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 inside a square corner tube for Re=100. 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