Physics Informed Neural Network (PINN) for the 2D Navier-Stokes equation
This module implements the Physics Informed Neural Network (PINN) model for the 2D Navier-Stokes equation. The NS equations are given by (du/dx + dv/dy) = 0, u du/dx + v du/dy + dp/dx - (d^2u/dx^x + d^2u/dy^2) / Re = 0, u dv/dx + v dv/dy + dp/dy - (d^2v/dx^2 + d^2v/dy^2) / Re = 0. It represents the fluid flow over a cylinder inside a wind tunnel depending on the Reynolds number. The PINN model predicts u(x, y), v(x,y) and p(x,y) for the input (x, y).
The effectiveness of PINNs is validated in the following works.
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M. Raissi, et al., Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations, arXiv: 1711.10561 (2017). (https://arxiv.org/abs/1711.10561)
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M. Raissi, et al., Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations, arXiv: 1711.10566 (2017). (https://arxiv.org/abs/1711.10566)
It is based on hysics informed neural network (PINN) for the 1D Wave equation on https://github.com/okada39/pinn_wave