AlloyVAE: A generative model for complex probabilistic field-to-field relationships in alloys

Abstract: The inherent compositional heterogeneity of multi-principal element alloys (MPEAs) gives rise to complex, spatially varying mechanical fields that cannot be uniquely determined from coarse-grained composition descriptors. This non-uniqueness introduces intrinsically probabilistic structure-property relationships, posing a fundamental challenge to conventional deterministic modeling and machine learning approaches that collapse such mappings into average predictions. Here, we present AlloyVAE, a physics-informed generative framework that learns the full conditional distribution of mechanical fields from microstructural inputs. Built upon a conditional variational autoencoder architecture, the model incorporates learned smoothing operators to enhance functional regularity and a self-consistency mechanism to enforce physical plausibility. Trained on atomistic simulation data, AlloyVAE accurately predicts distributions of residual stress fields from composition and short-range order, and enables the generation of multiple physically consistent realizations under identical input conditions. Beyond forward prediction, the framework supports inverse design by optimizing composition fields to achieve targeted mechanical responses, and is extensible to coupled mappings involving eigenstrain. By capturing one-to-many structure-property relationships in heterogeneous materials, this work establishes a probabilistic paradigm for materials modeling and design, providing a scalable alternative to conventional simulations for navigating high-dimensional compositional spaces.