Physics-Informed Gaussian Processes for Hardness Prediction in Refractory High Entropy Alloys

Refractory High Entropy Alloys have emerged as a compelling alternative to traditional metals, offering resilience in extreme environments that conventional alloys cannot withstand. With at least four, and often up to six principal elements, the resulting compositional space spans trillions of candidates, far too large to navigate through experiment alone given the cost and time involved. Finding novel alloys which exhibit the required mechanical properties such as hardness necessitates highly predictive models to guide any tractable search. While existing surrogate models to cheaply impute hardness leverage elemental features, they are often architected in a way where the prior physical inductive bias is not explicitly tunable. More importantly, they rely solely on composition-derived descriptors such as valence electron concentration and mixing entropy, missing features that may only be acquired through experimentation such as local inhomogeneity found in non-equilibrium microstructures present in all real materials. In this paper, we demonstrate that integrating a scalable and physically informed differentiable Gaussian process improves predictive performance over existing black-box models. We achieve this by embedding the Maresca-Curtin solid-solution-strengthening model as a prior mean and replacing its fixed atomic volumes with element-resolved effective volumes learned from data. The resulting model achieves a mean absolute error of 35.6 HV on the public Borg benchmark, outperforming the strongest black-box baselines by 1.3x. Furthermore, we convert X-ray diffraction (XRD) spectra and microscopy/EDS-derived elemental segregation partition coefficients into microstructural descriptors, showing that these experimentally derived features further improve performance to 7.5 HV MAE on the as-cast Experimental dataset because dendritic segregation cannot be captured by bulk composition alone. Our central contribution is a non-linear correction scheme that reveals systematic, non-affine residuals in elemental volumes which no standard reparameterization could reproduce. We demonstrate that this scheme successfully recovers the physical regimes identifying whether an alloy is screw or edge dominated. Together, these results establish a multiscale, physics-informed surrogate for hardness prediction in realistic experimental settings where data are costly, heterogeneous, and experimentally constrained.