---
configs:
- config_name: default
  data_files:
  - split: train
    path:
    - "train/Advection_4096.h5"
    - "train/Heat_4096.h5"
    - "train/KS_4096.h5"
    - "train/Burgers_1024.h5"
    - "train/NS_1024.h5"
  - split: valid
    path:
    - "valid/Advection_256.h5"
    - "valid/Heat_256.h5"
    - "valid/KS_256.h5"
    - "valid/Burgers_256.h5"
    - "valid/NS_256.h5"
---

## 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)](https://arxiv.org/abs/2412.13074) [(Code)](https://github.com/anthonyzhou-1/temporal_pdes/tree/main)

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 \\(\Delta t\\). Advection and Heat data are generated from [Masked Autoencoder are PDE Learners](https://github.com/anthonyzhou-1/mae-pdes), and KS data are generated from [Lie Point Symmetry Data Augmentation for Neural PDE Solvers](https://github.com/brandstetter-johannes/LPSDA). 
- Advection
  - 4096/256 samples, each sample of shape [250, 100] (num_timesteps, num_grid_points)
  - Advection speed \\(c\\) 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\\) 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\\) is constant

### 2D PDEs
These can be downsampled to produce samples with varying timescales \\(\Delta t\\). Burgers data are generated from [Masked Autoencoder are PDE Learners](https://github.com/anthonyzhou-1/mae-pdes), and NS data are generated from Fourier Neural Operator for Parametric Partial Differential Equations (repo no longer exists). Kolmogorov Flow data is from [APEBench](https://github.com/tum-pbs/apebench)
- Burgers
  - 1024/256 samples, each sample of shape [100, 64, 64] (num_timesteps, num_grid_x, num_grid_y)
  - \\(c_x, c_y\\) is uniformly sampled from [0.5, 1.0] and \\(\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.