a falling plate meter (Rayburn and Lozier 2003). A 143 cm² forage sample clipped to ground level was collected every fifth height measurement. Forage samples were frozen after collection to be later weighed, sorted for botanical composition (grass, legume, forb, weed, dead material), and dried to determine DM content. Forage DMs from paired clip samples were used with height measurements to build a regression to estimate forage mass within each subplot. Processed forage samples were ground to 1.5 mm using a Wiley mill and used to determine in vitro DM digestibility at 30, 48, and 72 h and forage nutrient content. Ground forage samples used for digestibility analysis were aggregated by Test Plot and Grazing Test (i.e. Samples from subplots 1–7 in Test Plot 1 were aggregated to form one submitted sample). Forage digrstiblity analyses were performed by Cumberland Valley Analytical Services (Waynesboro, PA, USA). Twenty-five post-grazing forage heights were collected using a falling plate meter to estimate forage disappearance.

Figure 1.

Eight-day grazing test schedule and sampling schema across seven 0.05-ha subplots within a 0.4-ha Test Plot. On D 0, baseline vegetation structure is recorded on Subplot 1 (25 pre-grazing sward-height measurements by falling plate meter) with five paired ground-clip samples collected for DM and botanical composition. From D 1 through D 7, cattle graze one subplot per day in sequence (Subplot 1 → 7). On each grazing day d, pre-grazing measurements (25 heights + five paired clips) are collected on the next subplot (d + 1), and on the following day (d + 1) post-grazing heights (25) are recorded on the subplot grazed on day d. External marker (inert bolus) dosing begins on Day 2 (0700 and 1400 h) and continues twice daily through D 7 to stabilize marker recovery. Fecal grab samples for marker analysis are collected at 1400 h on D 5 and at 0700 and 1400 h on D 6 and 7. This rolling design ensures, for each subplot, a complete pre-/grazing/post measurement triad while maintaining continuous herd rotation.

Table 4.

Throughput of grazing phenotyping by year and test, reporting the number of animals enrolled per test and the corresponding count of daily dry matter intake (DMI) records (i.e. animal-day observations with valid DMI estimates).

	Test 1		Test 2		Test 3		Test 4		Test 5		Total daily records
Year	Animals	Daily DMI records	Animals	Daily DMI ecords	Animals	Daily DMI records	Animals	Daily DMI records	Animals	Daily DMI records
2021	36	108	32	96	32	96	28	84	–	–	384
2022	36	108	32	96	32	96	28	84	24	72	456
2023	32	96	28	84	24	72	–	–	–	–	252

“Total Daily Records” is the sum of valid animal-day DMI observations across all tests within a year. A dash (—) indicates no test was conducted in that slot. Counts reflect the final, quality-controlled dataset after masking non-evaluable days (e.g. marker ramp-up, missing fecal samples, plot transitions).

Beginning on the second day of each rotation, animals received twice-daily oral boluses (0700 and 1900) of 10 g of an inert external marker through day 7 to achieve steady-state marker excretion and reduce recovery variability. Fecal grab samples were collected every 12 h from 1900 on day 5 through 0700 on day 8 and were frozen immediately upon collection. Fecal marker concentrations were determined using established laboratory procedures: chromium oxide (Cr₂O₃) analysis followed Williams et al. (1962), and titanium dioxide (TiO₂) analysis followed Fowler et al. (2022). Individual grazing DMI was calculated using the equations of Raymond and Minson (1955) based on fecal marker concentration and forage DM digestibility. In 2023 and 2024, TiO₂ replaced Cr₂O₃ to comply with Animal Care and Use Committee policy updates.

Upon being rotated from the seventh subplot on the eighth day, animals were collectively assigned to a Reservoir Plot and rotated to new Reservoir Plots as forage availability required. Animals had continuous access to the Test Plot IPWs when grazing the Reservoir Plots, allowing for collection of individual body weight and WI data over the entire grazing seasons. Grazing tests were repeated as forage availability allowed, with four, five, three, and one (8-d long) tests in 2021, 2022, and 2023, respectively. During the grazing study, methodology was altered slightly to improve data collection and permitted breadth of inquiry. In 2021, crossbred steers from the WV Department of Agriculture were phenotyped for performance and feed efficiency in the Wardensville drylot system. Animals with moderately divergent RFI were selected for the grazing test and randomly assigned into replicate groups. Each group was assigned to a Test Plot. For each subsequent grazing test, groups were randomly sorted and assigned. In 2022 and 2023, crossbred steers from the WV Department of Agriculture were phenotyped for performance and feed efficiency in the Wardensville drylot system. Animals with highly divergent RFI’s were selected for the grazing test and assigned into two groups of Efficient (negative RFI) or Inefficient (positive RFI) animals. Each group was randomly assigned to a Test Plot. For subsequent grazing tests, animals were maintained in the same groups, and groups were rotated to the next Test Plot. For example, if Efficient Group 1 was randomly assigned to Test Plot 1 during the first grazing test, it would be assigned to Test Plot 2 during the next grazing test. This ensured, barring severe drought, that each group grazed each Test Plot. Animals per year and per test as well as individual DMI record amassed can be found in Table 4.

Collection of climate data

Daily temperature, humidity, precipitation, wind speed, and barometric pressure data were obtained from NOAA (National Oceanic and Atmospheric Administration) Local Climatological Data stations nearest each research site (NOAA 2024). Climate data for the Reymann Memorial Farm REOC were sourced from the Winchester, VA Regional Airport station (∼40 km from site), and data for the Animal Science Farm REOC were sourced from the Morgantown Municipal Airport station (∼4 km from site). Both sites and their respective climate stations lie within the Appalachian Ridge-and-Valley physiographic region and experience similar synoptic weather patterns. Climate data for the Hy-Plains Feedyard (Montezuma, KS) validation dataset were sourced from the Dodge City, KS NOAA station (∼50 km from site). This station shares the same semi-arid High Plains region of southwestern Kansas as the H-Plains feedyard. Solar radiation (W-wave-dominant UVA) data were obtained via the NASA POWER Data API (NASA 2024). All climate variables were aggregated to daily minimums, maximums, means, and ranges. Temperature–humidity index (THI) was calculated using the National Research Council (NRC 2001) formulation:

$$\text{THI}=\left(1.8\times \mathrm{T}+32\right)-\left[\left(0.55-0.0055\times \text{RH}\right)\times \left(1.8\times \mathrm{T}-26.8\right)\right]$$

where T is daily mean ambient temperature (°C) and RH is relative humidity (%). THI categories were defined as <72 (no heat stress), 72–79 (mild), 80–89 (moderate), and ≥90 (severe), consistent with commonly applied cattle heat-stress thresholds used in extension and applied livestock guidance. The use of NOAA LCD data was intentional to ensure that all climate inputs were publicly available and reproducible, consistent with the study’s objective of developing a deployable intake-prediction framework.

LSTM modeling

All computations were performed in Google Colab Pro on a single NVIDIA Tesla T4 (16 GB, CUDA 12.1) with Python 3.11 and PyTorch 2.2.2. Random seeds were fixed in NumPy, PyTorch, and CUDA. Supporting libraries included scikit-learn 1.4 (preprocessing/metrics), Optuna 3.2 (hyperparameter search), pandas 2.x, and NumPy 1.26.

LSTM is a recurrent neural network architecture designed to model sequential data by maintaining a gated memory cell that regulates the flow of information across time steps, enabling the capture of both short- and long-term temporal dependencies. This structure is particularly well-suited for longitudinal livestock datasets, where intake is influenced by prior physiological state, environmental conditions, and recent intake dynamics.

Datasets and roles

Daily longitudinal records were assembled from three sources processed under a common pipeline. Drylot cohorts originated from Wardensville, WV, and Morgantown, WV; these formed the base drylot training pool. Pasture cohorts came from Wardensville, WV, in 2021, 2022, and 2023; these provided year-specific grazing information added incrementally in the iterative study. For external assessment, we held out three splits that were never used for training, model selection, calibration, or feature-engineering parameter estimation. The Unseen Regional Drylot Validation dataset (MT) consisted of a WVU drylot cohort from Morgantown, WV, where intake and body weight were collected using the same Vytelle Feed Intake Nodes and In-Pen Weighing (IPW) systems described above under a distinct management setting. The Unseen Non-Regional Drylot Validation dataset (HP) consisted of cattle from Hy-Plains Feedyard (Montezuma, KS), an independent commercial feedlot operation in a geographically and climatically distinct region; intake and body weight were collected using equivalent RFID-restricted bunk systems and standardized daily aggregation procedures. The Unseen Grazing validation dataset was formed by an electronic identification (EID)-level random partition of the 2023 Wardensville grazing cohort; these animals were entirely excluded from model training and tuning but were managed within the same research grazing complex described above. All validation datasets were processed using the identical preprocessing, feature-engineering, scaling, and window-construction pipeline derived from the training data without refitting.

For the full model, the drylot training pool was merged with the grazing training cohorts (2021–2023) and evaluated on the three Unseen validation sets. For the iterative framework, we reused the best full-model bundle (feature list, scaler, sequence length, and backbone checkpoint) and retrained only the prediction head while progressively adding grazing years (details below). In all cases, the three Unseen splits remained strictly held out.

Preprocessing

EIDs were coerced to string to preserve group integrity; rows lacking valid EIDs were removed. Temporal fields (date, startDate, dob) were parsed to derive age (days from birth) and testDays (days from trial start). Grazing rows with missing DMI were dropped to avoid bias. Within each EID, records were sorted chronologically prior to imputation. Missingness was handled hierarchically and strictly within animal to prevent cross-animal information leakage. Forward-fill and backward-fill were applied to short gaps (≤1 d) to preserve temporal continuity while avoiding propagation across extended missing intervals. Precipitation missingness was interpreted as no event and set to zero. Remaining gaps were imputed using k-nearest neighbors (k = 5). Alternative imputers (linear interpolation, spline, and mean substitution) were examined; KNN preserved within-animal variance without imposing excessive smoothness. All imputation steps were completed prior to sequence construction.

Feature engineering

Feature construction targeted temporal structure while preventing target leakage (Table 5). We computed rolling statistics (mean, SD, min, max over 3/5/7 d), rolling deltas (1/3/5/7 d), and accelerations (second differences) to represent direction and rate of change in intake and environment. Lagged predictors (1/2/3/7 d) provided explicit short-term history. Temperature–Humidity Index (THI) and its deltas were derived, along with interactions with intake-related predictors to capture acute vs. cumulative heat load. Polynomial terms (squared/cubic) for body weight and DMI captured nonlinearity; interaction terms (e,g. BW×temperature, DMI×humidity) captured coupling. Cyclical encodings (sin/cos) of day-of-week, day-of-year, and month preserved periodicity. Any feature that could directly encode the contemporaneous target (or its trivial transforms) was excluded or time-shifted to avoid leakage.

Table 5.

Feature engineering map indicating which transformations were constructed for each original variable.

Original variable	Rolling stats (mean, SD, min, max: 3,5,7d)	Rolling delta (1,3,5,7d)	Acceleration (ΔΔ)	Lag (1,2,3,7d)	Polynomial (²,³)	Interaction	Threshold binary	THI derived	Cyclical (sin/cos)
dmi	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	–
bodyWeight	Yes	Yes	Yes	Yes	Yes	Yes	–	–	–
age	–	Yes	–	–	–	–	–	–	–
testDays	–	Yes	–	–	–	–	–	–	–
avgTemp	Yes	Yes	Yes	Yes		Yes	Yes	Yes
maxTemp	Yes	Yes	–	–	–	–	–	–	–
minTemp	Yes	Yes	–	–	–	–	–	–	–
rangeTemp	Yes	Yes	–	–	–	–	–	–	–
avgHumid	Yes	Yes	–	Yes	–	Yes	–	Yes
maxHumid	Yes	Yes	–	–	–	–	–	–	–
minHumid	Yes	Yes	–	–	–	–	–	–	–
rangeHumid	Yes	Yes	–	–	–	–	–	–	–
avgPress	Yes	Yes	–	–	–	–	–	–	–
maxPress	Yes	Yes	–	–	–	–	–	–	–
minPress	Yes	Yes	–	–	–	–	–	–	–
rangePress	Yes	Yes	–	–	–	–	–	–	–
precip	Yes	Yes	–	–	–	–	–	–	–
radUVA	Yes	Yes	–	–	–	–	–	–	–
avgWind	Yes	Yes	–	–	–	–	–	–	–
maxWind	Yes	Yes	–	–	–	–	–	–	–
minWind	Yes	Yes	–	–	–	–	–	–	–
rangeWind	Yes	Yes	–	–	–	–	–	–	–
thi	Yes	Yes		Yes		Yes	Yes	–	–
day_of_week	–	–	–	–	–	–	–	–	Yes
day_of_year	–	–	–	–	–	–	–	–	Yes
month	–	–	–	–	–	–	–	–	Yes

“Rolling Stats” are rolling mean/SD/min/max over 3, 5, and 7 consecutive days; “Rolling Delta” (Δ) are first-order differences over 1, 3, 5, and 7 d; “Acceleration (ΔΔ)” are second-order differences of the corresponding series; “Lag” denotes shifted copies at 1, 2, 3, and 7 d; “Polynomial (², ³)” are squared and cubic terms; “Interaction” includes biologically motivated pairwise terms (e.g. BW × temperature, WI × humidity); “Threshold Binary” are exceedance indicators for pre-specified cut-points (e.g. high THI, precipitation > 0); “THI Derived” includes Temperature–Humidity Index and its short-horizon deltas and interactions; “Cyclical (sin/cos)” encodes calendar categories (day-of-week, day-of-year, month) using sine/cosine pairs to preserve periodicity. “Yes” indicates the transformation family was included for the variable; a blank cell indicates it was not constructed for that variable.

Scaling and target transform

Numeric predictors were scaled with a RobustScaler fit on the training split only. RobustScaler performs median/IQR normalization, which reduces sensitivity to heavy-tailed variables and short-duration extremes (e.g. precipitation spikes, THI surges) while preserving meaningful day-to-day variability. The DMI target was Box–Cox transformed after comparing log, log1p, Yeo–Johnson, and Box–Cox options using Q–Q plots, residual variance, and training stability. All predictions were inverse-transformed to kg·d⁻¹ for reporting.

Categorical handling

Categorical variables (breed, class, calendar categories) were encoded using learned embeddings rather than one-hot encodings. Embeddings project categories into a continuous vector space that captures similarity structure while avoiding the high-dimensional sparsity of one-hot inputs. For each categorical field, embedding dimensionality was set using a simple heuristic: half the number of unique categories, capped at 50 dimensions. For example, a variable with 12 categories received a 6-dimensional embedding, whereas a variable with more than 100 categories was limited to 50 dimensions. These heuristic balances representational capacity with parameter efficiency, reducing the risk of overfitting. Each embedding included an explicit “unknown” token to ensure stable inference when encountering previously unseen categories in validation or deployment. EID was used strictly to enforce animal-level data separation and was not included as a predictive feature.

Sequence model and prediction head

Daily records were converted into fixed-length sequences of 7 consecutive days used to predict DMI on d 8. Preliminary grid search experiments evaluated alternative lookback windows spanning 1–10 d; a 7-d window consistently minimized validation RMSE while maintaining stable convergence and adequate sequence counts per animal. This choice is also biologically grounded. Prior incremental-variable analyses demonstrated that 3–7 d horizons capture meaningful short-term energy balance dynamics and intake momentum in beef cattle (Blake et al. 2023b) Because the model was trained on seven-day windows, it requires seven consecutive days of historical covariates (body weight, intake-adjacent variables, and environmental conditions) before producing a valid prediction. In deployment, this defines a brief 7-d “cold start” period for newly observed animals or newly instrumented systems. Sequences were not allowed to cross animals, production-system transitions, or day gaps >1 d. The sequence encoder was a multi-layer LSTM model with dropout between recurrent layers. For each input window, the LSTM model produced a terminal hidden state summarizing the preceding 7 d. This hidden state was passed to a prediction head, which, in machine-learning terminology, refers to the small module attached to the base model that converts its learned representation into the final output. Here, the head was a two-layer feed-forward network (Linear → ReLU → Dropout → Linear → scalar). The head contains first-layer weights, first-layer bias terms, final-layer weights, and a final scalar bias applied immediately before producing the prediction as its four groups of learnable values. These values govern how the model maps model features to a single DMI estimate and are the only parameters modified during head-only fine-tuning.

Training minimized SmoothL1 (Huber) loss using Adam (learning rate ≈5 × 10⁻⁴). SmoothL1 combines the stability of L2 loss with the robustness of L1 for outliers, which is useful for daily-intake data that occasionally exhibit abrupt deviations. Adam was selected for its adaptive learning-rate behavior and strong performance on sequence models. Gradient-norm clipping (threshold 1.0) was applied each step to prevent exploding gradients in the multi-layer LSTM model. A ReduceLROnPlateau scheduler (factor 0.1, patience 10) lowered the learning rate when validation performance stagnated, improving late-epoch convergence. Early stopping (patience 15) terminated training once validation RMSE ceased improving to prevent overfitting. Batch size was fixed at 32. All development splits were constructed by EID to prevent cross-animal leakage and ensure that no individual contributed records to both train and validation/test sets.

Hyperparameter tuning

We used Optuna (TPE sampler) to tune hidden size, number of LSTM layers, dropout, learning rate (log-uniform search), batch size, loss (MSE vs. Huber), and target transform (none/log/Yeo–Johnson/Box–Cox). The search space spanned smaller and larger model capacities (e.g. hidden sizes from low hundreds upward and multiple recurrent-layer depths) and learning rates over approximately an order of magnitude around the final selected value. Each trial trained to convergence under identical EID-grouped development splits, with validation RMSE as the optimization objective. The selected configuration (hidden ≈256, layers ≈ 3, dropout ≈ 0.20, learning rate ≈ 5 × 10⁻⁴, batch = 32, Huber loss, Box–Cox transform) consistently produced lower grouped validation RMSE than both smaller-capacity and larger-capacity alternatives and was therefore fixed for all downstream experiments. External validation datasets were never used for hyperparameter selection.

Full-model training and external validation

The selected configuration was retrained on the merged drylot + grazing training pool with early stopping keyed to the original validation criterion, then evaluated on the internal test split and, independently, on the three Unseen external validations—Unseen Grazing, HP, and MT—processed identically to the training data.

Iterative fine-tuning

To test whether incremental grazing information improves grazing-system predictions without compromising drylot behavior, we ran four fine-tuning iterations using the same frozen LSTM encoder and the same RobustScaler as the full model. Only the prediction head was updated. Because the head is small and interpretable, limiting updates to the head isolates domain-specific adjustments to the mapping from representation → DMI. The iterations were:

• Iteration 1 (Iter 1): drylot only; bias-only updates (all head weights frozen; the final scalar bias term trainable).

• Iteration 2 (Iter 2): drylot + grazing-2021; bias-only updates.

• Iteration 3 (Iter 3): drylot + grazing-2022; bias-only updates.

• Iteration 4 (Iter 4): drylot + grazing-2023 (training subset); full-head updates (all head weights and biases trainable).

Bias-only updates allowed the model to apply a global correction to its predictions without altering how input features are interpreted, making the model useful for small datasets where the primary shift is in overall level rather than structure. Full-head updates in Iteration 4 provided additional flexibility for the more variable 2023 grazing conditions while still preventing changes to the temporal representation encoded by the model. During head training, we increased the weight loss for windows whose terminal day belonged to Grazing to emphasize accuracy in that system; weighting affects optimization but does not alter the target values. During model development, we conducted a limited exploratory sweep of grazing-window loss weights across a small grid (values spanning 4–15) under otherwise identical head-only training conditions (frozen encoder, fixed splits, identical stopping criteria, identical evaluation masks). Moderate emphasis consistently improved grazing-domain alignment relative to unweighted training, while excessively large weights increased sensitivity of the head to grazing-specific variance and produced linear mis-scaling in uncalibrated outputs without improving external validation error. Based on these observations, we adopted a monotone emphasis schedule (4→7→8→10) aligned with the progressive addition of grazing cohorts across iterations. These weights were then fixed and excluded from hyperparameter optimization to preserve auditability and prevent repeated searching against the same development signal. Weighting influenced gradient updates only and did not modify targets or evaluation metrics.

Post-hoc affine calibration

For each iteration, we produced two model variants: an uncalibrated model and a calibrated model. The uncalibrated variant was only the raw head output. The calibrated model applied a simple affine calibration fitted only within the iteration’s training mixture. Affine calibration refers to applying a linear rescaling and shift to the model’s predictions (i.e. adjusting the model output by a learned slope and intercept) to correct systematic offset or scale differences between production systems. This procedure does not retrain the model but is a post-hoc correction that modifies predictions only, leaving all model parameters unchanged. The affine adjustment corrects systematic linear scale and offset mismatches between domains and is therefore appropriate when residual bias is approximately linear (e.g. consistent over- or under-scaling across the response range). Affine transformations are widely used in calibration and transfer settings to reduce domain shift while preserving model structure and monotonicity (Minami et al. 2022; Kushida et al. 2024). Within deep learning more broadly, linear post-hoc calibration is recognized as a low-variance alternative to more flexible recalibration schemes when data available for calibration are limited (Wang 2023). An affine map does not correct nonlinear distortion (e.g. curvature at extreme intake values or under severe thermal stress). In scenarios where domain shift introduces nonlinear bias—such as heat-load thresholds or abrupt forage transitions—segmented or nonlinear calibration approaches (e.g. piecewise linear or spline-based monotone adjustments) may be more appropriate. In the present study, more flexible calibration procedures were considered conceptually; however, given the modest size of the proxy subsets used to estimate calibration parameters and the risk of overfitting, we deliberately restricted calibration to a two-parameter affine transformation. This preserves transparency, interpretability, and minimal degrees of freedom while correcting systematic linear bias without altering the learned temporal representation.

Calibration was performed using proxy rows drawn from the same domain as the target external set: grazing rows for Unseen Grazing and site-specific drylot rows for HP and MT when available (otherwise the pooled drylot subset was used). Calibration parameters were estimated after inverse transformation of predictions and required a minimum sample size for stability. No external validation labels were used at any stage. This adjustment provides a transparent correction for domain-level bias without altering the underlying learned relationships.

The calibrated variant applies a domain-specific affine map estimated only from proxy subsets inside the iteration’s training assembly (never from external validation labels). For Unseen Grazing, fitting used rows labeled Grazing in the training mix; for HP and MT, we preferred site-specific rows when available, otherwise a drylot proxy. Estimation used ordinary least squares after applying the same post-processing used at evaluation (e.g. inverse transforms), with a minimum window count enforced for stability. This calibration is a transparent monotone correction for domain-level offset/scale; it is not a second model and does not use external labels.

Window construction and evaluation mask

Windows were EID-safe and system-segmented: no window crossed animals, production-system changes, or day gaps >1 d. The model predicted the terminal day in each window. After inference, terminal predictions were aligned back to rows, and a terminal-window evaluation mask was formed by keeping rows where both the observation and the aligned prediction were finite. All reported metrics use this same mask for a given (iteration, model variant, validation domain), ensuring strict comparability.

Metrics and diagnostic tests

Primary metrics were RMSE, R², and MAE on inverse-transformed predictions. To express scale and uncertainty without refitting, we reported CVRMSE (RMSE/masked mean of y), NRMSE_sd (RMSE/masked SD of y), and nonparametric bootstrap 95% intervals for RMSE (400 resamples). Internal consistency was verified via R² ≈ 1 − RMSE²/Var(y) when all terms are computed on the same mask. A permutation-null RMSE was computed on masked rows to demonstrate separation from noise. None of these diagnostics modified model parameters.

Reproducibility and isolation

Random seeds were fixed for data loading and PyTorch. The full-model bundle (features, scaler, sequence length, checkpoint, transform metadata) was copied into each run directory; iteration artifacts (per-iteration head weights, manifests, and per-domain affine parameters) were versioned by timestamped folders. External validation CSVs were duplicated into run-scoped paths before writing predictions, so originals remained untouched. This preserves a clear separation between what is learned from training data and what is only measured on external, unseen validation sets.

Benchmarking

For benchmarking, daily DMI (DMI; kg·d⁻¹) was also predicted using the National Academies of Sciences, Engineering, and Medicine (NASEM 2016) equation for yearling beef cattle (equations 10–1). DMI was calculated as:

$$\text{DMI}\hspace{0.17em}\left(\text{kg}/\mathrm{d}\right)=\text{BW}0.75\times (0.2435\times \text{NEm}-0.0466\times {\text{NEm}}^2-0.0869)$$

where BW is body weight (kg) and NEm is dietary net energy for maintenance (Mcal·kg⁻¹ of DM). Predicted DMI (kg·d⁻¹) was obtained by dividing predicted NEm intake by dietary NEm concentration (Mcal·kg⁻¹), following NASEM (2016) guidelines. Body weight and diet energy values used for these calculations were derived from the same daily records and ration analyses described above.

Results and discussion

We evaluated the performance of LSTM models for predicting daily WI in beef cattle across three datasets: 1) a combined training set consisting of drylot and grazing systems, 2) an unseen regional drylot validation set (MT), and 3) an unseen non-regional drylot validation set (HP). The training dataset comprised WVU drylot records from Wardensville and Morgantown (n = 1,998) and WVU grazing records from Wardensville (n = 104; 2021: n = 36; 2022: n = 36; 2023: n = 32), with grazing animals included within the WVU drylot total due to drylot evaluation prior to pasture turnout. External validation datasets consisted of a regional Morgantown drylot cohort (n = 37) and a non-regional Hy-Plains drylot cohort (n = 98). Each model was assessed using root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²).

Full model

Across the full evaluation set, the LSTM model achieved materially lower error and higher explained variance than the NASEM equations (Table 1). Using identical terminal-window masks, the LSTM model returned RMSE = 1.329 kg·d⁻¹ with R² = 0.655, while NASEM produced 1.858 kg·d⁻¹ and 0.326, respectively—an absolute error reduction of 0.529 kg·d⁻¹ (≈28.5%). The same pattern holds when stratified by production system (Figures 2 and 3): in Drylot (N = 102,021), the LSTM model reached 1.330 kg·d⁻¹ and 0.651 versus NASEM’s 1.848 kg·d⁻¹ and 0.327 (≈28.0% lower RMSE); in Grazing (N = 338), the LSTM model delivered 1.180 kg·d⁻¹ and 0.507, whereas NASEM performed poorly (3.883 kg·d⁻¹; R² = −4.337), a reduction of 2.703 kg·d⁻¹ (≈69.6%) under the most variable conditions. Observed–predicted scatterplots (Figure 1) show the LSTM model tightly clustered about the 1:1 line, with NASEM exhibiting an inability to predict low DMI, biased dispersion, and large tails. Practically, this closes the loop that constrains current selection protocols to drylot: accurate individual grazing predictions at low error enable evaluation of feed efficiency where the majority of beef cattle actually live, not only in confined proxies. (Table 6; Figures 2–4) Prediction error was not uniformly distributed across the intake and body-weight spectrum. When stratified by observed DMI quartile, the lowest RMSE was observed in the third quartile (RMSE = 1.06 kg), representing mid-range intake levels. Error increased at physiological extremes: the lowest DMI quartile exhibited a 31% higher RMSE (1.39 kg), and the highest DMI quartile exhibited a 62% higher RMSE (1.71 kg) relative to the mid-range reference. A similar monotonic pattern was observed across body-weight strata. The lightest quartile exhibited the lowest RMSE (1.16 kg), whereas the heaviest quartile showed a 39% increase in error (1.60 kg). These results indicate that residual variance is concentrated at intake and size extremes rather than evenly distributed across the population.

Figure 2.

Observed vs. predicted dry matter intake (DMI; kg·d⁻¹) for the full evaluation set, comparing the LSTM model to NASEM equations. Points represent daily terminal-window observations; both models are evaluated on the identical terminal-window mask after inverse transforming predictions. The 1:1 line is shown for reference; each panel annotates RMSE and R² computed on the same mask.

Figure 3.

Observed vs. predicted DMI (kg·d⁻¹) for the Drylot subset of the full evaluation set, comparing the LSTM model to NASEM equations. Evaluation uses the identical terminal-window mask applied to both models after inverse transformation. The 1:1 line is shown; RMSE and R² are reported on the same mask.

Table 6.

Comparative external performance of the full Long Short-Term Memory (LSTM) model versus National Academies of Sciences, Engineering, and Medicine (NASEM) intake equations across scopes.

Scope	Model	R 2 (LSTM)	RMSE (LSTM)
Full	LSTM	0.655	1.329
	NASEM	0.326	1.858
Drylot	LSTM	0.651	1.33
	NASEM	0.327	1.848
Grazing	LSTM	0.507	1.18
	NASEM	−4.337	3.883

Metrics are coefficient of determination (R²) and root mean square error (RMSE, kg·d⁻¹) computed on inverse-transformed predictions using identical terminal-window evaluation masks within each scope. “Full” pools all evaluated records; “Drylot” and “Grazing” are system-stratified subsets. Negative R² for NASEM in Grazing indicates lack of linear association relative to the mean-only model under the same mask.

Figure 4.

Observed vs predicted DMI (kg·d⁻¹) for the Grazing subset of the full evaluation set, comparing the LSTM model to NASEM equations. Both models are evaluated on the identical terminal-window mask after inverse transformation. The 1:1 line is shown; RMSE and R² are reported on the same mask.

Two design choices separate this work from prior DMI studies and explain why it performs in pasture. First, the target is measured daily intake at the individual level across systems, not a pseudo-ground-truth generated by equations; this removes compounding target noise and lets the learner fit biological signal rather than formula residuals. Second, the model is explicitly sequential: the network ingests engineered week-scale trajectories—short-lag deltas, rolling statistics, and accelerations for intake-adjacent signals (e.g. water), animal state (e.g. body weight), and weather. Then, the model integrates those trajectories over 7 d before a compact head maps the latent state to DMI. In contrast to row-wise tabular learners (e.g. boosted trees) that can only emulate time by heavy feature expansion, the model maintains internal memory and updates state, which is aligned with physiology (today’s intake depends on yesterday’s path). This design is consistent with recent feedlot-focused reports emphasizing incremental and time-series variables as critical predictors; here, trained and tested in grazing as well as drylot, the sequential encoder turns those engineered deltas into the backbone of prediction.

To interpret most relevant model features, we computed permutation importance as ΔRMSE under sequence-aware, EID- and segment-bounded circular shuffling (ten replicates; fixed 3×IQR bounds; DMI-named and near-constant features excluded). The top contributors (Figure 5) were Production System (ΔRMSE = 0.027; IQR = 0.026–0.031), Body Weight Δ7 (0.021; 0.021–0.022), and Test Days (0.019; 0.018–0.019); next were dynamics of Daily Water Intake (Δ3: 0.018; 0.017–0.019; level: 0.018; 0.016–0.020), Temperature Range (°C) (0.018; 0.017–0.018), and Age (0.017; 0.013–0.018). Additional influential terms included Daily Water Intake Δ2 (0.016; 0.013–0.019), a seasonal signal (Month sin; 0.015; 0.013–0.018), THI (0.015; 0.014–0.016), further temperature-range deltas (Δ2: 0.014; 0.012–0.015; Δ3: 0.011; 0.010–0.012), and static Body Weight alongside Body Weight Δ3 (0.007; 0.007–0.008) and min humidity (lag-1) (0.007; 0.006–0.007). The model relies on management context (system), short-horizon changes in animal state (BW momentum, time on test) and water-use behavior and thermal load captured not only by THI but by day-to-day thermal swings (range, humidity minima) with mild calendar cyclicity. Relative to (Blake 2023a), which (in feedlot) ranked BW and weather aggregates highly, our top-15 shifts more weight to trajectory terms and cyclical encodings—consistent with mixed-system, year-round training and a sequential encoder. Compared with ArunKumar et al. (2025) on large but primarily confinement datasets emphasizing static morphology/ration descriptors in a row-wise learner, our ranking elevates short-run deltas the LSTM model can integrate directly in time, particularly water and microclimate variability that moves rapidly in pasture (Figure 5).

Figure 5.

Top-15 permutation feature importances for the full LSTM model, expressed as median ΔRMSE (kg·d⁻¹) under sequence-aware, EID- and segment-bounded circular shuffling (10 replicates; DMI-named and near-constant features excluded). Bars show median ΔRMSE; whiskers (if present) denote the interquartile range across replicates. Larger ΔRMSE indicates greater importance.

The prominence of short-horizon deltas and accelerations in the top-ranked predictors underscores a central methodological distinction between the present approach and static equation-based frameworks. Variables such as 3- and 7-d body-weight change, rolling intake deltas, and short-term thermal variability were consistently more influential than many single-day absolute measures. This pattern indicates that intake regulation is sensitive not only to current physiological state or ambient conditions but to their recent trajectory. Static equations such as NASEM are formulated around steady-state, single-day inputs (e.g. shrunk body weight, effective temperature index), implicitly assuming equilibrium relationships between intake and environment. Such formulations cannot represent transient deviations, compensatory responses, or acute perturbations (e.g. abrupt heat load, rapid forage shifts, or short-term suppression followed by rebound). By contrast, the sequential LSTM encoder integrates week-scale trajectories into a latent representation that captures directionality, momentum, and rate of change. The dominance of dynamic features therefore reflects the model’s sensitivity to short-term physiological and environmental fluctuations—a capability that static, single-day regression equations fundamentally lack. This trajectory-aware structure is particularly important under grazing conditions, where environmental variability and forage dynamics generate rapid intake adjustments that cannot be resolved by steady-state formulations.

LSTM networks were selected because daily DMI represents a longitudinal, path-dependent biological process shaped by cumulative environmental exposures, delayed physiological adjustments, and short-term intake momentum. Many conventional statistical frameworks and widely used machine-learning methods—including linear mixed-effects models, random forests, support vector machines, and gradient-boosted trees—are capable of capturing nonlinearities and complex interactions. However, these approaches treat observations as independent unless temporal structure is explicitly constructed through engineered summary variables (Cortes and Vapnik 1995; Pinheiro and Bates 2000; Breiman 2001; Friedman 2001). Feedforward neural networks operate under the same constraint, as they lack inherent memory and therefore require temporal context to be manually embedded within the input feature set (Bishop 1995; Goodfellow 2016).

Prior analyses conducted by our group demonstrated strong within-dataset accuracy using Random Forest-based models and repeated-measures approaches when evaluation included animals observed during model training (Blake et al. 2023a). Related work further indicates that GPBoost and extreme gradient boosting can successfully model intake when individual-level structure is explicitly learned (Sigrist 2022; ArunKumar et al. 2025). Nevertheless, these row-wise learners rely on static feature representations and can exhibit diminished generalization under animal- or environment-level distribution shift. By contrast, LSTM architectures are explicitly designed to model sequential data through gated memory mechanisms that regulate information retention and updating across time (Hochreiter and Schmidhuber 1997). This inductive bias enables the network to integrate short-term fluctuations in body weight, intake-adjacent signals, and environmental variability into a coherent latent trajectory before producing a prediction. The prominence of rolling deltas and accelerations in the present feature-importance analysis further supports that intake regulation is sensitive to recent directional changes rather than single-day steady-state conditions. Importantly, the objective of this study was not to maximize in-sample predictive fit but to develop a model capable of generalizing across animals and production systems while preserving temporal coherence. Sequential encoders are structurally aligned with that objective. While simpler machine-learning models may achieve competitive performance when extensive temporal features are manually engineered, the LSTM architecture allows those features to be integrated dynamically across time steps rather than treated as independent covariates. Thus, the use of recurrent architecture reflects alignment between model inductive bias and the biological structure of intake regulation rather than an arbitrary increase in algorithmic complexity.

The biological coherence of the highest-ranked predictors is consistent with known intake physiology. Short-horizon body weight dynamics (e.g. 7-d BW change) likely reflect momentum in energy balance more directly than single-day body weight alone. It also aligns with prior incremental-variable analyses demonstrating that multi-day temporal structure, particularly week-scale cycles, carries substantial predictive information for DMI (Blake et al. 2023b; Walker et al. 2024). Because DMI responds to cumulative nutrient demand and compensatory growth rather than instantaneous mass, multi-day deltas encode trajectory information aligned with intake regulation. Similarly, water-intake level and short-term water-intake deltas capture hydration–intake coupling, particularly under thermal stress, were drinking behavior and feed intake shift in tandem. Temperature range and humidity-derived variables (including THI and short-term thermal deltas) represent acute environmental instability rather than absolute conditions, consistent with evidence that rapid thermal transitions perturb intake more than steady-state heat.

The prominence of “production system” does not replace biological signal but, encodes management and exposure context (e.g. ration composition, forage availability, movement constraints, and microclimate structure) that cannot be fully reconstructed from scalar environmental variables alone. Importantly, environmental, trajectory, and behavioral features remain predictive within-system, indicating that the model is not solely reliant on categorical partitioning but integrates system context with physiologic dynamics. From a deployment perspective, the production-system label functions as a compact descriptor of management domain. However, the model’s predictive capacity does not collapse in its absence; environmental and trajectory-derived features remain informative within-system. In practical implementations where system labels may be incomplete, weather variability, intake-adjacent behavioral features, and short-term body-weight dynamics provide partial domain inference. We therefore view the production-system indicator as an efficiency-enhancing contextual feature rather than a biological substitute.

The grazing contrast with NASEM is instructive. Equation sets parameterized on average conditions and ration descriptors are structurally mismatched to open-air variability, where humidity–temperature coupling, forage access, and short-horizon weather shocks generate acute intake deviations. On what is, to our knowledge, the largest corpus of measured individual grazing intakes assembled to date, NASEM systematically over-predicted grazing DMI and lost linear association (negative R²), while the LSTM model maintained centered residuals and low error. The implication is straightforward: with measured labels, engineered short-horizon covariates, and a sequential encoder, one can recover the individual-level signal necessary to rank animals for efficiency in grazing systems, addressing the long-standing gap wherein efficiency is evaluated in drylot despite cattle spending most of their lives on pasture.

Finally, we adopted a deliberately conservative posture against overfitting. Sequences were built strictly within EID, broken at production-system boundaries and calendar gaps to prevent leakage; splits were grouped by EID; outlier handling (IQR) was applied once and then fixed across analyses; hyperparameters were tuned with Optuna’s TPE under aggressive trial pruning (median pruner) and a hard R² gate after a warm-up epoch window; training used early stopping, gradient clipping, and stepwise scheduling; and the final configuration was re-evaluated on strictly held-out masks with identical filtering. Post hoc, identity checks (R² ≈ 1 − RMSE²/Var(y) on the same mask) held within rounding, and permutation-null RMSEs were far larger than model RMSEs, indicating that the gains reflect learnable structure rather than variance capture. This suite of controls biases estimates toward under- rather than over-fitting, which is appropriate given our objective: a deployable, sequential model that generalizes across systems and, crucially, on pasture.

Iterative modeling

We evaluated four sequential head-tuning iterations (Iter1–Iter4) using a frozen LSTM encoder learned from the full model and the same feature/scaler bundle across all runs. At each iteration, two variants were produced from identical inputs: 1) an uncalibrated head that returned the raw model output and 2) a calibrated head that applied a post-hoc affine scale-and-shift to those outputs. Both models used full model architecture. Model performance was assessed on three strictly held-out external validations that were not used for training or for fitting calibration parameters. These external validation datasets were the MT, HP, and the Unseen Grazing. To ensure exact comparability, all metrics (RMSE, R²), were computed on the same terminal-window evaluation mask within each iteration × variant × validation set.

In this framework, the LSTM encoder condenses the last seven days of covariates into a compact trajectory representation per animal, and the prediction head—a small multilayer perceptron—maps that representation to a scalar DMI value. In Iter1–Iter3, we permitted bias-only updates to the head (i.e. adjustment of intercepts without changing slopes with respect to the encoder features), which removes mean-level error while preserving the geometry of the learned mapping. In Iter4, we allowed full-head updates (weights and biases) to test whether limited slope adjustments, applied without touching the backbone, could further reduce error once additional grazing supervision was present. After the head prediction, an optional affine calibration was applied as ŷ_cal = a·ŷ_uncal + b, where (a, b) were fit exclusively on proxy training subsets for each domain family and never on the Unseen validation labels; this step corrects repeatable linear scale/offset mismatches without introducing new nonlinearity. (Figures 6A–C and 7A–C).

Figure 6.

(A–C) RMSE (kg·d⁻¹) vs. iteration (Iter1–Iter4) for iterative head tuning with and without post-hoc affine calibration. Uncalibrated models are shown in navy triangles; calibrated models in gold circles. Panels: A = Unseen Regional Drylot (Morgantown/MT), B = Unseen Non-Regional Drylot (Hyplains, KS), C = Unseen Grazing (2023 Wardensville EID-random split). All metrics are calculated on the identical terminal-window evaluation mask per (iteration × variant × validation set). Affine calibration applies ŷ_cal = a·ŷ_uncal + b with (a, b) estimated only from proxy training subsets (no external validation labels).

Figure 7.

(A–C) R² vs. iteration (Iter1–Iter4) for iterative head tuning with and without post-hoc affine calibration. Uncalibrated models are shown in navy triangles; calibrated models in gold circles. Panels: A = Unseen Regional Drylot (Morgantown/MT), B = Unseen Non-Regional Drylot (Hyplains, KS), C = Unseen Grazing (2023 Wardensville EID-random split). R² values are computed on the identical terminal-window evaluation mask used in Figure 6 for the corresponding (iteration × variant × validation set). Affine calibration applies ŷ_cal = a·ŷ_uncal + b with parameters fit only on proxy training subsets.

Across Unseen Grazing (2023), the uncalibrated head achieved R²/RMSE values of 0.583/0.322 (Iter1), 0.584/0.322 (Iter2), 0.575/0.325 (Iter3), and 0.491/0.356 (Iter4). The calibrated counterpart yielded 0.576/0.325 (Iter1), 0.589/0.319 (Iter2), 0.584/0.322 (Iter3), and 0.585/0.321 (Iter4). Thus, with bias-only tuning, the grazing curves remained stable as cohorts were added, and a modest linear correction consistently improved agreement; when head weights were freed in Iter4, uncalibrated grazing performance declined, but a two-parameter affine (fit on proxy grazing data) restored accuracy to the same band observed earlier, indicating that the Iter4 deviation reflected a linear scale/intercept mismatch rather than loss of relevant representation (Table 7; Figures 6C and 7C).

Table 7.

Iterative head-tuning results on strictly held-out external validations, reported as R² and RMSE (kg·d⁻¹) for Iter1–Iter4 with and without post-hoc affine calibration.

Iteration	Validation dataset	Model	R 2	RMSE, kg
1	Regional Drylot	+Calibration	0.525	1.021
		−Calibration	0.489	1.059
	Non-regional Drylot	+Calibration	0.337	1.734
		−Calibration	0.34	1.73
	2023 Grazing	+Calibration	0.576	0.325
		−Calibration	0.583	0.322
2	Regional Drylot	+Calibration	0.525	1.021
		−Calibration	0.489	1.059
	Non-regional Drylot	+Calibration	0.337	1.734
		−Calibration	0.34	1.73
	2023 Grazing	+Calibration	0.589	0.32
		−Calibration	0.584	0.322
3	Regional Drylot	+Calibration	0.525	1.021
		−Calibration	0.487	1.062
	Non-regional Drylot	+Calibration	0.337	1.734
		−Calibration	0.34	1.729
	2023 Grazing	+Calibration	0.584	0.322
		−Calibration	0.575	0.325
4	Regional Drylot	+Calibration	0.495	1.053
		−Calibration	0.466	1.083
	Non-regional Drylot	+Calibration	0.349	1.717
		−Calibration	0.354	1.711
	2023 Grazing	+Calibration	0.585	0.321
		−Calibration	0.491	0.356

“Regional Drylot” = Unseen Regional Drylot Validation (Morgantown, WV; MT), “Non-Regional Drylot” = Unseen Non-Regional Drylot Validation (Hyplains Feed Yard, Montezuma, KS), and “2023 Grazing” = Unseen Grazing split (EID-random partition of 2023 Wardensville). Each iteration used the frozen full-model encoder and identical feature/scaler bundle; Iter1–Iter3 updated head biases only, Iter4 allowed full-head (weights + biases) updates. “+Calibration” applies ŷ_cal = a·ŷ_uncal + b fit only on proxy training subsets for the corresponding domain family; “–Calibration” is the raw head output. All metrics are computed on the same terminal-window evaluation mask within each (iteration × model variant × validation set).

Across HP, the uncalibrated head tracked essentially flat from Iter1–Iter3 at ≈0.340/1.730 and improved slightly at Iter4 to 0.354/1.711. The calibrated variant produced 0.337/1.734 (Iter1), 0.336/1.734 (Iter2), 0.337/1.734 (Iter3), and 0.349/1.717 (Iter4). Calibration parameters here were near identity (e.g. a ≈ 1.00, b≈−0.05 in Iter4), yielding curves that visually overlie the uncalibrated results and confirming stable drylot transfer under incremental grazing emphasis (Table 7; Figures 6B and 7B).

Across MT, uncalibrated results were 0.489/1.059 (Iter1), 0.489/1.059 (Iter2), 0.487/1.062 (Iter3), and 0.466/1.083 (Iter4). The calibrated head improved these to 0.525/1.021 (Iter1), 0.525/1.021 (Iter2), 0.525/1.021 (Iter3), and 0.495/1.053 (Iter4). Here, calibration consistently removed a repeatable linear bias (e.g. a ≈ 0.74, b≈∼2.15 in Iter1–Iter3), yielding a stable and material reduction in RMSE together with a lift in R², particularly in the smaller MT mask (Table 7; Figures 6A and 7A).

Three observations explain the shape of these curves. First, the scope of adaptation matters: bias-only tuning removes intercept error while preserving slopes, producing small, predictable shifts as grazing cohorts are added; freeing head weights under heavier grazing emphasis can tilt slopes enough to introduce linear misalignment on held-out individuals, which an affine correction reverses without touching the backbone. Second, the relative window weighting (grazing weight 4→7→8→10 across iterations) focuses limited head capacity on grazing alignment; with a frozen encoder, this can trade a linear over- or under-scaling in the raw head for a better fit on the training mixture. Third, the variance structure of each validation set modulates R² visibly for the same absolute RMSE changes: Grazing 2023 has a masked SD near 0.65 kg·d⁻¹, so ±0.01–0.02 kg in RMSE can move R² by several points; HP has an SD near 2.13 kg·d⁻¹, so R² is correspondingly less sensitive to the same absolute shifts; MT has a smaller effective N (masked), so removing linear bias produces consistent, non-trivial gains. During head-only fine-tuning, windows whose terminal day belonged to the Grazing production system were assigned a fixed multiplicative weight in the loss function, while drylot windows retained a weight of 1. This weighting influenced gradient updates during training only and did not alter target values or evaluation metrics. The grazing weight was fixed per iteration (Iter1 = 4; Iter2 = 7; Iter3 = 8; Iter4 = 10). These values were specified prior to final model evaluation and were not included in Optuna hyperparameter search.

Metric soundness was verified on the same evaluation masks used for the primary results. Identity checks (R² ≈ 1 − RMSE²/Var(y)) held within rounding in every (iteration × variant × validation set). Bootstrap uncertainty (400×) yielded tight CIs aligned with the reported points (e.g. Grazing Iter2-cal 0.319 [0.305, 0.335]; HP Iter4-uncal 1.714 [1.606, 1.831]; MT Iter1-cal 1.030 [0.886, 1.173]). Permutation-null RMSE was far larger than model RMSE in all cases (≈0.65–0.68 for Grazing 2023; ≈2.46–2.53 for HP; ≈1.78–2.03 for MT), indicating that the encoder-plus-head pipeline learns signal well above chance.

Two forces most plausibly govern the iteration-wise movements in R² and RMSE, most notably the Iter4 dip on the Unseen Grazing set before affine correction. First, the model’s degrees of freedom under domain emphasis matter. In Iter1–Iter3, updates were restricted to the head biases. That constraint removes mean-level error without altering slopes in the encoder’s latent space, so the mapping from seven-day trajectories to DMI retains its geometry even as grazing windows are added and up-weighted; the result is a stable, low-variance performance trajectory. Iter4 deliberately relaxed that constraint and allowed weight updates in the head. Those weight adjustments can rescale how latent axes tied to grazing seasonality, short-horizon thermal load, and recent BW dynamics contribute to the prediction. Because those axes project differently across domains, a single head can become linearly mis-scaled on the Unseen Grazing distribution while remaining adequate for drylot validations. The fact that a two-parameter affine restored Iter4 accuracy to the earlier band is diagnostic: the representation remained useful; the head’s gain/offset drifted.

Second, the variance structure of each external validation set modulates R², making identical absolute RMSE shifts look different across panels. The Unseen Grazing (2023) mask has a relatively tight standard deviation (≈0.65 kg·d⁻¹). On that scale, a ±0.01–0.02 kg·d⁻¹ change in RMSE moves R² by several points, so the Iter4 uncalibrated drop is visually pronounced. The HP dataset exhibits a much wider dispersion (≈2.13 kg·d⁻¹), so the same absolute RMSE change yields a smaller R² deflection. The MT mask sits between and has a smaller effective N; there, removing a repeatable linear bias through affine calibration produces consistent, non-trivial R² improvements. These scale effects explain the “dip-and-recovery” pattern on grazing in Iter4 (uncalibrated → calibrated) versus the comparatively muted drylot curves.

A third contributor is cohort heterogeneity as grazing supervision is added. Incorporating 2021 → 2022 → 2023 grazing introduces year-specific mixtures of forage conditions, weather regimes, and management. With the encoder frozen by design, the head is the only moving component available to absorb those shifts. Bias-only updates primarily correct cohort-mean offsets; full-head updates attempt to refit slopes with limited capacity, which can degrade linear alignment on the Unseen 2023 split if year-specific dynamics depart from the proxy grazing used to tune. The calibrated Iter4 result again indicates that the underlying features are informative; the head simply required a linear re-scaling to align with the held-out target distribution.

With respect to how much individual grazing intake data is required for accurate within-system prediction, prior work has not quantified this. The stability observed from Iter1 through Iter3 suggests early gains plateau under bias-only tuning. Additional improvements likely require either domain-specific affine calibration (as demonstrated) to remove persistent scale/offset mismatches or carefully controlled unfreezing of deeper layers with regularization and early stopping to prevent over-tilting slopes toward the newest cohort. Importantly, every step here was accomplished with deployable measurements (walk-on/pen scales), general animal metadata, and open climate covariates—no specialized imaging or proprietary sensors—so the iterative protocol remains practical for real herds.

In the broader context of iterative ML in animal agriculture, our approach is intentionally simple and domain-incremental rather than algorithmically ornate. Iterative schemes in animal breeding (Nayeri et al. 2019) typically operate with high-dimensional genotype matrices and complex, multi-stage estimation—iterative shrinkage, EM-like cycles, or staged incorporation of genomic information—while the data domain itself is essentially static. Here, iteration is defined by sequentially expanding the domain with new grazing cohorts, holding out three external validations (MT, HP, Grazing-2023) end-to-end, and strictly controlling the model’s degrees of freedom (bias-only vs full-head), with an optional two-parameter affine per domain. That design keeps the pipeline transparent, auditable, and field-deployable, yet still reveals, with precision, how incremental grazing supervision shifts error curves in practice.

Despite the relative scale of our dataset compared with prior work, the study still carries important limitations. The grazing cohorts analyzed here were collected at a single location (Wardensville, WV), which constrains the climatic, forage, and management diversity represented in the training and validation framework. Although the model performed robustly under the environmental variability present within this Appalachian system, its behavior under substantially different climatic regimes (e.g. humid subtropical, continental Midwest, or western rangeland environments) remains to be formally evaluated. Establishing cross-climate portability of sequential DMI models will require coordinated multi-location datasets spanning broader agroecological zones. Additionally, affine calibration assumes that residual domain mismatch is primarily linear. While this assumption held across the present external validations, more extreme environmental regimes, particularly high-heat scenarios where intake suppression may become nonlinear, could introduce curvature not correctable by a global scale-and-shift. Future work should evaluate segmented or nonlinear calibration strategies under expanded climatic diversity to determine whether they provide meaningful gains without sacrificing robustness or introducing instability in small-domain settings. Such expansion represents an important next step for advancing deployable intake prediction in grazing systems. The grazing cohorts remain modest in size and were all in a single location, which bounds the diversity of forages, climates, and management regimes the model has seen. Similarly, it is also important to note that the Unseen Grazing (2023) validation dataset, while strictly separated at the EID level from training animals, was geographically co-located with the Wardensville grazing cohorts used for model development. In addition, the Unseen Grazing validation cohort consisted of steers only; therefore, grazing-system accuracy for heifers and bulls cannot be assessed in this study, and class-specific performance under grazing should be evaluated in future multi-class grazing datasets. Although this design prevents animal-level information leakage, the validation set shares forage base, regional climate regime, and management structure with the training data. As a result, grazing validation performance reported here does not constitute true cross-location environmental generalization. Evaluation under grazing systems in distinct geographic regions, with differing forage species, climatic variability, and management practices, will be necessary to establish full environmental portability of the sequential DMI framework. Additionally, although the NOAA stations used are regionally representative, microclimate differences between airport stations and farm sites (particularly for precipitation and wind) may introduce localized divergence not fully captured in the model inputs.

It should be noted that the grazing trials were conducted under a structured rotational design in which animals were moved daily among small subplots. Short-duration rotational grazing can influence forage selection pressure, bite mass, and short-term intake dynamics compared with continuous grazing systems where animals remain in a single pasture for extended periods. Frequent rotation promotes regrowth and maintains forage in a vegetative state, which may stabilize forage quality and reduce extreme fluctuations in intake. Conversely, continuous systems may allow greater selective grazing but also greater variability in sward structure over time. Although the rotational approach used here reflects well-managed grazing practices, intake dynamics observed under this design may not fully represent those of continuously grazed systems.

An unavoidable limitation when predicting grazing DMI lies within the methodology used for gathering ground-truthed individual DMI measurements. Though it is arguably the best method for accurate estimation of individual grazing DMI, estimation accuracy using external markers is highly dependable on fecal recovery (FR). External markers such as Cr₂O₃ and TiO₂ rarely achieve perfect 100% recovery, and reported FR values commonly range from approximately 90% to >100%, depending on diet, marker, and sampling protocol (Titgemeyer et al. 2001; Myers et al. 2006; Glindemann et al. 2009; Schaafstra et al. 2019; Velásquez et al. 2021). Because DMI is calculated as a function of fecal output and diet digestibility, deviations of FR from unity propagate directly into intake estimates, and failure to correct for FR can lead to systematic under- or overestimation of DMI, particularly when recovery differs by forage source or forage-to-concentrate ratio (Owens and Hanson 1992; de Souza et al. 2015). In the present study, marker dosing and fecal sampling were standardized across animals and sampling days, and intake estimates were derived from repeated measures across a large number of animal-days. While random components of FR variability are expected to diminish with replication, systematic recovery bias cannot be fully eliminated and likely contributes to residual error in the intake data. Consequently, inherent marker-associated measurement error establishes a practical upper bound on achievable predictive accuracy in any model trained on these data. Future studies may wish to estimate total FR using collection bags affixed to the animal and explicitly account for the FR error in their modeling. However, it should be noted that changes in grazing behavior precipitated by use of collection bags may bias DMI estimation more than the inherent error in FR. Despite this constraint, model performance remained robust, suggesting that signal attributable to biological intake variation substantially exceeded methodological noise.

Another limitation and cause for continued work is the breed representation within the study. All animals in this analysis were Bos taurus; we did not include Bos indicus or indicus-influenced crossbreds, so domain shift to subtropical genetics and environments is an open question. Measurement noise is another unavoidable constraint. Even with low prediction errors, those errors are large enough, relative to between-animal differences, to preclude discrete ranking of individuals for RFI under grazing. This is not unique to modeling: in RFID-equipped bunk systems (e.g. commercial platforms), a fraction of feed disappearance is algorithmically treated as orts, introducing small but real uncertainty into “ground-truth” intake itself. Compounding this, because scalable and accurate measurement of grazing DMI remains difficult, the Beef Improvement Federation currently does not provide explicit, system-specific recommendations for test length to establish grazing RFI. These factors argue for caution in using any single model output to rank individuals in pasture. Interval estimates or thresholds (e.g. flagging extremes) are more defensible than strict ordinals currently. Additionally, all animals included in this study were Bos taurus breeds or Bos taurus–derived crossbreds in finishing-stage production systems. The dataset did not include Bos indicus or indicus-influenced cattle, nor did it include cow–calf or extensive rangeland systems outside the finishing context. Differences in thermotolerance, growth patterns, and intake dynamics across genetic types and production stages may influence model behavior. Evaluation across broader genetic backgrounds and production systems will therefore be necessary to establish full biological generalizability. Similarly, although this framework improves upon legacy equations, deployment still depends on RFID-enabled walk-on scales, individual intake nodes, and metered water systems. These technologies represent a capital investment that may exceed the threshold of many commercial cow–calf or small-scale operations. At present, the most immediate application is likely within research stations, structured performance tests, and seedstock or breeding programs where individual intake phenotyping infrastructure already exists or can be economically justified. Broader industry adoption will depend on continued declines in hardware costs, shared testing models, or cooperative infrastructure that distributes phenotyping capacity across producers.

Future work should exploit LSTM-based modeling’s strengths by incorporating intra-day resolution from autonomous equipment that already logs high-frequency events (bunk visits, bout duration, intake rate, walk-on scale weights), along with finer-scale weather telemetry. Realizing this will require deliberate database engineering: event-time storage that preserves irregular sampling, reliable time alignment across devices, and sequence builders that aggregate within-day structure (e.g. bouts) into daily windows without leakage. With those foundations, hierarchical sequence models (intra-day to inter-day) become practical, and we expect them to stabilize estimates during rapidly changing conditions (heat spikes, diet transitions).

The full model was accurate and portable across production systems, and the iterative experiments clarified how small, controlled degrees of freedom in the head, and optional affine scale/shift, behave as grazing supervision is added. Bias-only updates yielded stable trajectories; freeing head weights in the last iteration introduced a linear mis-scaling on the unseen grazing split that simple calibration reversed, without touching the backbone. Practically, this matters: the pipeline performs well with deployable inputs (animal metadata, walk-on/pen scales, open weather) and no proprietary imaging or specialized sensors. The combination of accuracy, generalizability, and pragmatic data requirements positions the approach to help improve sustainability: identifying animals that maintain performance at lower intake, quantifying heat-load responses to guide management, and informing selection decisions in ways that reduce feed use and emissions intensity while maintaining productivity.

Glossary

Abbreviations

ADG

average daily gain

AAALAC

Association for Assessment and Accreditation of Laboratory Animal Care International

API

application programming interface

BIF

Beef Improvement Federation

BW

body weight

CI

confidence interval

CVRMSE

coefficient of variation of RMSE (RMSE/mean)

DM

dry matter

DMI

dry matter intake

EID

electronic identification (animal ID)

HDX

half duplex

HP

Unseen Non-Regional Drylot Validation (Hyplains)

IPW

in-pen weighing (walk-on scale)

IQR

interquartile range

KS

Kansas (Hyplains site)

LCD

local climatological data

LSTM

long short-term memory

MAE

mean absolute error

MGW

Morgantown, WV airport station code

MT

Unseen Regional Drylot Validation (Morgantown)

NASA POWER

NASA Prediction of Worldwide Energy Resources

NASEM

National Academies of Sciences, Engineering, and Medicine equations

NEm

net energy for maintenance

NOAA

National Oceanic and Atmospheric Administration

NRMSE_sd

RMSE normalized by standard deviation (RMSE/SD)

REOC

Research, Education and Outreach Center (WVU)

RFID

radio frequency identification

RFI

residual feed intake

RMSE

root mean squared error

SD

standard deviation

THI

temperature–humidity index

TPE

tree-structured Parzen estimator (Optuna sampler)

UVA

ultraviolet A

WI

water intake

WVU

West Virginia University

Author contributions

Nathan E. Blake (Data curation [true], Formal analysis [true], Investigation [true], Methodology [true], Validation [true], Visualization [true], Writing—original draft [true]), K. E. ArunKumar (Data curation [true], Formal analysis [true], Investigation [true], Methodology [true], Writing—review & editing [true]), Matthew Walker (Formal analysis [true], Investigation [true], Writing—review & editing [true]), Tylor J. Yost (Investigation [true], Methodology [true], Writing—review & editing [true]), Domingo Mata-Padrino (Conceptualization [true], Formal analysis [true], Investigation [true], Methodology [true], Supervision [true], Writing—review & editing [true]), Ida Holásková (Data curation [true], Formal analysis [true], Methodology [true], Writing—review & editing [true]), Jarred W. Yates (Conceptualization [true], Funding acquisition [true], Investigation [true], Methodology [true], Writing—review & editing [true]), Duane Bishoff (Investigation [true], Methodology [true], Writing—review & editing [true]), Samanthia Johnson (Investigation [true], Methodology [true], Writing—review & editing [true]), Godstime Taiwo (Investigation [true], Methodology [true], Writing—review & editing [true]), Modoluwamu Idowu (Investigation [true], Methodology [true], Writing—review & editing [true]), Ibukun Ogunade (Investigation [true], Methodology [true], Writing—review & editing [true]), Darin Matlick (Conceptualization [true], Investigation [true], Methodology [true], Writing—review & editing [true]), Alexandria Smith (Investigation [true], Methodology [true], Writing—review & editing [true]), Brad Smith (Investigation [true], Methodology [true], Writing—review & editing [true]), Joseph Hatton (Funding acquisition [true], Investigation [true], Project administration [true], Writing—review & editing [true]), and Matthew E. Wilson (Conceptualization [true], Data curation [true], Funding acquisition [true], Investigation [true], Methodology [true], Project administration [true], Resources [true], Supervision [true], Writing—review & editing [true])

Funding

This material is based upon work that is partially supported by the National Institute of Food and Agriculture, U.S. Department of Agriculture, Hatch projects WVA 738 and WVA 743 under accessions 1024859 and 1025826. It was also partially supported by an equipment grant from Vytelle, graduate student support for N.E. Blake from Enriched Ag and grant support from the U.S. Department of Agriculture Natural Resources Conservation Service award no. 68-3D47-15-10. Scientific article no: 3479 of the West Virginia Agricultural and Forestry Experiment Station, Morgantown.

Conflict of interest statement. The authors declare no real or perceived conflicts of interest.

Data availability

Data may be available by contacting the corresponding author.