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

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.

Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, stiffness in the PDEs requires an extremely small time steps (e.g. $10^{-12}$ or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose U-Shaped Adaptive Fourier Neural Operators (U-AFNO), a machine learning (ML) model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g. the deformation of the liquid-metal interface) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in-spite of the chaotic nature of LMD. Our model reproduces the key micro-structure statistics and QoIs with a level of accuracy on-par with the high-fidelity numerical solver. We also investigate the opportunity of using hybrid simulations, in which we alternate forward leap in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.