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--- |
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configs: |
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- config_name: default |
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data_files: |
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- split: train |
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path: |
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- "train/Advection_4096.h5" |
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- "train/Heat_4096.h5" |
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- "train/KS_4096.h5" |
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- "train/Burgers_1024.h5" |
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- "train/NS_1024.h5" |
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- split: valid |
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path: |
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- "valid/Advection_256.h5" |
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- "valid/Heat_256.h5" |
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- "valid/KS_256.h5" |
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- "valid/Burgers_256.h5" |
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- "valid/NS_256.h5" |
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--- |
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## Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates |
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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) |
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Data is organized as: |
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``` |
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- Split [train/valid] |
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- u : nodal values of the PDE solution, in shape [num_samples, temporal_resolution, spatial_resolution] |
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- x : coordinates of the spatial domain, in shape [spatial_resolution] |
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- t : timesteps of the PDE solution, in shape [temporal_resolution] |
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- coefficients [alpha, beta, gamma, etc.]: coefficients of the solved PDE solution, in shape [num_samples, coord_dim] |
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``` |
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Details for each dataset are given below: |
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### 1D PDEs |
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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). |
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- Advection |
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- 4096/256 samples, each sample of shape [250, 100] (num_timesteps, num_grid_points) |
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- Advection speed \\(c\\) is uniformly sampled from [0.1, 2.5] |
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- Heat |
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- 4096/256 samples, each sample of shape [250, 100] (num_timesteps, num_grid_points) |
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- Viscosity \\(\nu\\) is uniformly sampled from [0.1, 0.8] |
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- Kuramoto-Sivashinsky (KS) |
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- 4096/256 samples, each sample of shape [400, 100] (num_timesteps, num_grid_points) |
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- Viscosity \\(\nu = 1\\) is constant |
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### 2D PDEs |
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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) |
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- Burgers |
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- 1024/256 samples, each sample of shape [100, 64, 64] (num_timesteps, num_grid_x, num_grid_y) |
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- \\(c_x, c_y\\) is uniformly sampled from [0.5, 1.0] and \\(\nu\\) is uniformly sampled from [7.5e-3, 1.5e-2] |
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- Navier-Stokes |
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- 1024/256 samples, each sample of shape [800, 64, 64] (num_timesteps, num_grid_x, num_grid_y) |
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- Coefficients are constant. Resolution is very high to test high-resolution training. |
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- Kolmogorov Flow |
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- 1024/256 samples, each sample of shape [200, 160, 160] (num_timesteps, num_grid_x, num_grid_y) |
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- Coefficients are constant. |
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