1D and 2D PDEs Dataset (Masked Autoencoders are PDE Learners)

Datasets

Data was generated according to parameters detailed in the paper using the code below.

• Message Passing Neural PDE Solvers (https://github.com/brandstetter-johannes/MP-Neural-PDE-Solvers?tab=readme-ov-file)
      - 1D KdV Burgers equation
      - 1D Heat equation, Periodic BCs
      - 1D inviscid Burgers equation
      - 1D Wave equation
• Lie Point Symmetry Data Augmentation for Neural PDE Solvers (https://github.com/brandstetter-johannes/LPSDA)
      - 1D KS Equation
• Fourier Neural Operator for Parametric Partial Differential Equations (https://github.com/khassibi/fourier-neural-operator) (Update: Repo no longer exists)
      - 2D Incompressible NS
• Towards multi-spatiotemporal-scale generalized PDE modeling (https://huggingface.co/datasets/pdearena/NavierStokes-2D-conditoned)
      - 2D Smoke Buoyancy
• Masked Autoencoders are PDE Learners (https://github.com/anthonyzhou-1/mae-pdes)
      - 2D Heat, Adv, Burgers equations
      - 1D Advection
      - 1D Heat (Requires a working FEniCS installation: https://fenicsproject.org/download/archive/)

Organization

Data is organized into the following structure:

• Split [train/valid/test]
  • u : nodal values of the PDE solution, in shape [num_samples, temporal_resolution, spatial_resolution]
  • x : coordinates of the spatial domain, in shape [spatial_resolution]
  • t : timesteps of the PDE solution, in shape [temporal_resolution]
  • coefficients [alpha, beta, gamma, etc.]: coefficients of the solved PDE solution, in shape [num_samples, coord_dim]