2ailesB/neural-parametric-solver-datasets

Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods

This space provides the datasets used in the paper "Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods".

• Project Page: https://2ailesb.github.io/paperpages/neural-solver.html
• ArXiV: https://arxiv.org/abs/2410.06820
• Code: https://github.com/2ailesB/neural-parametric-solver

PDEs

We provide 9 datasets:

• Helmholtz equation 1d: 4 versions for this PDE with varying difficulties depending on the range of the parameter $\omega$.
  • (0.5, 3): toy
  • (0.5, 10): medium
  • (0.5, 50): hard
  • (-5, 55): used for OOD experiments
• Poisson equation 1d: 2 versions of the Poisosn equation:
  • Scalar forcing term
  • Multiscale functional forcing term
• Non-Linear Reaction Diffusion PDE 1d (temporal)
• Advection PDE 1d (temporal): extracted from PDEBench datasets
• Heat 2d (temporal)

Please refer to our paper or code for additional details on the PDE, parameters range or Datasets and Dataloaders.

What's inside the datasets

Each dataset provide the PDE trajectory $u$ along with the PDE parameters, forcings terms (if involved), initial conditions (if involved), boundary conditions (if involved). The torch Datasets associated class return the data under a list containing: (params, forcings, ic, bc), position x, solution u, index of the trajectory.