AI求解PDE

一、波动方程的PINN解法：

Guo Y, Cao X, Liu B, et al. Solving partial differential equations using deep learning and physical constraints[J]. Applied Sciences, 2020, 10(17): 5917.

二、二维的Navier–Stokes方程组的PINN解法

矢量形式的不可压缩Navier-Stokes方程:

Chuang P Y, Barba L A. Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration[J]. arXiv preprint arXiv:2205.14249, 2022.

二维的Navier–Stokes方程组的PINN解法:

Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational physics, 2019, 378: 686-707.

三、秒速求解PDE！26种神经网络偏微分方程求解方法分享，涉及CNN、PINN等

基于神经网络的偏微分方程求解方法26篇论文

1.数据驱动下的偏微分方程神经网络求解方法
基于 CNN 的求解方法

Learning PDEs from data with a numeric-symbolic hybrid deep network
https://arxiv.org/pdf/1812.04426v2.pdf