This repository contains a minimal implementation of Physics-Informed Neural Networks (PINNs) in PyTorch. PINNs combine neural networks with physics-based constraints, making them particularly useful for solving problems described by ordinary/partial differential equations.

1. DataDrivenSolutionODE.ipynb
   • Demonstrates the application of PINNs for finding solutions to ordinary differential equations (ODEs).
2. DataDrivenDiscoveryODE.ipynb
   • This notebook explores the data-driven discovery of solutions to ordinary differential equations (ODEs) using PINNs.
3. DataDrivenSolutionPDE.ipynb
   • Extends the application of PINNs to partial differential equations (PDEs).
4. LaneEmdenDifferentialEquation.ipynb
   • Solving the well-known Lane-Emden differential equation using PINNs.
5. ODE-NAS.ipynb
   • Running a Neural Architecture Search (NAS) on PINNs for solving an ODE.
6. PDE-LBFGS.ipynb
   • Using Quasi-Newton LBFGS algorithm for faster convergence.
7. PDE-LBFGS-CUDA.ipynb
   • Add CUDA support to speedup the learning process.

To run these notebooks, ensure you have Python and PyTorch (preferably with CUDA support) installed. You can install the required packages using:

pip install -r requirements.txt

Clone the repository:

git clone https://github.com/your-username/PINN-tutorial.git cd PINN-tutorial

Open the desired notebook using Jupyter:

jupyter notebook DataDrivenDiscoveryODE.ipynb

Feel free to explore and modify the code to suit your needs.

For a deeper understanding of Physics-Informed Neural Networks and their applications, refer to the following resources:

• A tutorial on PINNs by Alireza Afzal Aghaei
• A neural network approach for solving nonlinear differential equations of Lane–Emden type
• Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations

This project is licensed under the GNU General Public License v3.0 - see the LICENSE file for details.