Update README.md

README.md

@@ -28,4 +28,27 @@ Data is organized as:
     - 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
+
+### 12D 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).
+- 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.