Scalable autoregressive deep surrogates for complex microstructure dynamics

Abstract

Complex microstructural pattern formation, such as dendrite growth, occurs across a wide range of materials and plays a crucial role in determining their properties and functional performance. While the phase-field method is a powerful computational approach for modeling microstructure dynamics, its substantial computational cost limits its integration into practical materials design workflows. Here, we introduce a machine-learning framework that employs autoregressive deep surrogates, trained on short trajectories from quantitative phase-field simulations of alloy solidification within limited spatial domains. Once trained, these surrogates accurately predict dendritic evolution over extended length and time scales, achieving speed-ups exceeding two orders of magnitude. We demonstrate the effectiveness of this approach through examples of isothermal growth and directional solidification of a dilute Al–Cu alloy, confirming its capability to predict complex microstructural pattern formation. Quantitative comparisons with phase-field benchmarks reveal excellent agreement in the tip-selection constant, morphological symmetry, and primary spacing evolution, further validating our approach.