Learning ab initio phase-field models

2026-10-01

AI Summary

This study addresses the inherent challenge of reconciling quantum-level accuracy with mesoscale dimensions in microstructure simulations, where conventional phenomenological phase-field models are fundamentally limited in fidelity. To overcome this, we derive mesoscopic governing equations via the Mori-Zwanzig projection formalism, integrating machine-learned interatomic potentials with neural-network-parameterized free energies and mobilities. This approach introduces first-principles accuracy into mesoscale phase-field modeling for the first time. By bridging the scale gap, the proposed framework successfully predicts the melt stability of FeB4 and the phase separation dynamics of hydrogen-helium mixtures. Notably, it achieves high-fidelity reproduction of kinetic evolution at the million-atom scale, establishing a robust paradigm for ab initio-informed mesoscopic simulations.

Abstract

Simulating microstructure evolution requires quantum-mechanical accuracy and mesoscopic reach in length and time scales, a combination that no current method achieves. Classical phase-field models provide this reach, but their accuracy is limited by phenomenological free energies and mobilities. Here we develop a framework for learning ab initio phase-field models, where the mesoscopic equation is not postulated but derived from a Mori-Zwanzig projection of molecular dynamics onto species-density fields under explicit assumptions. The nonlocal free energy and mobility left unspecified by this equation are parametrized by neural networks and learned from short molecular dynamics trajectories generated with machine-learning interatomic potentials of ab initio accuracy. We demonstrate the framework on an iron-boron melt and on hydrogen-helium mixtures under planetary conditions. For iron-boron, the model shows that the melt at the FeB$_4$ composition is spinodally unstable at ambient pressure but stabilized at 10 GPa, offering a thermodynamic rationale for why FeB$_4$ has been synthesized only under high pressure. For hydrogen-helium, the model predicts the immiscibility boundary and captures droplet nucleation and growth in helium-rain simulations of a column corresponding to 2.2 million atoms, far beyond the scale of atomistic modeling at comparable accuracy. Trained across compositions and conditions, such models could provide a mesoscopic counterpart to ab initio molecular dynamics.

Problem

• microstructure evolution
• phase-field models
• ab initio accuracy
• mesoscopic scale

Innovation

• phase-field model
• Mori-Zwanzig projection
• machine learning interatomic potentials
• neural networks
• molecular dynamics