Active learning for the accelerated discovery of complex concentrated NiCoCr alloys in additive manufacturing

Abstract

Many conventional alloys are poorly suited to laser-based additive manufacturing (also known as 3D printing) because of complex laser-material interactions and thermal histories. Identifying new printable alloys out of vast compositional spaces is a daunting task, particularly for complex concentrated alloys of three or more elements. Here, we integrate active learning with additive manufacturing to accelerate the discovery of NiCoCr complex concentrated alloys via a high-throughput highway. We identify six new printable alloys that are up to ~40% harder than the popular equiatomic NiCoCr at room temperature. Among them, two new alloys exhibit complementary advantages: Ni₁₂Co₆₂Cr₂₆ retains ~50% higher hardness than NiCoCr at 600 °C, whereas Ni₃₆Co₁₄Cr₅₀ reduces oxidation mass gain by 85% at 1000 °C compared with conventional superalloys. Our study demonstrates that optimum performance can reside far from equiatomic proportions and can be uncovered with substantially fewer experiments when exploration is guided by application-specific objectives. The modular workflow provides a general route to rapidly discover new printable, alloys for targeted demanding service conditions.

Introduction

Laser-based additive manufacturing (AM) enables geometries unattainable by conventional processing, making it essential for aerospace applications that demand both extreme design complexity and high-performance structural materials^1–3. While AM provides the hardware flexibility to realize such intricate designs, the available materials portfolio remains dominated by legacy alloy systems that were developed empirically and guided largely by engineering intuition for casting and directional solidification. Legacy alloys, including industry standards such as Inconel 718 (patented in 1962)⁴ and CM247LC (developed in 1978)⁵, were engineered for cooling rates orders of magnitude lower than the 10³-10⁸ Ks^-1 experienced during laser-based processing⁶. Consequently, traditional superalloys frequently exhibit laser processing-induced metallurgical defects, including solidification cracking, hot tearing, and liquation cracking, as the material is unable to accommodate the rapid thermal contraction^6,7. These limitations motivate alloy design strategies tailored to laser-based additive manufacturing.

To date, discovery efforts have branched into various strategies. Recent alloy design strategies have pursued targeted compositional modification of legacy superalloys to accommodate the extreme thermal gradients of AM, including strategies aimed at narrowing solidification intervals and improving liquid feeding during terminal solidification^8,9. However, such approaches remain constrained by the underlying chemistries and phase architectures of legacy systems, often offering incremental improvements in printability without fully exploiting the broader composition-process design space enabled by additive manufacturing. In parallel, growing attention has shifted toward the vast compositional landscapes of medium-entropy alloys (MEAs) and high-entropy alloys (HEAs), a class of materials that has exhibited exceptional performance in extreme environments^10–12. Within this expanding field, the Cantor-derived¹³ NiCoCr medium-entropy system has emerged as a standout candidate, providing the highest room-temperature strength among the equiatomic derivatives¹⁴ while maintaining remarkable fracture toughness and ductility at cryogenic temperatures¹⁵. Recent efforts to further optimize this system through minor alloying were performed by Smith et al., who demonstrated that systematic compositional tuning of a NiCoCr base alloy, GRX-810, combined with additive manufacturing, enabled a two-fold increase in tensile strength ( ~ 129 MPa at 1093 °C) alongside markedly improved creep resistance and oxidation performance compared to traditional polycrystalline superalloys¹⁶. Yet, even in such advanced alloy systems, the underlying matrix composition remains tethered to the equiatomic regime, treating equiatomic proportions as a rigid baseline for modification. However, first-principles calculations indicate that even within the NiCoCr ternary system, modest deviations from equiatomic composition can significantly alter phase stability and stacking fault energy¹⁷, highlighting the strong compositional sensitivity of the underlying deformation mechanisms. These findings suggest that extending exploration into the non-equimolar design space provides the potential to uncover superior property combinations that currently remain effectively invisible to conventional search strategies.

While physics-based screening tools such as density functional theory (DFT) and calculation of phase diagrams (CALPHAD) provide valuable thermodynamic insights for alloy design, they face severe scalability limits¹⁸. The high dimensional space is too vast for exhaustive experimental verification¹⁹ and remains computationally expensive for high-fidelity modeling of one system^17,20, let alone thousands. To circumvent these barriers, data-driven machine learning (ML) has emerged as a powerful accelerator for materials discovery^21–23. However, conventional ‘Big Data’ approaches are poorly suited to AM alloy design, where tightly coupled composition-process-structure interactions and sparse, non-transferable datasets limit models trained on isolated composition or process-property relationships. This mismatch is evident in both process optimization, where robust neural networks may require more than 5.5 × 10⁵ synthetic simulations²⁴, and property prediction, where models trained on ~240 as-cast alloys^25,26 cannot be reliably extrapolated to the non-equilibrium thermal history of AM. This mismatch is further underscored by evidence that even in data-rich materials benchmarks, up to 95% of entries are statistically redundant for property prediction²⁷. Active learning (AL) offers an alternative to conventional ML by coupling uncertainty-aware surrogate models with iterative experimental selection, enabling efficient navigation of large design spaces while minimizing experimental cost²⁸. For example, this high efficiency was demonstrated by developing an arc melted FeNiCoAlTa multi-principal element alloy that achieves a ~ 1.8 GPa yield strength and ~25% uniform elongation within four experimental iterations¹⁰. However, adapting this paradigm for the design and additive manufacturing of new alloys presents a unique challenge, as the discovery process must not only identify potentially high-performing alloys but also constrain experimental validation to physical reality, ensuring that the exploration of the design space is grounded by the limits of printability.

In this work, we introduce ALPHA-AM, an Active Learning framework for Process-optimized High-potential Alloys in Additive Manufacturing, which integrates domain knowledge, high-throughput experimentation, and manufacturability-aware optimization to accelerate alloy discovery for AM. The workflow consists of three interconnected segments (Fig. 1). (I) Data-driven alloy design (Fig. 1a): an active learning loop couples surrogate Gaussian process models with a constraint-aware acquisition function to propose candidate compositions that balance predicted performance with printability. Experimental validation feeds directly back into the models, enabling iterative refinement of the composition-property landscape. (II) Stability-based process optimization (Fig. 1b): to ensure manufacturability, a dedicated optimization loop samples a multidimensional processing space using single-track experiments and identifies robust parameter windows that yield geometrically stable, fully dense deposits. These optimized conditions anchor all subsequent alloy fabrication, ensuring that observed microstructural and mechanical trends arise from composition rather than processing variability. (III) Accelerated additive manufacturing (Fig. 1c): down-selected alloy candidates are mapped onto a universal substrate geometry and fabricated via high-throughput laser directed energy deposition, enabling rapid, consistent synthesis and characterization across iterations.

Fig. 1. The ALPHA-AM Workflow.

a Data-driven alloy design workflow integrating CALPHAD-guided feature construction, high-throughput experimentation, and surrogate modeling. Active learning is employed to efficiently navigate the alloy design space using a tunable, constraint-aware acquisition function to select candidate compositions for experimental validation. b Stability-based process optimization using Latin hypercube sampling, single-track printing, and three-dimensional geometric analysis to identify robust, repeatable processing windows. c Accelerated additive manufacturing of down-selected compositions using high-throughput laser directed energy deposition, enabling fabrication of samples suitable for microstructural, mechanical, and environmental characterization.

We demonstrated the efficacy of ALPHA-AM by applying it to the well-known NiCoCr MEA system, converging on alloys that exhibit improved mechanical and environmental performance. In particular, we identify two standout alloys: Co-rich Ni₁₂Co₆₂Cr₂₆ demonstrates 46.2% greater hardness than the equiatomic baseline at 600 °C, while the eutectic Ni₃₆Co₁₄Cr₅₀ achieves a 12-fold reduction in oxidation mass gain at 1000 °C compared to reference superalloys. Our work further demonstrates that enhanced properties exist outside conventional equiatomic proportions and establishes a modular platform for the rapid, autonomous discovery of manufacturable alloys for extreme environments.

Results

Data-driven new alloy design

The ALPHA-AM framework was iteratively applied to the NiCoCr ternary alloy system with the objective of identifying alloys that combine high room-temperature hardness, printability, and potential for elevated-temperature applications. Here, printability was defined conservatively as the ability to achieve crack-free alloys under directed energy deposition, where any observable cracking was treated as an alloy failure within the screening framework. Within the active learning loop, room-temperature hardness was targeted as an initial proxy property, enabling efficient screening of compositionally driven strengthening mechanisms. Two acquisition strategies were considered: a low-risk policy that prioritized manufacturability and minimized hot cracking, and a high-risk policy that tolerated greater crack susceptibility to pursue higher hardness. The active learning loop, shown in Fig. 1a, provided the basis for navigating this design space and served as a first-stage, mechanism-informed down-selection of promising alloys, where room-temperature hardness was used to screen strengthening behavior prior to higher-fidelity validation through high-temperature mechanical and environmental testing.

To guide the active learning loop, we employed physics-informed surrogate models that jointly predict hardness and probabilistic crack susceptibility (P_safe), enabling a risk-aware selection strategy that ranks candidates by expected performance weighted against manufacturing uncertainty. Leveraging domain knowledge guided by equilibrium CALPHAD (Figs. S1–S2), we efficiently captured the initial compositional landscape using 27 experimentally validated alloys (Fig. S3). When parameterized by the 21 most informative descriptors pertaining to thermodynamics, phase constitution, and thermophysical properties (Table S1; Figs. S4–S8), this initial dataset yielded surrogate models with exceptional predictive fidelity. The resulting hardness model yielded a R² of 0.95 (RMSE = 52 HV) under leave-one-out cross-validation (Table S2; Fig. S9), which is interpreted as a measure of local surrogate fidelity within the explored design space. Under adaptive sampling, such metrics may be influenced by selection bias and therefore do not necessarily reflect global generalization performance. The crack-susceptibility model incorporated both experimentally derived and physics-informed descriptors, including phase constitution, thermophysical features, and Kou’s solidification cracking susceptibility index, and demonstrated robust discrimination with an AUC of 0.97 (Table S3; Fig. S10).

To navigate the trade-off between mechanical performance and manufacturability, we employed Constrained Expected Improvement (CEI) as the optimal acquisition policy, with alternative strategies evaluated in Tables S4–S5 and Figs. S11–S12. Rather than relying on simple mean predictions, we exploit the probabilistic output of the surrogate models to identify high-value compositional outliers, lying on the statistical tails of the performance landscape. Expected improvement is evaluated relative to the best experimentally observed hardness (f_best) using the predicted mean $\mu$(x) and uncertainty $\sigma$(x), where the cumulative distribution function ($\Phi$) captures the likelihood of surpassing current performance and the probability density function ($\varphi$) emphasizes candidates in underexplored regions. This improvement is further weighted by the probability of remaining crack-free, P_safe(x), biasing selection toward compositions that deliver meaningful performance gains while remaining experimentally viable. A schematic illustration of this strategy is provided in Fig. S13.

Across six ALPHA-AM iterations, CEI-directed exploration was governed by predefined probabilistic feasibility thresholds that act as risk-policy parameters within a cost-sensitive decision framework. Specifically, higher probability cutoffs bias selection toward high-specificity (low false-positive) regions to minimize experimental failure, while lower thresholds permit exploration near the feasibility boundary. Feasible probability thresholds for crack-free candidate selection lie between 0.5 and 1.0, with values approaching 0.5 admitting crack-prone candidates, whereas stricter thresholds (e.g., 0.95) can over-constrain exploration; thus, 0.85 and 0.75 were selected as balanced operating points along this trade-off. The transition between these thresholds was further informed by monitoring uncertainty reduction during the active learning campaign, where relaxation of the constraint was initiated once information gain within the initial low-risk regime diminished (discussed further below). For further information on decision boundary thresholds, refer to Supplementary section 1.5. Under this framework, a low-risk strategy (P_safe > 0.85) directed exploration away from the equiatomic baseline toward Ni-rich compositions between 26 and 37 wt.% Ni, as shown in Fig. 2a. Under a higher risk strategy (P_safe > 0.75), CEI-guided exploration shifted toward Co-rich compositions between 43 and 62 wt.% Co, where alloys with improved hardness were identified. Each alloy was chosen from a quantitative trade-off between hardness improvement and manufacturability as encoded in the CEI acquisition function shown in Fig. 2b–c. For each generation of the active learning loop, a Pareto frontier evolved from the expected improvement-P_safe trade-off. In the conservative, low-risk case, alloys were identified with moderate hardness improvement but high reproducibility and low cracking probability. In contrast, relaxing the safety threshold to P_safe > 0.75 enabled a high-risk, high-reward pathway, whereby the CEI values increased an order of magnitude (0.4-7) identifying alloys with greater predicted hardness but increased cracking susceptibility.

Fig. 2. Active learning of complex-concentrated ternary alloys.

a Compositional evolution of constrained expected improvement (CEI) selected alloys across six active-learning generations, showing the shift from Ni-rich to Co-rich regions as the P_safe constraint is relaxed from 0.85 to 0.75. b, c CEI acquisition landscapes mapping expected improvement against P_safe for all generated candidates. Color indicates CEI score, and Pareto frontiers highlight the trade-off between predicted hardness and manufacturability. d Predicted versus experimental hardness for CEI-selected alloys, demonstrating high surrogate fidelity (R² = 0.95, RMSE = 52 HV). e Printability evolution relative to the hot-cracking boundary: Generations 1-4 remain fully printable; Generation 5 crosses into the crack-prone regime; incorporation of the failure data enables Generation 6 to redirect into a printable, improved hardness region, establishing the learned composition-process limit governing manufacturability.

For each acquisition round, the top CEI-scoring candidate was fabricated, characterized, and then mechanically tested for hardness. Subsequently, this data was reintegrated into the AL loop, reducing predictive uncertainty in the newly explored regions and guiding the acquisition policy toward the next generation of alloy acquisition. Figure 2d–e highlights ALPHA-AM’s adaptive refinement across generations, capturing both performance gains and the concurrent collapse of predictive uncertainty. Under the low-risk policy (P_safe > 0.85), Generations 1-3 produced fully printable alloys with steadily decreasing predictive uncertainty. The GPR model’s initial uncertainty of 53.0 HV fell by 5.6% after incorporating Generation 2 data and by an additional 0.5% after Generation 3, indicating that the model had begun to saturate the local hardness landscape. Such behavior is expected once a locally smooth property region has been adequately sampled and further data provide diminishing information gain^29,30. Within this printable domain, Generation 3 achieved a 22.5% hardness improvement over equiatomic NiCoCr (231 HV). Relaxing the safety threshold (P_safe > 0.75) enabled exploration of a previously unsampled Co-rich regime, which produced higher-reward candidates but also increased initial uncertainty to 102.94 HV, reflecting the model’s lack of prior knowledge. As new data were collected, uncertainty collapsed rapidly by 18.4% in Generation 5 and 29.3% in Generation 6, demonstrating efficient information gain in this compositional frontier. Although Generation 5 crossed the experimental hot-cracking boundary, incorporation of this failure data prompted the model to recalibrate its printability landscape and autonomously redirect toward a safe region. The resulting Generation 6 alloy remained printable and delivered the highest hardness improvement of the campaign (39.4%). This initial alloy screening provided six unique alloy compositions that laid a foundation for more detailed high-temperature mechanical testing.

Stability-based process optimization

Following CEI-guided alloy identification, a dedicated stability-based process optimization phase was implemented to define a robust processing window that ensures stable, repeatable fabrication of dense, defect-free 3D builds for subsequent analysis. The optimization campaign spanned a process parameter space consisting of laser power (P), scanning speed (v), and combined multi-hopper powder feed rate (RPM). Using Latin Hypercube Sampling (LHS), 90 unique process combinations were generated to efficiently and uniformly sample this multidimensional space (Fig. S14a), avoiding bias and clustering while minimizing the number of required experiments³¹. The randomized combinations were fabricated as 10 mm single tracks (Fig. S14b) for analysis.

Building on our previous work utilizing 2D cross-sectional melt pool analysis³², transient melt-pool instabilities are captured through 3D digital reconstruction, with each single track fully reconstructed using 3D optical scanning (Fig. S14c). This allowed extraction of key geometric descriptors such as track width, height, surface roughness, and their statistical variations (mean, standard deviation, minimum, maximum). Representative digital reconstructions of two extrema are shown in Fig. 3a: the upper panel corresponds to a stable, low-variation track with consistent melt-pool morphology, whereas the lower panel shows a highly unstable, defect-prone track exhibiting pronounced height and width fluctuations. From this dataset, a combined 3D stability landscape (Fig. 3b) was derived, where valleys in the width and height variation planes correspond to processing minima defining optimal stability.

Fig. 3. Single-track stability-based process optimization in L-DED.

a 3D digital reconstruction of single-track deposits used to define track stability. The upper panels show, defect-free track with minimal geometric variation, while the lower panels depict a defect-prone deposit with pronounced geometric fluctuations. b Combined 3D stability landscape of 90 Latin Hypercube sampled process conditions, showing width (orange) and height (blue) variation surfaces. Valleys in both surfaces represent process-stability minima, conditions that produce highly repeatable track geometries. c, d Two-dimensional process maps of normalized laser power versus scan speed at a fixed powder feed rate (0.5 RPM), showing stable (low σ) and unstable (high σ) processing regimes for width (c) and height (d) variation. Experimental data points are marked as black circles. Red contours denote processing conditions yielding insufficient dilution ( < 20%) as determined via YOLO-v8 melt-pool segmentation, whereas black contours outline the stability boundaries.

To further visualize the process window, two-dimensional process maps of normalized power and scanning speed at a constant powder feed rate of 0.5 RPM are highlighted in Fig. 3c–d. Stable processing regions were identified by both low geometric variance (σ < 0.06 mm) and optimal dilution ratios between 20 and 50% of melt pool depth³³. To determine dilution boundaries, single tracks were cross-sectioned, polished, and analyzed using a YOLO v8 convolutional neural network (CNN) to extract quantitative melt-pool geometries (Fig. S14d). Red contours in Fig. 3c–d denote process combinations yielding insufficient dilution, while black contours outline the stability boundaries. Extended process optimization maps are provided in Fig. S15.

Through this enhanced stability-based optimization framework, the process space was systematically reduced to a stable, fully dense regime suitable for the AM of novel NiCoCr alloys. These optimized conditions formed the foundation for subsequent CEI-guided alloy experimental validation and high-throughput testing. The optimized window, derived from stability criteria is governed primarily by melt pool process physics and applied within a constrained Ni-Co-Cr composition space with similar thermophysical behavior, serving as a transferable baseline for isolating compositional effects rather than composition-specific process optima. Further details on the stability-based process optimization are found in Supplementary Note A: Section 1.6.

New ternary alloys

Each of the highest-ranking CEI candidate alloys from Generations 1-6 was fabricated under the optimized processing window defined by our stability-based process optimization framework. All alloys that remained free of hot cracking achieved relative densities approaching 0.99, as shown in Fig. S16. Subsequently, each of these candidates was subjected to detailed compositional, phase, and microstructural characterization. While compositions were tuned in-situ to achieve the highest compositional accuracy possible relative to the predicted values, inherent elemental segregation caused local inhomogeneity during solidification³⁴. The parity between targeted and actual composition for each element is shown in Fig. 4a. Compositional deviations remained between 1-3% within single-phase regions; typical for powder‑based DED processing^35–37. In multiphase alloys, Ni and Cr exhibited the largest phase-to-phase compositional differences between 8-10 wt.%, attributed to microsegregation during non-equilibrium solidification. Scheil-type solidification simulations for the NiCoCr system (Fig. S5) predict that in primary FCC alloys, Ni remains closer to the average FCC matrix composition, whereas alloys with enhanced Cr content enrich the last-solidifying interdendritic liquid. The resulting Ni/Cr partitioning between the interdendritic and eutectic regions (Fig. S5) are consistent with classical microsegregation theory, where solutes with k ≠ 1 redistribute between dendrite cores and interdendritic liquid during solidification [50].

Fig. 4. Active learning guided microstructural evolution.

a Targeted versus measured compositions for Ni, Co, and Cr, across all experimentally validated alloys, with inherent phase segregation of Ni and Cr highlighted. b X-ray diffraction patterns illustrating the active learning guided phase evolution, with corresponding SEM micrographs c–h. New information provided to the active learning model evolves the phase distribution and microstructure from c single-phase FCC matrix (Generation 1) to d–e eutectic FCC + BCC structures (Generation 2-3) under high P_safe acquisition policies. Under low P_safe acquisition policies the matrix is reset to a single-phase FCC matrix (Generation 4) f, followed by g primary-BCC/secondary-FCC structures in Generation 5 and finally h phase-destabilized FCC/HCP mixtures (Generation 6).

Across successive generations, the ALPHA-AM framework induced a systematic phase evolution, where the pursuit of higher hardness and high-temperature performance inherently drove microstructural refinement. Convergence between property optimization and structural modification reflects the surrogate model’s ability to capture and exploit processing-structure-property linkages, essential for materials-by-design strategies informed by machine learning^38,39. Each generation’s phase evolution is shown in Fig. 4b as determined by XRD, alongside the corresponding SEM microstructures in Fig. 4c–g. Under the low-risk strategy (P_safe > 0.85), alloys from Generations 1-3 progressively transitioned from a single-phase FCC solid solution toward more complex architectures: Generation 1 (panel c) exhibited a homogeneous cellular FCC morphology typical of solute-trapped solidification, while Generation 2 (panel d) revealed mixed cellular and terminal eutectic structures marked by the emergence of BCC peaks in Fig. 4b. By Generation 3 (panel e), the alloy fully evolved into a dual-phase FCC + BCC eutectic structure with pronounced lamellar banding. Upon relaxing the CEI safe cracking criterion (P_safe > 0.75), Generation 4 (panel f) reset the matrix to a fully FCC structure. Subsequent generations actively destabilized this phase: Generation 5 (panel g) was pushed beyond the eutectic regime into a primary-BCC, secondary-FCC architecture, where Cr-rich BCC regions with hardness values 2.6–3.0 GPa higher than the adjacent Ni-rich FCC ligaments constrained local deformation, forcing strain to accumulate along the thin FCC channels during cyclic reheating. Together with a small amount of brittle σ-phase decorated interfaces, highly focused stress concentrations manifested as sub-micron ( < 1 µm) crack tips within the FCC ligaments^40,41. These cracks subsequently propagated along the BCC-FCC interfaces under continued thermal cycling during deposition. See Supplementary Note B: Mechanical behavior, section 2.2, Figs. S17–S18 for more information. Following the cracking observed in Generation 5, this failure data was reintroduced into the ALPHA-AM loop, allowing the surrogate models to update the printability boundary and redirect exploration. Generation 6 (panel h) resulted in a predominantly FCC matrix containing finely dispersed HCP laths.

The strong microstructural sensitivity to relatively small compositional changes arise from the proximity of the NiCoCr system to multiple competing phase fields under rapid solidification. CALPHAD equilibrium calculations (Fig. S1) show that modest shifts in Ni, Co, and Cr content within a compositionally complex regime move alloys between FCC, FCC + BCC eutectic, σ, and HCP stability regimes, while Scheil simulations with solute-trapping corrections (Fig. S5) indicate that non-equilibrium solidification further amplifies these transitions through composition-dependent partitioning. Under L-DED cooling rates (10³–10⁴ Ks^-1), incremental composition changes produce qualitatively different phase architectures⁴². In Co-rich compositions, reduced stacking fault energy stabilizes metastable HCP lamellae within an FCC matrix⁴³. These HCP lamellae strengthen the matrix through interfacial hardening and slip-transfer resistance⁴³, explaining the improved hardness and marking a successful model-guided correction after the Generation 5 failure.

Unlocking new ternary alloy with improved mechanical performance

The ALPHA‑AM framework enabled systematic down‑selection from a vast compositional space to a focused set of six high‑performing NiCoCr‑based alloys suitable for further experimental evaluation as shown in Fig. 5. To validate the alloys identified through CEI‑guided acquisition under elevated temperature conditions where NiCoCr alloys have shown promising mechanical performance^16,20,44 two key experimental evaluations were conducted: (I) high‑temperature hardness testing up to 600 °C, and (II) oxidation testing up to 1000 °C. These complementary tests served to assess both mechanical and environmental stability.

Fig. 5. Mechanical and environmental evaluation of ALPHA-AM–designed NiCoCr alloys.

a Thermal degradation rate (RT-600 °C) versus room temperature hardness of ALPHA-AM alloys benchmarked against various superalloys, HEAs, and steels. b Specific mass change curves illustrating oxidation kinetics at 800 °C and 1000 °C versus Ni/Co superalloys and MEA/HEAs. c multi-criteria radar assessment comparing key metrics (hardness, retention, oxidation resistance, and printability) for Generation 3 (Ni₃₆Co₁₄Cr₅₀, blue) and Generation 6 (Ni₁₂Co₆₂Cr₂₆, red). d Ternary composition map showing the evolution of the crack probability landscape, defining the critical crack boundary that governs manufacturability.

High temperature hardness testing up to 600 °C represents a mechanistically consistent extension of the initial screening metric, as deformation in solid-solution strengthened alloys over moderate homologous temperatures remains governed by thermally activated dislocation motion described by classical power-law relationships^45,46. Under these conditions, room-temperature hardness reflects the intrinsic resistance to dislocation motion through its proportionality to flow stress⁴⁷, which is preserved under thermal activation and governs the relative ranking of alloys at elevated temperature, making it an efficient screening metric in early‑stage alloy development⁴⁸. Figure 5a compares the hardness retention profiles of ALPHA‑AM alloys with literature‑reported FCC MEAs/HEAs^49–51, austenitic and pearlitic steels^52–54, and solid‑solution strengthened superalloys^55–57. At room temperature, ALPHA‑AM alloys exhibit substantially higher room-temperature hardness than representative commercial benchmarks, including Inconel 625 (220 ± 30 HV), a corrosion and oxidation-resistant solid-solution strengthened Ni-based superalloy⁵⁷, and Haynes 25 (251 HV), a Co-based alloy widely used in aerospace combustion environments⁵⁵. Against these reference systems, ALPHA-AM alloys achieved room-temperature hardness improvements of up to 19.4%. This improvement reflects the deliberate exploration of non-equiatomic NiCoCr compositions that access competing FCC, FCC + BCC, and metastable phase fields under rapid solidification, producing composition-dependent phase constitution and elemental partitioning. With increasing temperature, all alloys displayed expected thermal softening indicated by the thermal degradation rate in Fig. 5a; however, the degree of strength retention varied considerably across CEI generations. The highest-performing composition, Generation 6 (Ni₁₂Co₆₂Cr₂₆), sustained exceptional hardness at elevated temperature, outperforming equiatomic NiCoCr by 46.2% at 600 °C⁵⁰, while still maintaining a 4.4% advantage over Inconel 625. The progressive increase in elevated-temperature hardness across generations reflects the systematic compositional refinement achieved by ALPHA-AM, which increasingly favored chemistries capable of retaining higher hardness.

Because compositional tuning in Ni/Co alloys inherently alters the identity, protectiveness, and adherence of oxide scales, we evaluated oxidation behavior for the down selected NiCoCr alloys at 800 °C and 1000 °C to assess any trade-offs associated between the enhanced mechanical performance and environmental alloy stability. Figure 5b compares the absolute specific mass change of the ALPHA‑AM‑designed alloys with representative MEA/HEAs^58–65, Ni^66–75 and, Co-superalloys^76,77. At 800 °C, all ALPHA-AM alloys exhibited uniformly low mass gains of 0.10–0.96 mg cm⁻², consistent with the formation of continuous, adherent Cr₂O₃ scales that provide long term oxidation resistance. Compared to the state of the art, Generation 3, containing a FCC/BCC eutectic microstructure, outperformed equiatomic NiCoCr by 0.29 mg cm⁻²⁵⁸, a 25.1% improvement. When benchmarked against popular γ′ strengthened superalloys such as Inconel 718 (K4169), ALPHA-AM derived alloys boasted a maximum improvement of 0.27 mg cm⁻² over 100 h⁷⁴. At 1000 °C, of the alloys derived from the high P_safe acquisition policy, Generation 3 maintained the ability to form a fully stable Cr₂O₃‑based scale throughout exposure (Figs. S19–S20), with a 100-h specific mass change of 0.20 mg cm⁻², while Generations 1 and 2 exhibited spallation. Similarly, alloys from the low P_safe acquisition pathway experienced oxide spallation. Specifically, low P_safe alloys exhibited a specific mass change of −1.97 mg cm⁻², due to the formation of brittle (Ni,Co)Cr₂O₄ spinel oxides, known to degrade oxidation stability^58,78. Figures S21–S22 illustrate the morphological contrast between stable Cr₂O₃ scales and spalled spinel layers, providing mechanistic insight into the degradation pathways. In comparison to solid solution strengthened Inconel 625⁷⁹ oxidized at 1000 °C, our best performing alloy (Generation 3), showed a 1.10 mg cm⁻² lower specific mass change, a 84.6% reduction. Against Inconel 738, a precipitate strengthened superalloys known for its corrosion and oxidation resistance⁸⁰, we saw a 0.048 mg cm⁻² improvement (a 19% reduction). Collectively, based on these results, we down selected Generation 3 (Ni₃₆Co₁₄Cr₅₀) as the optimal ALPHA-AM alloy for high temperature oxidation. It should be noted that these values provide a maxima for NiCoCr ternary alloy system, as any temperatures greater than 1050 °C and in the presence of H₂O can destabilize Cr₂O₃ scales^81,82.

Through the ALPHA-AM workflow, the initially vast NiCoCr compositional space was down-selected to six high-performing alloys. From this set, Generation 3 and Generation 6 emerged as optimal compositions for two distinct high-temperature regimes; Generation 3 exhibiting improved oxidation resistance with modest high-temperature hardness increases, and Generation 6 showing enhanced high-temperature hardness retention. These alloys, along with their corresponding generation, composition, room-temperature hardness, high-temperature hardness retention, oxidation resistance, and cracking probability, are highlighted in the radar plot (Fig. 5c). Although both alloys appear to occupy a narrow region of a simple ternary phase space, their divergent strengths illustrate the value of targeted exploration through ALPHA-AM: small compositional shifts can produce distinct application-specific responses. This selective refinement underscores the broader utility of ALPHA-AM, demonstrating that the framework can isolate alloy candidates across diverse alloy systems and application criteria.

Beyond identifying promising compositions, the ALPHA-AM framework continually refined its understanding of manufacturability as new data were collected. Each experimental iteration including successful and failed builds updated the GPC model, enabling the model to revise its beliefs about solidification-cracking susceptibility across the NiCoCr space. As a result, the predicted cracking landscape evolved over the course of exploration, as shown in Fig. 5d. The critical crack boundary, beyond which hot cracking will occur, shifted toward greater tolerance for Ni-rich compositions, while becoming more restrictive in the Co-rich region, reflecting the model’s updated beliefs from Generation 1-6. Through the alloy discovery campaign, the printable domain is refined, ensuring that future searches are guided away from unmanufacturable chemistries and toward regions with genuine application potential.

Discussion

In modern alloy design for additive manufacturing, navigating vast compositional spaces while accounting for real-world processing constraints remains a central challenge. The difficulty lies in simultaneously achieving improved mechanical response, ensuring acceptable manufacturability, and maintaining efficiency within the confines of resource-intensive experimental workflows. To address these issues, the ALPHA-AM framework presents a unified strategy that integrates physics-informed materials representation, data-efficient surrogate modeling, and process-aware AL to meet four critical objectives: (1) accelerate alloy discovery by efficiently down-selecting from an expansive compositional space to a focused subset of alloys aligning a target property of interest, with genuine application potential. (2) Ground the exploration process in physical reality by embedding real-world manufacturability constraints, ensuring that experimental validation is not wasted pursuing impractical or unprintable alloy chemistries. (3) Mitigate process-driven defects by coupling alloy selection with geometric stability-based process optimization, linking mechanical property trends to compositional effects rather than confounding process variability. (4) Enable closed-loop, iterative refinement of composition-process-property linkages through successive experimental validation. With these features, ALPHA-AM offers a modular and generalizable pathway for designing improved, manufacturable alloys, bridging the gap between computational alloy discovery and real-world additive manufacturing deployment.

The effectiveness of ALPHA-AM arises from the deliberate coupling of physics-informed materials representation with data-efficient surrogate learning, enabling high predictive fidelity despite operating in an experimentally constrained regime. By constructing the initial design space using CALPHAD-guided thermodynamic trends and mechanistic materials descriptors, the framework constructed distilled the NiCoCr system into a compact physics-informed representation. Using 21 features across 27 unique alloys, the resulting surrogate achieved 95.1% predictive accuracy for hardness. Within the active-learning loop, each experimental iteration not only provided improved alloys but contributed to model refinement: under the low-risk acquisition policy, predictive uncertainty decreased by upwards of 5.6%, while relaxing the manufacturability constraint and exploring a previously unsampled Co-rich domain, decreased uncertainty by a maximum of 29.3%. Collectively, the uncertainty collapse and rapid materials refinement in unexplored domains demonstrate that ALPHA-AM efficiently allocates experimental effort toward the most informative regions of the composition-process landscape, enabling reliable surrogate learning at a fraction of the data typically required in machine-learning-driven alloy design^10,24,83.

The constrained active learning within the ALPHA-AM framework successfully down-selected from the large ternary NiCoCr compositional space, using room-temperature hardness as an initial screening method to iteratively identify six new high performing alloys. Of these six alloys, two showed further improvements under more rigorous testing conditions, culminating in the selection of Generation 6 (Ni₁₂Co₆₂Cr₂₆), optimized for high strength retention at elevated temperatures, and Generation 3 (Ni₃₆Co₁₄Cr₅₀), optimized for environmental stability. Mechanically, the hot hardness optimized Generation 6 alloy, achieved up to a 19.4% increase in room-temperature hardness over commercial benchmarks, while maintaining a 46.2% advantage in hardness retention at 600 °C compared to the popular equiatomic NiCoCr. Simultaneously, the framework delivered improved environmental resilience, with the stability-optimized Generation 3 alloy exhibiting 84.6% lower specific mass change than Inconel 625 and a 19% reduction compared to Inconel 738 at 1000 °C. All the alloys evaluated within this study were fabricated within a stability-derived process window, enabling samples free of major processing defects, indicating that the selected parameter space provides a robust baseline for comparative assessment across compositions. It should be noted that further improvements in process quality and performance could be achieved through composition-specific process optimization, where the stability-based process-mapping framework can be re-applied to each down selected alloy to refine deposition conditions through targeted, high-resolution parameter tuning. Without active learning strategies, these alloys would be difficult to pinpoint under traditional one-at-a-time alloy design approaches, emphasizing the need for systematic exploration strategies that alter the conventional focus on single-component or equiatomic compositions in multi-principal element alloys. Our findings demonstrate that compositions outside the equiatomic regime, in the broader compositionally complex space can provide improved, application-specific properties.

This study presents an integrated solution between physics-informed materials representation and AL, all grounded within a manufacturability-constrained platform, which effectively expands the scope of modern alloy discovery. Crucially, our framework goes beyond simple property mining; it establishes a unified methodology that constrains performance optimization by manufacturability, ensuring that improved properties are realized under robust, defect-free additive manufacturing conditions. Consequently, researchers and engineers can utilize this framework to develop application-specific materials. Several limitations of the present study should be noted. The current validation within a ternary space limits the “curse of dimensionality”⁸⁴; extending to quaternary or quinary systems will necessitate transfer-learning strategies and optimized traversal algorithms to manage the higher dimensionality, which have proven successful in a broad range of fields^85,86. Additionally, while the present work employs targeted acquisition strategies to efficiently navigate the design space, future efforts may incorporate hybrid or multi-objective acquisition policies, including the introduction of random or space-filling sampled candidates, to further interrogate model performance beyond localized predictive regions. Furthermore, while the present work exploits alloys strengthened by solid-solution and dual-phase strengthening mechanisms, it does not address the alloy systems where strengthening evolves with increasing temperature. In precipitation-strengthened or oxide-dispersion-strengthened (ODS) alloys, microstructural evolution processes may introduce non-linear, temperature-dependent mechanical responses that may not be captured by the current screening approach. So far, the framework has not yet been extended to predict more complex mechanical properties such as ductility and fatigue which depend on additional deformation and failure mechanisms beyond those captured by hardness. While the current descriptor set captures many relevant physics, accurate prediction and validation of such properties will require incorporation of bulk mechanical testing data (e.g., tensile or compression), which represent an important direction for future work. Ultimately, ALPHA-AM serves as a foundation to drive the digital transformation of manufacturing, shifting from trial-and-error to autonomous, physics-driven discovery.

Methods

Experimental setup

The materials, equipment, and procedures used to fabricate the NiCoCr-based alloys under the ALPHA-AM framework were developed at the Laboratory for Extreme Mechanics and Additive Manufacturing (Toronto, Canada). Beginning with the raw material, spherical gas-atomized elemental powders of Ni (99.8% purity), Co (99.9%), and Cr (99.9%) were obtained from Shanghai Truer Technology. The powders exhibited flow rates of 14.3, 8.79, and 16.3 g per 50 s, respectively, with particle sizes ranging from 15 to 45 μm (Fig. S23). Each powder was loaded into PLC-controlled disk feeders (GTV GmbH PF 2/2) that were calibrated according to hopper rotation speed to ensure accurate mass flow delivery. The corresponding powder feed rates for Ni, Co, and Cr are shown in Fig. S24a–c, respectively. The calibrated powder feed rates enabled precise in situ composition tuning to achieve target chemistries during deposition.

All samples were fabricated using a custom-built laser directed energy deposition (L-DED) platform developed in-house, schematically shown in Fig. S25. The system integrates a three-axis Tormach 1100 M CNC machine with a 1 kW continuous-wave IPG Photonics YLR fiber laser (λ = 1070 nm). Powders fed from a multi-hopper system were combined and delivered through a COAX14 v5 coaxial deposition nozzle (Fraunhofer USA Inc.) with argon gas used as both carrier and shielding medium to minimize oxidation. The nozzle stand-off distance was maintained at 7.5 mm for all builds, with layer heights determined from the optimized stability framework. Temperature of the substrate in this system was controlled by a custom-made thermal sink, bonded to each substrate using silicon-based boron nitride thermal paste and maintained at a temperature of 21.3 °C.

Deposition paths were automated via custom G-code scripts generated using G.L.O.W., an open-source G-code generator developed in-house⁸⁷. The scripts enabled synchronized control of laser power (P), scan speed (v), powder feed rate (f), and argon flow rate to ensure reproducibility across all builds. High-throughput Gcode was generated for both single-track experiments as well as multilayer prints. Printing was performed on 16 mm thick low-alloy steel substrates with dimensions of 75 × 150 mm for single track experiments and 50.8 mm diameter pucks for high-throughput synthesis. For the high-throughput synthesis, each experimental run produced nine samples measuring 9 × 9 × 6 mm on a single substrate, which followed a serpentine interlayer scanning strategy with 50% track overlap and 90° rotation between successive layers (Fig. 1b). Cooldown times of 1 s between tracks and 30 s between layers were implemented to minimize heat accumulation during builds. After deposition, the top 2 mm of each build was removed by wire electrical discharge machining to achieve the final geometry shown in Fig. S26. Build quality and printability were assessed from transverse optical micrographs of each alloy, with the presence or absence of hot cracking encoded as a binary feature for surrogate model training (Fig. S27).

Machine learning models for printable alloys

To model the hardness and printability behavior, several regression and classification models were evaluated using the processed dataset of 27 experimental points. For the regression task, Gaussian Process Regression (GPR), Linear Regression, Support Vector Regression (SVR), and Decision Tree Regression were compared based on their suitability for small datasets and interpretability. Each model underwent 5-fold grid-search hyperparameter tuning, with performance evaluated through both leave-one-out cross-validation (LOOCV) and stratified 5-fold validation. The coefficient of determination (R²) and root mean squared error (RMSE) were used to assess model accuracy and generalization. GPR, employing a composite RBF-WhiteKernel, achieved the highest predictive reliability (R² ≈ 0.95, RMSE ≈ 52HV), and was thus chosen as the primary regression model.

For the classification of hot-cracking susceptibility, Gaussian Process Classification (GPC), Logistic Regression, Random Forest, and Decision Tree Classifiers were tested using the same feature set. Evaluation metrics included accuracy, ROC-AUC, and average precision from precision-recall curves to assess class discrimination under limited data conditions. Consistent with the regression results, GPC achieved the most stable and interpretable probabilistic performance, yielding the lowest AUC variance and robust classification accuracy, making it the selected classification model.

Both models were validated primarily through LOOCV to maximize data utilization. Together, the GPR-GPC pair formed the backbone of the ALPHA-AM surrogate modeling framework for property prediction and safety assessment. Additional implementation details, feature selection rationale, and hyperparameter configurations are provided in Supplementary Note A: Surrogate models and active learning, Section 1.3–1.4.

Acquisition strategies

For this work, several acquisition strategies were tested within the ALPHA-AM framework to determine the most effective method for navigating the compositional search space while maintaining manufacturability. Testing multiple strategies was essential to assess how varying balances of exploration and exploitation would influence both property optimization and experimental reliability under additive manufacturing constraints.

The acquisition strategies evaluated included Thompson Sampling, Upper Confidence Bound (UCB), Constrained Probability of Improvement (CPI), and Constrained Expected Improvement (CEI). Thompson Sampling was used to encourage highly exploratory sampling of the design space, ensuring that untested and potentially high-performing regions were not overlooked. UCB balanced exploration and exploitation by weighting the predicted mean and variance of the Gaussian Process Regression model, allowing control over how aggressively the algorithm pursued uncertain regions. CPI introduced a safety constraint derived from the Gaussian Process Classification model’s probability of remaining crack-free (P_safe), prioritizing candidates with a high probability of safe improvement. Finally, CEI extended this by incorporating both the magnitude and probability of improvement, directly coupling expected property gains with manufacturability considerations.

In practice, Thompson Sampling and UCB produced diverse but less reliable candidates with elevated prediction uncertainty concentrated near the boundaries of the design space. CPI performed conservatively, selecting alloys within well-sampled, low-risk regions but showing limited property advancement. CEI, by contrast, provided the optimal balance, exploiting both the mean prediction and associated uncertainty from the GPR model while applying the P_safe constraint from the GPC model, ensuring uncertainty-aware and constraint-driven alloy selection. The CEI for a candidate alloy (x) is defined as:

$$\mathit{CEI}=P_{s\mathrm{afe}}\left(x\right)·\left(\left(\mu \right(x)-f_{\mathrm{best}})\cdot \Phi \left(Z\right)+\sigma \left(x\right)\cdot \varphi \left(Z\right)\right)$$ 1

$$Z=\frac{\mu \left(x\right)-f_{\mathrm{best}}}{\sigma \left(x\right)}$$ 2

where P_safe(x) is the probability that alloy x remains crack-free as estimated by the GPC. The term $\mu$ represents the predicted mean hardness for the given candidate, while $\sigma$ is the predictive standard deviation, both obtained from the GPR surrogate. f_best denotes the highest experimentally observed hardness so far, serving as the benchmark for improvement. $\Phi$ and $\varphi$ are the cumulative distribution function and probability density function of the standard normal distribution, respectively, which together weight the probability that a candidate will exceed f_best by a given margin⁸⁸. Further details on each acquisition strategies is provided in Supplementary Note A: Surrogate models and active learning, Section 1.5.

Material characterization and evaluation

Samples produced under the ALPHA-AM framework were prepared for detailed microstructural, mechanical, and environmental characterization. For scanning electron microscopy (SEM) and X-ray diffraction (XRD), specimens deposited on the custom high-throughput substrate were automatically ground and polished using a Buehler Ecomet system. Grinding was performed with SiC papers of 240, 600, and 1200 grit, followed by polishing with 3 μm and 1 μm diamond suspensions and a final finish using a 0.05 μm alumina. Up to nine samples were prepared simultaneously, enabling high-throughput SEM analysis under secondary-electron, back-scattered-electron, and energy-dispersive X-ray (EDS) modes using a Hitachi SU7000 instrument. XRD characterizations were carried out via an automatic high-throughput scan on the specimen array using a Bruker D8 Discovery diffractometer in theta/2theta mode with a step of 0.04° (2θ), a scan speed of 1 s/step, and a range of 20–80° (2θ). XRD of oxidized samples was additionally carried out using a Rigaku Miniflex diffractometer under similar conditions.

Mechanical testing was performed on an RTEC MFT-5000 tribometer equipped with hardness module and Berkovich diamond tip. Room-temperature hardness measurements were carried out at a load of 4.9 N and a dwell time of 10 s, with ten indents per alloy to ensure statistical reliability. CEI-selected alloys were further evaluated for high-temperature hardness between room temperature and 600 °C. A rotary indentation module incrementally offset each indent radially to prevent interference between imprints, while temperature was automatically increased in 100 °C intervals with a 30-min stabilization dwell before each test. High-temperature oxidation resistance was assessed at 800 °C and 1000 °C using coupons (9 × 9 × 1 mm) finished to 15 μm surface roughness. Each specimen was placed in a ceramic crucible and exposed in air with a heating rate of 18 °C min⁻¹. Samples were periodically removed for mass measurement and returned to the furnace until reaching a total dwell of 100 h. Specific mass-change data were used to quantify oxidation kinetics for each alloy. Further details on oxidation testing are provided in Supplementary Note B: Mechanical behavior, Section 2.3.

Author contributions

Ajay Talbot: conceptualization, formal analysis, investigation, methodology, project administration, software, validation, visualization, writing—original draft, writing—review & editing. Soumya Sobhan Dash: formal analysis, investigation, methodology, writing—review & editing. Jialu Li: formal analysis, investigation, software, writing—review & editing. Changjun Cheng: Investigation, Writing—review & editing. Madhi Ramesh: investigation, writing—review & editing. Xiao Shang: methodology, visualization, writing—review & editing. Jiahui Zhang: methodology, visualization, writing—review & editing. Cristian Cojocaru: investigation, writing—review & editing. Jason Hattrick-Simpers: methodology, visualization, writing—review & editing. Yu Zou: formal analysis, funding acquisition, methodology, resources, supervision, writing—review & editing.

Data availability

All data supporting the findings of this study are available in the paper and the Supplementary Information. The dataset used for training the machine learning model in this study are available at GitHub (https://github.com/JialuLiR/ALPHA-AM-NiCoCr/tree/main).

Code availability

The code used to generate the L-DED deposition paths is provided via the open-source G.L.O.W platform (https://github.com/ArthurJWH/GLOW).The codes used for machine learning is provided in a GitHub open-source GitHub repository (https://github.com/JialuLiR/ALPHA-AM-NiCoCr/tree/main).

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s44334-026-00098-5.