漂移校正多物理信息神经网络耦合 PDE 求解器

IF 1.8 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Kevin Wandke;Yang Zhang
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引用次数: 0

摘要

求解支配多物理场系统动力学的耦合偏微分方程(PDE)既重要又具有挑战性。众所周知,有限元法(FEM)等现有数值方法计算量大,而物理信息神经网络(PINN)等机器学习技术在对复杂系统或过程进行长时间尺度建模时往往会出现问题。为了克服这些局限性,我们提出了一种新的框架 "漂移校正多物理信息神经网络"(DC-MPINN),专门用于在不牺牲精度的情况下,在较长的时间尺度上高效地解决耦合多物理问题。这种新方法引入了一种用于时域分解的架构,可纠正守恒量的漂移,还引入了一种可解决耦合多物理场问题的复合损失函数。我们在几个基准问题中展示了 DC-MPINN 优于传统有限元方法的性能。这种方法代表了多物理场计算技术的进步,增强了我们理解和预测各学科物理过程行为的能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Drift-Correcting Multiphysics Informed Neural Network Coupled PDE Solver
Solving the coupled partial differential equations (PDEs) that govern the dynamics of multiphysics systems is both important and challenging. Existing numerical methods such as the finite element method (FEM) are known to be computationally intensive, while machine learning techniques, like the physics-informed neural network (PINN), often falter when modeling complex systems or processes over long timescales. To overcome these limitations, we propose a new framework “Drift-Correcting Multiphysics Informed Neural Network” (DC-MPINN), specifically designed to solve coupled multiphysics problems efficiently over extended timescales–without sacrificing accuracy. This new method introduces an architecture for temporal domain decomposition that corrects drift of conserved quantities, as well as a composite loss function that allows solving coupled multiphysics problems. We demonstrate the superior performance of DC-MPINN over traditional FEM approaches in several benchmark problems. This approach represents a step forward in multiphysics computational techniques, enhancing our ability to understand and predict the behavior of physical processes across various disciplines.
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来源期刊
CiteScore
4.30
自引率
0.00%
发文量
27
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