/Solving-PDEs-PINNs

Primary LanguageJupyter Notebook

Solving PDEs with Physics-Informed Neural Networks (PINNs) and Lagaris Approch

This repository contains Python code and Jupyter notebooks that demonstrate the use of Physics-Informed Neural Networks (PINNs) for solving Partial Differential Equations (PDEs).

Introduction

Solving PDEs using traditional numerical methods can be computationally expensive, especially for high-dimensional problems. PINNs offer an alternative approach that leverages the power of neural networks to solve PDEs using limited data. In this project, i have demonstrate the use of PINNs for solving a variety of PDEs.I also implemented a methodology similar to PINNs (Raissi) i.e Lagaris Approach. These are the papers I used methodologies from.

  1. Lagaris et. al. (1997) https://arxiv.org/pdf/physics/9705023.pdf
  2. Raissi et. al. (2017) https://arxiv.org/pdf/1711.10561.pdf [PINNs]

Examples

The following examples are included in this repository:

  • 1D-Advection.ipynb: Solving the 1D Advection equation using a PINN. image

  • PDE_using_Lagaris_Approch.ipynb: we solved one PDE given in the paper using Lagrais Approch using one dense layer and 10 neurons. image

  • PDE_using_PINNs.ipynb : We took same PDE as above and solved using PINNs (Raissi Approch) , as given the PINNs paper

Results

PDE solution using PINNs PDE solution using Lagaris Approch
image image
1D-Advenction using PINNs

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Contributing

Contributions to this project are welcome. If you would like to contribute, please fork the repository and submit a pull request.