ayz2/temporal_pdes

Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates

Datasets for Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates. (Paper) (Code)

Data is organized as:

- Split [train/valid]
    - 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]

Details for each dataset are given below:

1D PDEs

These can be downsampled to produce samples with varying timescales $\mathrm{\Delta }t\backslash Delta\; t$. Advection and Heat data are generated from Masked Autoencoder are PDE Learners, and KS data are generated from Lie Point Symmetry Data Augmentation for Neural PDE Solvers.

• Advection
  • 4096/256 samples, each sample of shape [250, 100] (num_timesteps, num_grid_points)
  • Advection speed $cc$ is uniformly sampled from [0.1, 2.5]
• Heat
  • 4096/256 samples, each sample of shape [250, 100] (num_timesteps, num_grid_points)
  • Viscosity $\nu \backslash nu$ is uniformly sampled from [0.1, 0.8]
• Kuramoto-Sivashinsky (KS)
  • 4096/256 samples, each sample of shape [400, 100] (num_timesteps, num_grid_points)
  • Viscosity $\nu =1\backslash nu\; =\; 1$ is constant

2D PDEs

These can be downsampled to produce samples with varying timescales $\mathrm{\Delta }t\backslash Delta\; t$. Burgers data are generated from Masked Autoencoder are PDE Learners, and NS data are generated from Fourier Neural Operator for Parametric Partial Differential Equations (repo no longer exists). Kolmogorov Flow data is from APEBench

• Burgers
  • 1024/256 samples, each sample of shape [100, 64, 64] (num_timesteps, num_grid_x, num_grid_y)
  • $c_x,c_{y}c\_x,\; c\_y$ is uniformly sampled from [0.5, 1.0] and $\nu \backslash nu$ is uniformly sampled from [7.5e-3, 1.5e-2]
• Navier-Stokes
  • 1024/256 samples, each sample of shape [800, 64, 64] (num_timesteps, num_grid_x, num_grid_y)
  • Coefficients are constant. Resolution is very high to test high-resolution training.
• Kolmogorov Flow
  • 1024/256 samples, each sample of shape [200, 160, 160] (num_timesteps, num_grid_x, num_grid_y)
  • Coefficients are constant.