PINNs in PyTorch

PINN implementations for Burgers, KdV, Navier–Stokes, Schrödinger and related PDEs.

This project collects PyTorch implementations of physics-informed neural networks (PINNs) for a range of canonical PDEs, following the Physics-Informed Deep Learning framework.

🔍 Summary

PINNs approximate the solution of a PDE by training a neural network (u_\theta(x, t)) that:

  • Fits observed data points.
  • Minimizes the PDE residual and boundary / initial condition violations via automatic differentiation.

This allows solving both forward (solve PDE) and inverse (identify parameters) problems in a unified way.

🧪 PDEs covered

Experiments in the repo include:

  • Burgers’ equation – nonlinear advection-diffusion.
  • KdV equation – nonlinear wave propagation.
  • Navier–Stokes – incompressible fluid dynamics.
  • Schrödinger equation – quantum wave dynamics.

For each equation, the repo provides:

  • Network architectures for (u_\theta).
  • Physics-informed loss functions combining data and residuals.
  • Training scripts / notebooks that reproduce classical PINN demos.

📂 GitHub repository