Scalable data-driven modeling of microstructure evolution by learning local dependency and spatiotemporal translation invariance rules in phase field simulation

TL;DR

This paper introduces a minimalist CNN approach for phase-field simulations that learns local dependencies and translation invariance, enabling scalable, reliable microstructure evolution predictions from limited data.

Contribution

The work reveals that CNNs, aligned with physical priors, can effectively model microstructure evolution with minimal training data, surpassing traditional data requirements.

Findings

CNN models capture locality and translation invariance in phase-field simulations.

Small datasets from early-stage simulations enable long-term, scalable predictions.

Model generalizes well to larger systems and longer timescales.

Abstract

Phase-field (PF) simulation provides a powerful framework for predicting microstructural evolution but suffers from prohibitive computational costs that severely limit accessible spatiotemporal scales in practical applications. While data-driven methods have emerged as promising approaches for accelerating PF simulations, existing methods require extensive training data from numerous evolution trajectories, and their inherent black-box nature raises concerns about long-term prediction reliability. This work demonstrates, through examples of grain growth and spinodal decomposition, that a minimalist Convolutional Neural Network (CNN) trained with a remarkably small dataset even from a single small-scale simulation can achieve seamless scalability to larger systems and reliable long-term predictions far beyond the temporal range of the training data. The key insight of this work lies in revealing that the success of CNN-based models stems from the alignment between their inductive biases and the physical priors of phase-field simulations specifically, locality and spatiotemporal translation invariance. Through effective receptive field analysis, we verify that the model captures these essential properties during training. Therefore, from a reductionist perspective, the surrogate model essentially establishes a spatiotemporally invariant regression mapping between a grid point's local environment and its subsequent state. Further analysis of the model's feature space demonstrates that microstructural evolution effectively represents a continuous redistribution of a finite set of local environments. When the model has already encountered nearly all possible local environments in the early-stage training data, it can reliably generalize to much longer evolution timescales, regardless of the dramatic changes in global microstructural morphology.