Extended pseudo-spectral physics-informed neural networks for phase-field models

2026-06-23

AI Summary

This work addresses the challenge of unknown constitutive relations—such as bulk free energy density and interfacial thickness parameters—in phase-field models by proposing an Extended Spectral Physics-Informed Neural Network (ESPINN) framework. ESPINN uniquely integrates Fourier pseudospectral methods with physics-informed neural networks, enabling simultaneous reconstruction of the bulk chemical potential and gradient coefficient from just a single pair of transient snapshot data. Built upon the Cahn–Hilliard equation and leveraging automatic differentiation together with spectral discretization, the method achieves high-accuracy, statistically stable identification of free energy structures in noise-free settings. Under noisy conditions, robustness is significantly enhanced with only a few additional snapshots, demonstrating exceptional data efficiency and strong adherence to physical consistency.

Abstract

Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution. In practice, these constitutive quantities are rarely known a priori and must be inferred from limited dynamical observations. In this work, an extended pseudo-spectral physics-informed neural network (ESPINN) framework is developed for the inverse identification of phase-field models from transient snapshot data. It enables the simultaneous recovery of both the bulk chemical potential and unknown gradient coefficients. Numerical experiments on the one-dimensional Cahn-Hilliard equation demonstrate accurate and statistically stable reconstruction in the noiseless regime, with substantial constitutive information recoverable from even a single snapshot pair. In the presence of noise, reconstruction accuracy degrades gracefully, and increasing the number of snapshots improves robustness by reducing variance across runs. These results establish ESPINN as a data-efficient and physically consistent approach for learning free-energy structure in continuum models of phase separation.

Problem

• phase-field models
• inverse identification
• constitutive quantities
• free-energy density
• gradient coefficients

Innovation

• physics-informed neural networks
• phase-field models
• pseudo-spectral method
• inverse identification
• Cahn-Hilliard equation