Update README.md

README.md

@@ -8,10 +8,32 @@ tags:
 pretty_name: Neural Parametric Solver
 ---
 
-Datasets related to "Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods". 
+## Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods 
 
-Project Page: https://2ailesb.github.io/paperpages/neural-solver.html
+This space provides the datasets used in the paper "Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods". 
 
-ArXiV: https://arxiv.org/abs/2410.06820
+- Project Page: https://2ailesb.github.io/paperpages/neural-solver.html
+- ArXiV: https://arxiv.org/abs/2410.06820
+- Code: https://github.com/2ailesB/neural-parametric-solver
+
+### PDEs
+We provide 9 datasets:
+- Helmholtz equation 1d: 4 versions for this PDE with varying difficulties depending on the range of the parameter $\omega$.
+  - $[0.5, 3]$: toy
+  - $[0.5, 10]$: medium
+  - $[0.5, 50]$: hard
+  - $[-5, 55]$: used for OOD experiments
+- Poisson equation 1d: 2 versions of the Poisosn equation:
+  - Scalar forcing term
+  - Multiscale functional forcing term
+- Non-Linear Reaction Diffusion PDE 1d (temporal)
+- Advection PDE 1d (temporal): extracted from PDEBench datasets
+- Heat 2d (temporal)
+
+Please refer to our [paper](https://arxiv.org/abs/2410.06820) or [code](ttps://github.com/2ailesB/neural-parametric-solver) for additional details on the PDE, parameters range or Datasets and Dataloaders. 
+
+### What's inside the datasets
+
+Each dataset provide the PDE trajectory $u$ along with the PDE parameters, forcings terms (if involved), initial conditions (if involved), boundary conditions (if involved). 
+The [torch Datasets](https://github.com/2ailesB/neural-parametric-solver/tree/main/ngd_datasets) associated class return the data under a list containing: (params, forcings, ic, bc), position x, solution u, index of the trajectory. 
 
-Code: https://github.com/2ailesB/neural-parametric-solver