用物理约束神经网络加速多孔介质中溶质传输模拟。
Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sources
- 结合有限元法与物理信息深度算子网络，分步求解流场与浓度分布。
- 相比传统方法速度提升数量级，且保持高精度，适合实际场景应用。
- 针对尖锐源设计自适应采样策略，有效捕捉浓度陡变区域。
我们提出一种混合框架，将有限元法（FEM）与物理信息深度算子网络（Physics-Informed DeepONet）相结合，用于建模来自尖锐局部高斯源的多孔介质中流体传输问题。该系统由稳态达西流方程和时变对流-扩散方程构成。方法首先使用FEM求解达西系统，获取速度场，并将其传递给物理信息深度算子网络，该网络学习从源函数到溶质浓度分布的映射关系。这种模块化策略在保持FEM级流场精度的同时，实现了运输动力学的快速推理。为应对尖锐源引起的陡峭梯度，引入了针对主干网络采样点的自适应采样策略。数值实验表明，本方法与参考解高度一致，同时相较传统求解器实现数量级的速度提升，适用于相关实际场景。代码已开源：https://github.com/erkara/fem-pi-deeponet。
原文摘要 · Abstract (English)
We present a hybrid framework that couples finite element methods (FEM) with physics-informed DeepONet to model fluid transport in porous media from sharp, localized Gaussian sources. The governing system consists of a steady-state Darcy flow equation and a time-dependent convection-diffusion equation. Our approach solves the Darcy system using FEM and transfers the resulting velocity field to a physics-informed DeepONet, which learns the mapping from source functions to solute concentration profiles. This modular strategy preserves FEM-level accuracy in the flow field while enabling fast inference for transport dynamics. To handle steep gradients induced by sharp sources, we introduce an adaptive sampling strategy for trunk collocation points. Numerical experiments demonstrate that our method is in good agreement with the reference solutions while offering orders of magnitude speedups over traditional solvers, making it suitable for practical applications in relevant scenarios. Implementation of our proposed method is available at https://github.com/erkara/fem-pi-deeponet.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。