Trait-based machine learning modeling of soluble carbohydrate content in Trachyspermum ammi exposed to organic and chemical fertilization and salicylic acid

Abstract

Accurate assessment of biochemical traits in medicinal plants is essential for supporting environmentally responsible agriculture, improving crop quality, and enhancing the nutritional and pharmacological value of plant-derived products. Although medicinal plants are rich in bioactive compounds, conventional methods for measuring key biochemical components, such as soluble carbohydrates, are often time-consuming, destructive, and resource-intensive. Trachyspermum ammi L. (Ajwain) is valued for its antioxidant, antimicrobial, and digestive properties, highlighting the need for rapid, reliable, and non-destructive evaluation methods. Despite previous studies on fertilization effects on growth and bioactive compounds in T. ammi, research integrating morpho-physiological data with machine learning to predict key biochemical traits remains limited. In this study, we applied Multilayer Perceptron (MLP) and Gaussian Process Regression (GPR) models to estimate soluble carbohydrate content in a non-invasive and efficient manner. A dataset including morphological, biochemical, physiological, and macronutrient traits was used as input variables. Fertilization regimes and salicylic acid (SA) treatments were applied to induce variability in plant traits but were not directly included as model features, ensuring that predictions were trait-based. Models were trained and evaluated on n = 45 samples using five-fold cross-validation. Among the tested models, MLP and GPR achieved the highest predictive accuracy, particularly when the full feature set was used. Predictions based solely on biochemical and physiological traits were nearly as accurate as those using all variables, suggesting that these traits provide reliable and cost-effective estimates. Considering the limited dataset, results should be interpreted with caution, and future studies using larger, independent datasets are recommended to further assess model robustness and generalizability. These findings demonstrate the practical potential of the proposed machine learning approach for rapid, non-destructive assessment of biochemical traits in medicinal plants and may inform the development of GUI-based decision-support tools for precision agriculture and phytopharmaceutical research.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12870-026-09466-x.

Introduction

Trachyspermum ammi (L.) Sprague, commonly known as Ajwain or carom seeds, is an aromatic annual herb belonging to the Apiaceae family. Valued for its culinary and medicinal properties, T. ammi has a long history of use in Ayurveda, Unani, and traditional medicine systems across South Asia and the Middle East. Its seeds are rich in essential oils and bioactive compounds such as thymol, γ-terpinene, p-cymene, and α-pinene, which contribute to its antimicrobial, anti-inflammatory, and carminative effects. Recent studies have highlighted the potential of T. ammi for functional foods and phytopharmaceutical development. Owing to its potent therapeutic properties, this plant shows promise in managing gastrointestinal, respiratory, and metabolic disorders. The convergence of traditional knowledge and modern pharmacological evidence underscores its multifunctional medicinal value and potential for future clinical and nutraceutical applications.

Fertilization practices, particularly organic and biological inputs, have received considerable attention due to their ability to enhance plant growth, productivity, and phytochemical accumulation while maintaining environmental sustainability. For instance, Azadinejad et al. demonstrated that organic fertilization improved nutrient uptake and flower yield in Borago officinalis [1]. Despite the increasing demand for high-quality medicinal herbs and the global shift toward sustainable cultivation, knowledge regarding the effects of fertilization on morpho-physiological traits and biochemical composition of T. ammi remains limited. This study evaluates the effects of organic and chemical fertilizers on morpho-physiological parameters, nutrient uptake, and phytochemical content in T. ammi, contributing to evidence-based strategies for optimizing its cultivation and medicinal efficacy.

Machine learning (ML) has been increasingly applied to predict physiological traits, bioactive compound content, and crop yield in medicinal plants. For example, Richard-Bollans et al. used ML to identify plants with antimalarial potential [2]; Nazarenko et al. combined spectrometric data with ML for rapid and precise compound detection [3]; Mazaheri-Tirani et al. predicted long-term physiological effects of zinc oxide nanoparticles on Carum copticum using ML algorithms [4]. Specifically for T. ammi, Niazian et al. modeled seed yield using artificial neural networks and MLR [5], while Huang et al. predicted fruit chemical composition based on mineral content [6]. Recent studies also show that integrating ML with physiological and nutrient data can improve prediction of nutrient accumulation and allocation in horticultural crops. For example, ML frameworks have successfully classified grafting combinations in cucumber plants based on tissue nutrient profiles [7], and supervised ML models including LSSVM predicted CO₂-EOR outcomes with meticulous preprocessing, such as outlier detection via Mahala Nobis distance, achieving highly reliable predictions [8]. Artificial neural networks have also forecasted cumulative oil production and CO₂ storage capacity with high accuracy and low RMSE in complex residual oil zones [9].

The success of these data-driven strategies underscores the potential of ML methods to predict biochemical traits in medicinal plants, such as soluble carbohydrate content, by leveraging comprehensive morpho-physiological, biochemical, and nutrient datasets. Given the increasing relevance of ML in agriculture and medicinal plant research, this study aims to explore the potential for predicting soluble carbohydrate content in T. ammi under organic and chemical fertilization regimes. By integrating morpho-physiological data with artificial intelligence techniques, this research seeks to inform cultivation strategies that may enhance both quality and yield. This approach may enable rapid assessment of critical quality traits, such as soluble carbohydrate content, without relying solely on traditional chemical analyses, thereby supporting reduced chemical inputs and promoting environmental sustainability.

To the best of our knowledge, no prior study has applied ML specifically to predict soluble carbohydrate content in Ajwain (T. ammi), although ML-based predictions of primary metabolites have been conducted in other medicinal plants and crops. This gap underscores the need to develop robust predictive models capable of estimating key biochemical traits. Based on this rationale, we hypothesized that non-linear ML models would outperform traditional MLR in predicting soluble carbohydrate content in T. ammi using morpho-physiological, biochemical, and macronutrient traits.

The study was conducted in several systematic steps: First, a comprehensive dataset including morphological, biochemical, physiological, and macronutrient traits of T. ammi was collected under organic and chemical fertilization regimes and salicylic acid treatments. Second, the dataset was preprocessed and prepared to ensure quality and consistency. Third, multiple ML models, including GPR, RBF, MLP, DT, RF, and MLR, were trained and validated using 5-fold cross-validation. Fourth, predictive performance of each model was evaluated using R², RMSE, and MAPE. Finally, results were analyzed to identify the most effective models and key traits influencing soluble carbohydrate content, and practical implications for precision agriculture and phytopharmaceutical development were discussed.

Materials and methods

Soil physicochemical characteristics

The soil used in the experiment was classified as silt loam, comprising 25% sand, 49% silt, and 26% clay. Soil texture was determined using the hydrometer method (Bouyoucos). The pH of the saturated paste was 8.3, and the electrical conductivity (ECe) of the saturated extract was 2.1 dS m⁻¹, measured with a standard pH meter and conductivity meter. Organic matter (OM) content was 1.36%, determined via the wet oxidation method, and total nitrogen (N) content was 0.13%, following Bremner’s procedure. Available phosphorus was 13.24 mg kg⁻¹, measured using the sodium bicarbonate extraction method (Olsen), and available potassium was determined according to the method of Helmke and Sparks.

Experimental conditions and agronomic practices

The field experiment was conducted at the Medicinal Plants Farm of Shahid Bakeri Higher Education Center in Miandoab (36.5°N, 46.6°E; 1314 m above sea level). During the experimental period, mean environmental conditions included an average temperature of ~ 20 °C, mean monthly precipitation of 0.32 mm, and average relative humidity of 44.5%. Certified seeds of T. ammi were obtained from Pakan Bazr Company (Isfahan, Iran).

The experiment was conducted as a factorial experiment in a completely randomized design with three replications (blocks). The fertilizer factor included five levels, and the salicylic acid factor included three levels, resulting in 15 treatment combinations across the three replications and a total of 45 experimental plots. The seeds were sown at a depth of approximately 10 mm in plots measuring 2 m × 2 m, giving a total area of 4 m² per plot. The distance between rows was 50 cm, and the distance between plants within each row was 4 cm, so each plot contained five planting rows. The distance between adjacent plots was 1.5 m. Irrigation was applied immediately after sowing to facilitate germination. At harvest, to measure the desired traits, the side rows and 0.5 m from the beginning and end of each plot were removed. Five plants were sampled from a 1 m² area in the center of each plot, and the mean of these five plants was considered as the value for that plot. This setup allowed accurate measurement of the desired traits while minimizing border effects and ensuring standardized experimental units. All statistical analyses were then performed using data from these 45 experimental units (n = 45).

Experimental design

The experiment was conducted as a factorial arrangement within a completely randomized block design (CRBD) with two factors. The first factor was fertilization, with five levels: control (no fertilizer), cow manure, compost, vermicompost, and chemical fertilizer.

Cow manure, compost, and vermicompost were applied at rates of 30, 20, and 10 t ha⁻¹, respectively, and incorporated into the soil before planting. The chemical fertilizer application details remain unchanged: phosphorus (75 kg ha⁻¹) from triple superphosphate and potassium (50 kg ha⁻¹) from potassium sulfate were applied at planting, while nitrogen (75 kg ha⁻¹) supplied as urea was applied in split doses-half at planting and the remaining half at the appropriate growth stage. The second factor was salicylic acid (SA) at three levels: 0, 0.5, and 1 mM. For the SA treatment, after the emergence of two true leaves, solutions of 0.5- and 1-mM SA were sprayed at five stages, every 15 days. Distilled water was used for control treatments. Throughout field preparation and the entire growth period (from planting to harvesting), no chemical fertilizers, herbicides, pesticides, or fungicides were applied. The combined fertilization and salicylic acid (SA) treatments were used to generate a wide range of morphological, physiological, and biochemical variability among plants. For machine learning analyses, models were trained using measured plant traits as input variables rather than directly encoding treatment factors.

Harvesting and plant identification

Plants were harvested at the flowering stage for subsequent biochemical and agronomic evaluations. After removing the two side rows and 50 cm from the beginning and end of each plot as a border, 5 samples were taken from one square meter of plants in the middle of the plot, and the value of each parameter was measured and then their average was reported for each plot. The plant material was authenticated by Dr. Abolfazl Alirezalu (Urmia University), and a voucher specimen (Herbarium Code: 1537) has been deposited in the Herbarium of Urmia University for future reference.

Measurement of growth parameters

At the onset of flowering, key morphological traits were recorded. Stem length (cm) was measured using a ruler, and the number of lateral stems was counted from all branches emerging at the base of each plant. After harvest, stem diameter (mm) was measured at three points along the main stem (base, middle, and top) using a digital caliper, and the average was calculated. Plant height was measured with a measuring tape, and the number of branches per plant and seed yield were recorded. To evaluate reproductive performance, thousand-seed weight was determined by weighing 1000 randomly selected mature seeds using an analytical balance, following standard protocols [10].

Essential oil isolation and post-extraction processing

Plant samples were carefully shade-dried at a controlled ambient temperature of 25 °C for 22 days. To prevent heat accumulation and ensure uniform drying, the samples were arranged on mesh trays away from direct sunlight, allowing adequate air circulation and minimizing the risk of thermal degradation of essential oil constituents. Essential oils were extracted by hydro-distillation using a Clevenger-type apparatus for 3 h, with the process repeated three times. The collected oils were stored in dark glass containers to prevent light-induced degradation, and residual moisture was removed using anhydrous sodium sulfate, in accordance with the British Pharmacopoeia [11].

Spectrophotometric determination of chlorophyll a and b in leaf tissue

Chlorophyll a and chlorophyll b contents in leaf tissues were determined according to the method of Arnon (1949). Fresh leaf samples were thoroughly rinsed with deionized water to remove surface contaminants. Photosynthetic pigments were extracted from the fourth fully expanded leaf from the top of each plant at the end of the experimental period. A 0.1 g portion of fresh leaf tissue was ground in 5 mL of 80% (v/v) acetone under dark conditions to prevent pigment degradation. The homogenate was then centrifuged at 5,000 × g for 10 min to clarify the extract. Absorbance was measured at 645 nm and 663 nm using 80% acetone as a blank, corresponding to chlorophyll b and chlorophyll a, respectively [12].

Quantification of free proline in leaf tissues

The concentration of free proline in leaf tissues was estimated using a modified protocol based on Rowshan et al. (2014). For this analysis, 5 g of fresh leaf tissue was homogenized in 10 mL of 3% aqueous sulfosalicylic acid. The mixture was then filtered through Whatman No. 1 filter paper to obtain a clear extract. An equal volume (2 mL) of the filtrate was mixed with 2 mL of acid-ninhydrin reagent and 2 mL of glacial acetic acid in a test tube. The reaction mixture was thoroughly mixed and allowed to proceed, after which 4 mL of toluene was added. Following vigorous shaking, the chromophore-containing organic phase was separated, and its absorbance was measured at 520 nm using a UV–visible spectrophotometer. Free proline content was calculated from a standard curve prepared with known concentrations of L-proline and expressed as mg/g of fresh tissue [13].

Determination of total phenolic content

The total phenolic content of the samples was determined using the Folin–Ciocalteu colorimetric method, with slight modifications, as described by Moein et al. (2015). In brief, 500 µL of plant extract or gallic acid standard solution was mixed with 2.5 mL of 10% (v/v) Folin–Ciocalteu reagent, followed by the addition of 2 mL of 7.5% (w/v) sodium carbonate solution. The mixture was incubated at 25 °C for 60 min in the dark to prevent photo-oxidation. The absorbance of the resulting blue-colored complex was measured at 765 nm using a UV–Visible spectrophotometer (Lambda 950, Perkin-Elmer, USA). A calibration curve was prepared using gallic acid standard solutions at concentrations of 0.0093, 0.0187, 0.0375, 0.075, and 0.15 mg/L. Total phenolic content was expressed as milligrams of gallic acid equivalent per gram of extract (mg GAE/g extract). All measurements were performed in triplicate to ensure accuracy [14].

Macronutrient analysis of leaf tissues (N, P, K)

Leaf nitrogen (N), phosphorus (P), and potassium (K) concentrations were determined following Khalid & Shedeed (2015) with minor modifications [15]. Briefly, leaf samples were rinsed, shade-dried, and ground to a fine powder. For P and K determination, samples were digested with concentrated nitric acid and analyzed using the vanadate–molybdate colorimetric method and flame photometry, respectively. Nitrogen content was measured using the classical Kjeldahl method. All measurements were performed in triplicate to ensure reproducibility.

Quantification of soluble carbohydrate content

Soluble carbohydrate content was quantified using a modified phenol–sulfuric acid method (Dubois et al., 1956) [16]. Fresh tissue was homogenized in distilled water, filtered, reacted with phenol and sulfuric acid, and absorbance was measured at 485 nm. Glucose standards were used for calibration, and results were expressed as mg g⁻¹ FW. All measurements were conducted in triplicate. Previous studies on T. ammi indicate that organic fertilizers, particularly vermicompost, enhance morphophysiological and biochemical traits, including total phenolics, chlorophyll a and b, carotenoids, soluble carbohydrate content, and macronutrient concentrations (N, P, K) [17]. These findings support the physiological relevance of the selected traits as inputs in predictive models of soluble carbohydrate content.

Physiological basis for selection of morphological, biochemical, and macronutrient traits as model inputs

To comprehensively predict soluble carbohydrate content in T. ammi, a set of morphological, biochemical, and macronutrient traits were selected as model input variables based on their direct or indirect roles in carbohydrate production, transport, and storage.

Morphological and yield-related traits, including plant height, number of branches, stem diameter, seed yield, and thousand-seed weight, were chosen due to their fundamental role in determining photosynthetic capacity and assimilate allocation. Taller plants with larger leaf area capture more light energy, promoting photosynthesis and carbohydrate accumulation. A higher number of branches increases total leaf surface area, enhancing energy capture and carbohydrate synthesis. Stem diameter reflects the plant’s capacity for water and nutrient transport, supporting efficient carbohydrate distribution. Seed yield and thousand-seed weight serve as indicators of carbohydrate allocation to reproductive sinks, integrating both production efficiency and translocation capacity.

Biochemical and physiological traits, such as chlorophyll a and b, proline, total phenolic compounds, and essential oil content and yield, were incorporated due to their mechanistic relevance to photosynthetic efficiency and stress resilience. Chlorophyll pigments directly influence light absorption and ATP/NADPH generation, driving carbohydrate synthesis. Proline acts as an Osmo protectant, stabilizing photosynthetic enzymes and maintaining cellular homeostasis under stress, indirectly supporting carbohydrate accumulation. Phenolics act as antioxidants, safeguarding chlorophyll and the photosynthetic apparatus from oxidative stress, while essential oil content indicate the plant’s metabolic activity and the allocation balance between carbohydrate and lipid biosynthesis. Total soluble carbohydrate content was treated as the model target variable and was not included as an input feature (Table 1).

Table 1.

Morphological, biochemical, and macronutrient traits used as input variables in machine learning models

Feature (Variable)	Unit	Category
Plant height	cm	Morphological
Number of branches	count	Morphological
Stem diameter	mm	Morphological
Seed yield	g/plant	Morphological
Thousand-seed weight	g	Morphological
Chlorophyll a	mg/g FW	Biochemical
Chlorophyll b	mg/g FW	Biochemical
Carotenoids	mg/g FW	Biochemical
Proline	µmol/g FW	Biochemical
Essential oil content	%	Biochemical
Nitrogen (N)	%	Macronutrient
Phosphorus (P)	mg/g FW	Macronutrient
Potassium (K)	mg/g FW	Macronutrient

Leaf macronutrients, including nitrogen (N), phosphorus (P), and potassium (K), were also considered for their central role in photosynthesis, energy transfer, and assimilate translocation. Nitrogen is essential for the synthesis of amino acids, proteins, and photosynthetic enzymes; phosphorus is critical for ATP production and energy metabolism; and potassium regulates osmotic balance, enzyme activation, and carbohydrate transport to storage organs. Importantly, the fertilization regimes and salicylic acid (SA) treatments were applied as part of the experimental design to induce variability in plant traits but were not directly included as input variables in the machine learning models.

Outlier detection

To identify potential influential outliers in the dataset, Cook’s distance was calculated for all observations across the measured traits. Cook’s distance is a widely used diagnostic measure that evaluates the influence of individual observations on regression estimates. According to established statistical guidelines, observations with Cook’s distance values greater than 1 are considered potentially influential. In the present study, all observations exhibited Cook’s distance values below this threshold, indicating the absence of influential outliers in the dataset.

Dataset partitioning and implementation of K-Fold cross-validation

In this study, three main categories of input variables were considered for modeling soluble carbohydrate content as the target variable: (1) morphological and yield traits, including plant height, number of branches, stem diameter, seed yield, and thousand-seed weight; (2) biochemical and physiological traits, such as chlorophyll a, chlorophyll b, proline, total phenolic compounds, oil percentage, and oil yield; and (3) macronutrient concentrations of nitrogen, phosphorus, and potassium. Additionally, a combined dataset incorporating all these features was also utilized. These inputs were fed into several machine learning algorithms-namely RBFNN, MLPNN, DT, RF, and GPR-as well as a MLR model to predict soluble carbohydrate content. To standardize the dataset and improve model performance, all variables were normalized to have zero mean and unit variance. This normalization was applied directly to the raw replicate-level observations rather than averaged values, ensuring that each sample contributed individually to the modeling process.

To prevent data leakage, all preprocessing steps, including normalization and hyperparameter optimization, were performed strictly within the training data of each fold during the 5-fold cross-validation process. Normalization parameters (mean and standard deviation) were computed exclusively from the training data and subsequently applied to the corresponding test fold, which remained completely independent and was used solely for final model evaluation. Overall, the dataset contained n = 45 replicate-level observations, and all machine learning models were trained and validated using this full set of samples under a 5-fold cross-validation scheme. To enhance the robustness and generalizability of the predictive models, a 5-fold cross-validation approach was applied. In this method, the entire dataset was randomly divided into five equal partitions. In each round of validation, one partition was held out as the test set, while the remaining four were used for training the models. This procedure was repeated five times, ensuring that each subset served exactly once as the validation set. Final model evaluation metrics were obtained by averaging the results across all folds. This methodology follows the approach described by Kumar et al. (2024), who employed similar machine learning and cross-validation techniques for modeling climate change impacts on vector-borne diseases [18].

Summary of the applied machine learning models

This section provides an overview of the machine learning techniques used to predict soluble carbohydrate content in T. ammi based on morphological, biochemical, physiological, and macro-nutrient features. The algorithms evaluated include MLR, RBFNN, MLPNN, DT, RF, and GPR. The following subsections summarize the key characteristics, advantages, and limitations of each method applied in this study. The RBF efficiently handle nonlinear data and often converge quickly; however, choosing an appropriate basis function can be challenging [19]. The Multilayer Perceptron neural network is powerful in capturing complex nonlinear patterns, although its success depends heavily on careful hyperparameter tuning [20, 21]. The RBFNN offer an intuitive and efficient modeling method but are prone to overfitting, especially with complex datasets [22]. The RBF reduce overfitting through ensemble learning and perform well with high-dimensional data, but they require significant computational resources [23]. Finally, Gaussian Process Regression provides a flexible nonparametric framework that models prediction uncertainty effectively and is suitable for small datasets; however, its computational cost increases notably with larger data volumes [24].

The following subsections present detailed descriptions of the structure and implementation of each machine learning model applied in this research.

Multilayer Perceptron Neural Network (MLPNN)

The MLPNN is a feedforward neural network used in this study to model nonlinear relationships between input variables and the target trait. The network consists of an input layer, one or more hidden layers, and an output layer. Nonlinear activation functions were applied in the hidden layers to enable effective pattern learning. Model training was performed by optimizing network weights and biases through minimization of prediction error using established optimization algorithms, ensuring reliable model performance and generalization [25, 26].

Radial Basis Function Neural Networks (RBFNN)

The RBFNN was applied to capture nonlinear relationships between the input variables and the response. The model consists of an input layer, a radial basis hidden layer, and an output layer. Network training involved determining the centers and widths of the radial basis functions, followed by optimization of the output weights to minimize prediction error and enhance model accuracy [19, 27].

Decision Tree (DT)

The DT models were employed as non-parametric learning methods for regression analysis. The trees were constructed by recursively partitioning the input space based on selected features and optimized splitting criteria, with pruning strategies applied to reduce overfitting and improve generalization. This rule-based structure enables DTs to effectively model complex relationships between input variables and the target response [22, 28, 29].

Random Forest (RF)

The RF was used as an ensemble learning approach for regression analysis in this study. The model combines multiple DT trained on bootstrapped subsets of the data with random feature selection to improve predictive performance and reduce overfitting. Final predictions were obtained by averaging the outputs of individual trees, providing robust modeling of nonlinear relationships between input variables and the response [23, 30].

Gaussian Process Regression (GPR)

The GPR was applied as a non-parametric Bayesian regression method to model the relationship between input variables and the target trait. The model is defined by a covariance kernel function, which governs the smoothness and structure of the fitted function and enables probabilistic predictions. This approach allows effective modeling of complex data patterns while providing uncertainty estimates associated with the predictions [24].

Model implementation and hyperparameter optimization

To estimate soluble carbohydrate content, several regression models including MLR, RBFNN, MLPNN, DT, RF, and GPR were implemented in MATLAB R2019b. All models were tuned using deterministic grid-based hyperparameter optimization procedures with predefined search spaces, as detailed below. For the MLPNN, a grid-based search was conducted to determine the optimal network architecture. The investigated hyperparameters included the number of hidden layers (1–3), the number of neurons per layer (5–20 with a step size of 1), activation functions (linear, sigmoid, and tangent-sigmoid), and training algorithms (Levenberg–Marquardt, Bayesian regularization, conjugate gradient, steepest descent, and Newton). These hyperparameters were selected through multiple trials to minimize the output error function, defined as the difference between the actual outputs and the MLPNN predictions. The final MLPNN configuration consisted of a single hidden layer with 8 neurons using a sigmoid activation function, and the Levenberg–Marquardt algorithm was identified as the most effective training algorithm among those evaluated. For the RBFNN, the spread parameter was optimized using a deterministic coarse-to-fine grid-based search within the range of 0.001 to 1.0. An initial fine-resolution grid was used to identify promising regions of the parameter space, followed by a refined local search around the optimal region. At each candidate spread value, model performance was evaluated using five-fold cross-validation, and the optimal spread parameter (0.025) was selected based on minimum RMSE. For the DT model, a grid-based search was performed to tune key structural parameters, including the maximum number of splits (20–100 with a step size of 5), minimum leaf size (1–5), and pruning options. These parameters were systematically evaluated to minimize the prediction error between the measured and model-predicted outputs. The optimal DT configuration employed a maximum of 65 splits, a minimum leaf size of 2, and pruning enabled. For the RF model, hyperparameters including the number of trees (50–200 with a step size of 10), minimum leaf size (1–4), and different predictor selection strategies were examined using a grid-based search. The optimal RF configuration was selected by minimizing the prediction error and consisted of 110 trees with an interaction-curvature-based predictor selection strategy. The GPR model were developed using four different kernel functions: exponential, squared exponential, rational quadratic, and Matern. The kernel parameters were optimized using a numerical optimization algorithm to minimize the prediction error, with the exponential kernel yielding the best performance among the evaluated configurations. Prior to training all models, all input variables were standardized to have zero mean and unit variance. Hyperparameter tuning and model evaluation were conducted using five-fold cross-validation to ensure unbiased performance assessment. The final optimized hyperparameters for all models are summarized in Table 2.

Table 2.

Summary of optimized hyperparameters for each machine learning model, using all input variables

Algorithms	Basic Parameters
MLP	Training Algorithm= ‘Levenberg–Marquardt’, Activation Function= ‘sigmoid’, Number of hidden layers = single hidden layer with 8 neurons
RBFNN	The width of the RBF function= ' spread = 0.025’
DT	Type: regression; Maximum number of splits: 65; Minimum leaf size: 2; Pruning: enabled.
RF	Type: regression; Number of trees: 110; Predictor selection strategy: interaction–curvature.
GPR	Kernel function: exponential; Optimizer= ‘fmincon’; Input standardization: enabled.

Performance evaluation

To evaluate the effectiveness of the machine learning models and the MLR approach in predicting soluble carbohydrate content, three standard statistical metrics were employed: Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (R²), as presented in Eqs. (1), (2), and (3). Together, these indicators provide a comprehensive assessment of model performance by quantifying the discrepancy between predicted and observed values.

1

2

3

In these equations, n denotes the number of observations, while Y_est and Y_meas refer to the predicted and measured values of soluble carbohydrate content, respectively. The symbol represents the mean of the observed values. A high-performing model is characterized by lower values of RMSE and MAPE-indicating minimal prediction error-and a higher R² value, reflecting a strong correlation between estimated and actual outcomes. These performance criteria serve as a reliable framework for comparing model accuracy and robustness, thereby facilitating the selection of the most suitable predictive method for estimating carbohydrate levels in T. ammi under different fertilization regimes.

Bootstrap uncertainty analysis

To quantify uncertainty in model performance metrics, bootstrap-based 95% confidence intervals were calculated for R², RMSE, and MAPE. The bootstrap procedure was applied to paired observed values and the corresponding cross-validated predictions obtained from the same dataset. As no influential outliers were identified based on Cook’s distance analysis, all observations were retained for the bootstrap resampling process. The resampling was performed without altering the original model training strategy or the cross-validation framework, ensuring that the estimated confidence intervals reflected the intrinsic variability of the model performance metrics.

Results and discussion

Prediction of soluble carbohydrate content in T. ammi using machine learning models

Table 3 summarizes the predictive performance of MLR and several machine learning models-including MLPNN, GPR, RBFNN, RF, and DT-for estimating soluble carbohydrate content in T. ammi. Models were evaluated using a five-fold cross-validation, and bootstrap-based 95% confidence intervals support the stability of MLPNN and GPR performance despite the limited sample size (n = 45, Table 4).

Table 3.

Performance metrics of various machine learning models for soluble carbohydrate content estimation

Model types		Total (all input variables)		Morphological and Yield Traits		Biochemical and Physiological Traits		Macronutrient contents
		Train	Test	Train	Test	Train	Test	Train	Test
MLR	R2	0.9110	0.8916	0.8127	0.7297	0.8652	0.8449	0.4995	0.4957
	RMSE	0.0126	0.0139	0.0088	0.0103	0.0177	0.0187	0.0214	0.0229
	MAPE	5.8350	9.2293	19.3865	23.6603	9.7717	12.3499	35.6384	40.9385
MLPNN	R2	1.0000	0.9902	0.9431	0.8784	1.0000	0.9859	0.9982	0.9504
	RMSE	0.0002	0.0017	0.0014	0.0069	0.0011	0.0027	0.0013	0.0037
	MAPE	0.5087	2.8758	2.0836	8.5256	0.6819	3.6820	0.7234	5.4168
GPR	R2	0.9998	0.9891	0.9732	0.9043	0.9996	0.9778	0.9979	0.9564
	RMSE	0.0002	0.0024	0.0017	0.0041	0.0003	0.0029	0.0003	0.0034
	MAPE	0.4783	3.8722	1.0892	6.5369	0.7435	4.7245	0.7088	4.6248
RBFNN	R2	1.0000	0.9763	0.9542	0.8600	0.9841	0.9401	0.9582	0.9181
	RMSE	0.0007	0.0030	0.0026	0.0096	0.0025	0.0047	0.0053	0.0075
	MAPE	0.9731	4.0743	4.0804	10.8307	3.0198	5.9108	4.1894	8.0277
RF	R2	0.9969	0.9668	0.9456	0.8284	0.9792	0.9329	0.9824	0.8605
	RMSE	0.0006	0.0048	0.0040	0.0106	0.0021	0.0063	0.0021	0.0065
	MAPE	1.1042	4.1340	6.9298	11.5399	1.8076	5.9470	1.2105	8.1753
DT	R2	0.9556	0.9525	0.8531	0.7809	0.9375	0.9292	0.9134	0.8249
	RMSE	0.0042	0.0052	0.0077	0.0105	0.0063	0.0069	0.0060	0.0104
	MAPE	4.3419	5.8570	11.5411	17.6965	6.3011	6.4416	11.3586	14.9521

Table 4.

Bootstrap-based 95% confidence intervals for model performance metrics

Model	Total (all input variables)			Biochemical and Physiological Traits
	R 2 (95% CI)	RMSE (95% CI)	MAPE (95% CI)	R 2 (95% CI)	RMSE (95% CI)	MAPE (95% CI)
MLR	0.8916 (0.8580–0.9160)	0.0139 (0.0122–0.0163)	9.2293 (8.0200–10.9400)	0.8449 (0.8090–0.8790)	0.0187 (0.0162–0.0219)	12.3499 (10.7100–14.6600)
MLPNN	0.9902 (0.9830–0.9960)	0.0017 (0.0014–0.0022)	2.8758 (2.3600–3.4800)	0.9902 (0.9840–0.9960)	0.0027 (0.0022–0.0033)	3.6820 (3.0800–4.3900)
GPR	0.9891 (0.9780–0.9950)	0.0024 (0.0020–0.0030)	3.8722 (3.1900–4.7100)	0.9778 (0.9630–0.9890)	0.0029 (0.0024–0.0036)	4.7245 (3.9400–5.7800)
RBFNN	0.9763 (0.9610–0.9870)	0.0030 (0.0026–0.0037)	4.0743 (3.4100–4.8600)	0.9401 (0.9160–0.9610)	0.0047 (0.0040–0.0057)	5.9108 (4.9700–7.0900)
RF	0.9668 (0.9480–0.9810)	0.0048 (0.0040–0.0059)	4.1340 (3.5200–4.9300)	0.9329 (0.9060–0.9540)	0.0063 (0.0053–0.0076)	5.9470 (4.9800–7.1300)
DT	0.9525 (0.9310–0.9690)	0.0052 (0.0045–0.0064)	5.8570 (4.9100–6.9800)	0.9292 (0.9010–0.9510)	0.0069 (0.0059–0.0083)	6.4416 (5.3900–7.7400)

Values are reported as metric value (95% bootstrap confidence interval). Confidence intervals were computed using 500 bootstrap resamples of paired observed and cross-validated predicted values

Four feature sets were considered: (i) all variables, (ii) morphological and yield traits, (iii) biochemical and physiological traits, and (iv) macronutrient contents. Biochemical and physiological traits-including chlorophyll, proline, and phenolics-emerged as the strongest predictors of soluble carbohydrate content, reflecting photosynthesis efficiency, osmotic adjustment, and oxidative stress protection, whereas morphological traits and macronutrients alone were less predictive, highlighting the mechanistic relevance of functional traits in Ajwain.

Advanced ML models (MLPNN and GPR) effectively captured complex nonlinear relationships, though results should be interpreted cautiously due to the small sample size. The primary goal was predictive accuracy rather than ranking individual predictors, and interpretation focused on biologically meaningful pathways rather than post-hoc feature attribution, which could be explored in future studies using techniques such as SHAP.

Comparison with previous research highlights methodological distinctions. Huang et al. (2021) reported that ANN outperformed MLR in predicting loquat fruit quality traits, with mineral nutrients as major contributors [6]. In medicinal plants, studies like Nazarenko et al. (2016) have largely focused on species classification using LC–MS fingerprints, requiring extensive reference datasets. In contrast, our trait-driven approach quantitatively predicts soluble carbohydrate content from easily measurable morphological, physiological, and biochemical traits, offering a complementary, cost-effective, and non-destructive alternative suitable for experimental and field conditions [31]. Unlike loquat, where mineral content was dominant, Ajwain carbohydrate content is more closely linked to biochemical and physiological traits, emphasizing species-specific metabolic regulation and the need for tailored predictive models.

This multi-scenario evaluation identifies key traits informing carbohydrate prediction and provides a robust basis for selecting accurate and generalizable models. Integrating ML with physiological, biochemical, and morphological data improves crop trait prediction and guides fertilization strategies, demonstrating practical relevance in precision agriculture [32, 33].

Formal inferential tests (e.g., ANOVA) were not applied, as the focus was on predictive performance. Metrics such as cross-validated R², RMSE, and MAPE indicate comparative trends rather than statistically confirmed distinctions [34–36]. Given the limited sample size and exploratory nature of this study, differences between models should be interpreted descriptively rather than as definitive rankings.

Using the full set of input features, the Multilayer Perceptron Neural Network (MLPNN) achieved the highest predictive accuracy on the test set (R² = 0.9902; RMSE = 0.0017; MAPE = 2.88), with consistent performance across cross-validation folds, indicating robust generalization. Although training R² reached 1.0, test metrics confirmed the absence of overfitting, and all preprocessing was applied within training folds to prevent data leakage.

GPR and RBFNN also performed strongly (R² > 0.99; RMSEs: 0.0024, 0.0030; MAPEs: 3.87, 4.07), capturing complex nonlinear patterns efficiently. In contrast, MLR showed lower accuracy (R² = 0.8916; MAPE = 9.23), reflecting its limited capacity to model intricate relationships, while DT demonstrated moderate performance (R² = 0.9525) but higher errors.

When restricted to morphological and yield traits, predictive accuracy declined for all models, highlighting the weaker mechanistic link of these traits to carbohydrate metabolism. GPR and MLPNN maintained moderate performance (R² = 0.9043 and 0.8784; RMSE = 0.0041 and 0.0069; MAPE = 6.54 and 8.53), indicating that even limited input features contain meaningful patterns. MLR performance dropped substantially (R² = 0.7997; RMSE = 0.0103; MAPE = 23.66), confirming its inadequacy with restricted feature sets.

When biochemical and physiological traits were used as inputs, predictive performance closely matched that of the full feature set, emphasizing their mechanistic relevance in carbohydrate accumulation. MLPNN achieved the highest accuracy, indicating that chlorophyll, proline, and phenolics—reflecting photosynthetic efficiency, osmotic adjustment, and oxidative stress protection—are strong predictors of soluble carbohydrate content [33].

It should be noted that this analysis focuses on the predictive contribution of different feature groups rather than ranking individual variables. While post-hoc interpretability techniques (e.g., SHAP values or partial dependence plots) can provide feature-level insights, their application is limited by the small sample size (n = 45), particularly for flexible nonlinear models. Therefore, feature-level interpretability should be prioritized in future studies with larger and more diverse datasets.

Models relying solely on macronutrient content showed substantially reduced accuracy, demonstrating that biochemical and physiological variables are essential for precise carbohydrate prediction. Under organic fertilization, particularly vermicompost, enhanced predictability aligns with physiological mechanisms: nutrient enrichment and beneficial microbial communities improve plant metabolism, stress resilience, and growth, providing a biological basis for the superior predictive power of mechanistically linked traits.

This approach integrates morpho-physiological data with advanced ML models (MLPNN, GPR) to provide a rapid, non-destructive, and accurate method for estimating soluble carbohydrate content, reducing reliance on labor-intensive chemical assays. It aligns with Agriculture 5.0 concepts by enabling real-time, non-invasive monitoring of key plant traits, supporting efficient crop management and stress mitigation [33].

To further evaluate model stability, bootstrap-based 95% confidence intervals were calculated for R², RMSE, and MAPE using both the full feature set and the biochemical–physiological trait subset (Table 4). The relatively narrow confidence intervals for MLPNN and GPR indicate stable performance estimates, supporting the robustness of these models despite the limited sample size.

Despite the high predictive accuracy, limitations remain due to the small sample size (n = 45), which constrains model generalizability and may increase overfitting risk, particularly for flexible nonlinear algorithms. Cross-validation and fold-wise preprocessing help mitigate this risk but do not eliminate it. Future studies should validate models using independent, multi-location, or multi-season datasets and incorporate uncertainty analyses to enhance robustness. Accordingly, results should be interpreted with caution, and larger datasets are recommended to further evaluate model generalizability.

Regression plots (Fig. 1) support these findings, showing that predictive performance remains largely consistent when models are trained using only biochemical and physiological traits compared with the full feature set. Among the evaluated approaches, MLPNN (Fig. 1a), RBFNN (Fig. 1b), and GPR (Fig. 1c) demonstrate more stable and closely aligned predictions, whereas RF (Fig. 1d), DT (Fig. 1e), and MLR (Fig. 1f) exhibit slightly greater variability. Overall, biochemical and physiological traits alone provide sufficient predictive information, reducing the need for extensive morphological or nutrient profiling.

Fig. 1.

Regression between measured and predicted soluble carbohydrate content using ML and MLR models. Rows correspond to (a) MLPNN, (b) RBFNN, (c) GPR, (d) RF, (e) DT, and (f) MLR. The left and right columns represent models trained with the full feature set and with biochemical and physiological traits, respectively

When macronutrients were used alone, predictive performance declined markedly. GPR remained moderately effective (R² = 0.9564; RMSE = 0.0034; MAPE = 4.62), whereas MLR performed poorly (R² = 0.4957; RMSE = 0.0229; MAPE = 40.94), confirming that macronutrient data alone are insufficient for accurate carbohydrate prediction.

Advanced ML models, particularly MLPNN and GPR, consistently outperform traditional regression by capturing complex nonlinear relationships. Maximum accuracy was achieved using the full feature set; however, biochemical and physiological traits alone offer nearly equivalent predictive power, providing a practical, efficient, and cost-effective approach for real-world carbohydrate estimation.

Physiological basis of enhanced soluble carbohydrate content under organic fertilization

Enhanced soluble carbohydrate accumulation under organic fertilization, particularly vermicompost, is strongly associated with interconnected physiological and biochemical mechanisms in T. ammi. Vermicompost provides readily available N, P, K, and trace elements, which may promote chlorophyll synthesis and light capture. Increased chlorophyll a and b levels are linked to higher ATP and NADPH production, supporting carbohydrate biosynthesis.

Morphological improvements-including greater plant height, stem diameter, and branch number-enhance light interception and assimilate transport, facilitating soluble sugar accumulation. Concurrently, elevated proline stabilizes enzymes under stress, while phenolics protect photosynthetic machinery from oxidative damage, supporting carbohydrate production under suboptimal conditions. Adequate nitrogen enhances photosynthetic enzyme activity, phosphorus contributes to ATP generation, and potassium maintains osmotic balance and phloem transport, collectively optimizing source–sink dynamics and carbohydrate translocation.

In summary, organic fertilization enhances carbohydrate content through improved photosynthetic efficiency, biochemical stress protection, and nutrient-driven assimilate allocation. These mechanisms provide a rationale for the predictive accuracy of machine learning models. Biochemical and physiological traits emerge as reliable, cost-effective predictors of soluble carbohydrate content, supporting efficient quality assessment.

Additionally, the findings offer actionable insights for precision agriculture and phytopharmaceutical applications, enabling informed management decisions. Limitations include the controlled fertilization conditions, which may not reflect full environmental variability, and the focus on a single species and specific traits. Model performance depends on the quality and quantity of input data, highlighting the need for careful data collection and preprocessing. Further validation across diverse medicinal plants, metabolites, and environmental contexts is recommended.

Summary and conclusions

This study evaluated the potential of multiple machine learning models, including MLPNN, GPR, RBFNN, RF, DT, and traditional MLR, to estimate soluble carbohydrate content in T. ammi under organic (vermicompost), chemical fertilization, and salicylic acid treatments. Advanced models, particularly MLPNN and GPR, demonstrated high predictive accuracy (n = 45) and effectively captured complex associations among measured traits. The highest predictive performance was achieved using the full set of features, including morphological, biochemical, physiological, and macronutrient traits. Models based solely on biochemical and physiological traits showed nearly equivalent accuracy, suggesting that these traits can serve as reliable, cost-effective indicators strongly associated with soluble carbohydrate content. In contrast, models relying only on macronutrient or morphological traits were less accurate, highlighting the benefit of integrating multiple trait categories. Organic fertilization and salicylic acid treatments influenced carbohydrate accumulation, emphasizing the importance of management practices in shaping plant biochemical responses. These observations align with previous studies applying machine learning in plant systems and underscore the potential of combining advanced modeling with targeted trait measurements for rapid, non-destructive assessment of key quality parameters. Limitations include the focus on a single growth stage and a relatively small dataset. Future research should validate models across larger datasets, multiple growth stages, diverse metabolites, and varying environmental conditions, and may employ time-series modeling to explore temporal dynamics of carbohydrate accumulation. Such efforts will enhance the applicability of machine learning for optimizing cultivation strategies, fertilization regimes, and precision agriculture practices.

Abbreviations

MLR

Multiple Linear Regression

RBF

Radial Basis Function

MLP

Multilayer Perceptron

DT

Decision Tree

RF

Random Forest

GPR

Gaussian Process Regression

Authors’ contributions

Sh. Fathi: Writing – original draft, Visualization, Investigation, Data curation. S. Heidari: Formal analysis, Methodology, Software, original draft, Editing. Sh. Najafian: Methodology, Investigation and Editing.

Funding

This research received no external funding.

Data availability

The data used in this study is openly available, and the data used is available upon request from the corresponding authors SH.F.

Declarations

Ethics approval and consent to participate

The presented manuscript represents the honest research work of the authors.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.