Towards Spatio-Temporal Extrapolation of Phase-Field Simulations with Convolution-Only Neural Networks

2026-01-08

arXiv.org

AI Summary

This work addresses the prohibitive computational cost of traditional phase-field simulations in large-scale liquid metal dealloying (LMD), which hinders efficient prediction of complex microstructure evolution. The authors propose the first fully convolutional, conditionally parameterized U-Net surrogate model, integrating physics-informed inpainting, convolutional self-attention mechanisms, and flood-fill correction. Coupled with a conditional diffusion model to generate physically consistent initial conditions, the framework enables large-scale spatiotemporal extrapolation of LMD phase-field dynamics without reliance on expensive numerical solvers for initialization. The method supports flexible time-step skipping and generalizes across multi-component alloys. Experimental results demonstrate relative errors below 5% for key physical quantities within the training domain and under 15% during long-term extrapolation, achieving up to a 36,000-fold speedup—reducing simulations that typically require weeks to mere seconds.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: (Large) Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Phase-field simulations of liquid metal dealloying (LMD) can capture complex microstructural evolutions but can be prohibitively expensive for large domains and long time horizons. In this paper, we introduce a fully convolutional, conditionally parameterized U-Net surrogate designed to extrapolate far beyond its training data in both space and time. The architecture integrates convolutional self-attention, physically informed padding, and a flood-fill corrector method to maintain accuracy under extreme extrapolation, while conditioning on simulation parameters allows for flexible time-step skipping and adaptation to varying alloy compositions. To remove the need for costly solver-based initialization, we couple the surrogate with a conditional diffusion model that generates synthetic, physically consistent initial conditions. We train our surrogate on simulations generated over small domain sizes and short time spans, but, by taking advantage of the convolutional nature of U-Nets, we are able to run and extrapolate surrogate simulations for longer time horizons than what would be achievable with classic numerical solvers. Across multiple alloy compositions, the framework is able to reproduce the LMD physics accurately. It predicts key quantities of interest and spatial statistics with relative errors typically below 5% in the training regime and under 15% during large-scale, long time-horizon extrapolations. Our framework can also deliver speed-ups of up to 36,000 times, bringing the time to run weeks-long simulations down to a few seconds. This work is a first stepping stone towards high-fidelity extrapolation in both space and time of phase-field simulation for LMD.

Problem

• phase-field simulation
• liquid metal dealloying
• spatio-temporal extrapolation
• computational efficiency
• microstructural evolution

Innovation

• convolutional U-Net
• spatio-temporal extrapolation
• phase-field simulation
• conditional diffusion model
• physically informed padding