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---
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.
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