Physics-Informed Gaussian Process Classification for Constraint-Aware Alloy Design

TL;DR

This work tackles constraint-aware alloy design by introducing physics-informed Gaussian Process Classifiers (GPCs) that embed physics-based prior mean functions, enabling probabilistic, uncertainty-aware classification for both categorical and continuous constraints. The latent GP is trained on the discrepancy between observed labels and physics priors, with a sigmoid transform mapping to class probabilities; multi-class handling uses one-vs-rest ensembles. Across three case studies, including phase stability benchmarking with CALPHAD priors, active learning of categorical phase constraints, and continuous constraint satisfaction for yield strength, the approach consistently improves accuracy, recall, and robustness while reducing data requirements. The results demonstrate faster, more reliable exploration of feasible design spaces, offering a practical, open-source pathway toward constraint-aware, ICME-driven alloy design with reduced experimental cost. The framework is especially valuable for integrating domain knowledge into probabilistic models, providing calibrated uncertainty and facilitating closed-loop discovery.

Abstract

Alloy design can be framed as a constraint-satisfaction problem. Building on previous methodologies, we propose equipping Gaussian Process Classifiers (GPCs) with physics-informed prior mean functions to model the boundaries of feasible design spaces. Through three case studies, we highlight the utility of informative priors for handling constraints on continuous and categorical properties. (1) Phase Stability: By incorporating CALPHAD predictions as priors for solid-solution phase stability, we enhance model validation using a publicly available XRD dataset. (2) Phase Stability Prediction Refinement: We demonstrate an in silico active learning approach to efficiently correct phase diagrams. (3) Continuous Property Thresholds: By embedding priors into continuous property models, we accelerate the discovery of alloys meeting specific property thresholds via active learning. In each case, integrating physics-based insights into the classification framework substantially improved model performance, demonstrating an efficient strategy for constraint-aware alloy design.

Figures (7)

• Figure 1: A 1D demonstration of a GPC with an informative prior. The informative prior has a decision boundary at x = 50 while the true decision boundary is at x = 26. In the first iteration a single data point on the left side bolsters confidence in the prior, decreasing the probability of passing to 0 where we have observed a failure. By the 11th iteration the true decision boundary is approximated. There is only a region of uncertain predictions from the classification at $~40 < x < ~50$.
• Figure 2: Classification of continuous properties using Gaussian Process Regression (GPR). (a) Illustration of the GPR-based classification process, where red dots represent the limited training observations used to fit the GPR model. The GPR predicts normal distributions for each value of $x$, and probabilities of meeting or failing a specified threshold are determined using the Cumulative Distribution Function (CDF). Classification is based on whether the probability of meeting the constraint exceeds 0.5, with results visualized across the domain. (b) Visualization of the corresponding bell curve for a single GPR prediction, highlighting the mean prediction and the probabilities of exceeding or falling below the threshold.
• Figure 3: Model errors for the standard GPC (Uninf.), Thermo-calc (TC), and the GPC with the physics-informed prior (Inf.) when predicting across all phases.
• Figure 4: Comparison of vanilla and physics-informed Bayesian active learning for phase stability predictions in the Fe-Ni-Co system at 1000$^{\circ}$C. The top row displays the vanilla AL scheme, while the bottom row shows the physics-informed AL scheme. Colors represent class probabilities via an RGB scheme, with green indicating FCC, blue indicating FCC+BCC, and red indicating BCC. In early iterations, the physics-informed model heavily relies on its prior knowledge. By iteration 15, it significantly improves recall for the BCC phase, and by iteration 20, it demonstrates greater robustness to class imbalance compared to the vanilla approach, achieving more precise decision boundaries.
• Figure 5: Active learning performance metrics averaged over 200 campaigns. The plotted results show the average error metrics with their standard deviations, providing a more reliable assessment of AL method performance and progression.