Solving Differential Equations with Neural Networks

[1] Lagaris, I., Likas, A., & Fotiadis, D. 1997, Computer Physics Communications,104, 1

Roadmap:

The repository contains three parts:

Tensorflow version - code based on the Tensorflow library, enables simple :
- Works:
  - ODEs with easy Dirichlet and Neumann initial conditions (Examples no. 1-3),
  - Systems of coupled ODEs (Example no. 4),
  - PDEs with Dirichlet boundary condition (Example no. 5),
- To be done:
  - Neumann boundary conditions for PDEs (Examples no. 6-7 - written, not converging),
  - Custom weights initialization,
  - Better optimization procedure (BFGS),
Numpy_version - code from scratch based only on numpy for solving differential equations via the trial solution with a shallow network:
- Works:
  - ODEs with Dirichlet and Neumann boundary conditions Examples (no. 1-3),
  - PDEs with Dirichlet Conditions (Example no. 5),
- To be done:
  - Neumann boundary conditions for PDEs,
  - Systems of coupled ODEs,
  - optimization of the tensor operations,
Others - some other experiments:
- Keras version - very inelastic and inelegant code.