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

• URL: http://arxiv.org/abs/2406.17119v2
• Date: Mon, 8 Jul 2024 17:23:22 GMT
• Title: Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
• Authors: Christophe Bonneville, Nathan Bieberdorf, Arun Hegde, Mark Asta, Habib N. Najm, Laurent Capolungo, Cosmin Safta,
• Abstract summary: We propose U-Shaped Adaptive Fourier Neural Operators (U-AFNO), a machine learning (ML) model inspired by recent advances in neural operator learning. We use U-AFNOs to learn the dynamics mapping the field at a current time step into a later time step. Our model reproduces the key micro-structure statistics and QoIs with a level of accuracy on-par with the high-fidelity numerical solver.
• Score: 0.7329200485567827
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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