DG-PINNs

This repository contains the code for the paper:

• Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations

In this work, we proposed a new PINN framework: data-guided physics-informed neural networks.

• DG-PINNs: A novel two-phase framework for solving inverse problems in PDEs.
• Pre-training phase focuses on data loss; fine-tuning phase embeds physical laws.
• Improves efficiency and maintains accuracy compared to existing PINNs.

Schematic of DG-PINNs

Here we show the schematic of DG-PINNs for solving inverse problems in PDEs.

Naming convention of code

Take the heat equation for example:
DG_PINN_heat_equation_NTK_M1 -- the sensitivity analysis on $M_1$
DG_PINN_heat_equation_NTK_Nd -- the sensitivity analysis on $N_d$
DG_PINN_heat_equation_NTK_noise -- the study of the noise-robustness of DG-PINNs
DG_PINN_vs_PINN_heat_equation_NTK -- the study of the efficiency of PINNs and DG-PINNs

Data for NS equation

We use the same data in the original paper of PINN for the NS equation, which can be downloaded in this link https://github.com/maziarraissi/PINNs/blob/1b3e90e82c47d49aee290aa481550f5e9c582d9a/main/Data/cylinder_nektar_wake.mat

Citation

@article{zhou2024dgpinn,
title={Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations},
author={Wei Zhou, Y.F. Xu},
journal={arXiv preprint arXiv:2407.10836},
year={2024}
}