Physics-Informed Neural Networks: Python Codes for Solving ODEs, ODEs systems, PDEs, and St. Venant Equations (Beta version)

This repository contains Python implementations of Physics-Informed Neural Networks (PINNs) and traditional numerical methods for solving a variety of differential equations commonly found in physical modeling. The codes are designed as a computational framework for experimentation and leaning.

The collection includes:

• Neural network approximations of univariate functions and parametric functions.

• PINN solutions for ordinary differential equations (ODEs), for ODE systems and for partial differential equations (PDEs).

• PINN and Finite Difference solutions of the St. Venant equations, to compare the performance of both methods.

• Visualization of activation functions: logistic, tanh and relu.

These codes are intended for people interested in computational modeling, scientific machine learning, and the application of neural networks to physical problems. Users can adapt the scripts to different equations, boundary/initial conditions, or neural network architectures.