通过具有U-Net骨干的混合自适应傅里叶神经算子加速相场模拟
Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
AI总结：
本文提出U-AFNO模型，结合U-Net局部特征提取与傅里叶空间视觉Transformer，用于加速液态金属脱合金相场模拟，在完全自回归设置下准确预测场动力学并优于混合方案。
摘要：
腐蚀性液体与金属合金之间的长时间接触会导致渐进式脱合金。针对这种液态金属脱合金（LMD）过程，已经发展了相场模型。然而，控制方程通常涉及耦合的非线性偏微分方程（PDE），在数值求解上具有挑战性。特别是，PDE中的刚性要求极小时的时间步长（例如10^{-12}或更小）。当需要将LMD模拟运行到较晚的时间范围时，这一计算瓶颈尤其成问题。这推动了能够通过一次跳过多个连续时间步来在时间上向前跳跃的替代模型的发展。在本文中，我们提出了U形自适应傅里叶神经算子（U-AFNO），这是一种受神经算子学习最新进展启发的机器学习（ML）模型。U-AFNO采用U-Net来提取和重建物理场中的局部特征，并将潜在空间通过一个在傅里叶空间中实现的视觉Transformer（ViT）（AFNO）。我们使用U-AFNO来学习将当前时间步的场映射到后续时间步的动力学。我们还识别了描述腐蚀过程的全局感兴趣量（QoI）（例如液态金属界面的变形），并表明尽管LMD具有混沌性质，我们提出的U-AFNO模型仍能够准确预测场动力学。我们的模型以与高保真数值求解器相当的精度水平重现了关键的微观结构统计量和QoI。我们还研究了使用混合模拟的机会，在混合模拟中，我们交替使用U-AFNO进行时间上的向前跳跃与高保真时间步进。我们证明，尽管对某些替代模型设计选择有利，但我们提出的U-AFNO模型在完全自回归设置下始终优于混合方案。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
