| --- |
| license: cc-by-4.0 |
| language: |
| - en |
| pretty_name: Geometry-Aware PDE Benchmark Dataset |
| tags: |
| - pde |
| - scientific-machine-learning |
| - operator-learning |
| - computational-physics |
| - darcy-flow |
| - poisson-equation |
| - geometry-aware-learning |
| viewer: false |
| --- |
| |
| # Geometry-Aware PDE Benchmark Dataset |
|
|
| ## Dataset Description |
|
|
| This dataset contains geometry-aware partial differential equation (PDE) |
| simulation data for scientific machine learning, operator learning, and |
| generative PDE modeling experiments. It includes three subsets: |
|
|
| - **Darcy**: static Darcy-flow samples on polygonal geometries. Each geometry |
| includes a triangular mesh, a 128 x 128 coefficient grid, signed-distance |
| information, and scalar solution values on mesh nodes. |
| - **Poisson**: static Poisson-equation samples on polygonal geometries. It has |
| the same mesh structure as Darcy and additionally includes source-term fields. |
| - **CE_Gauss**: time-dependent CE-Gauss dynamic-geometry sequences. Each sample |
| stores an 80-frame sequence on a 128 x 128 grid with three state channels, |
| domain masks, signed-distance fields, coordinates, and window metadata. |
| |
| The dataset is intended for benchmarking models that must handle irregular or |
| dynamic geometries, spatial masks, signed-distance conditioning, and both static |
| and temporal PDE prediction tasks. |
| |
| ## Directory Structure |
| |
| ```text |
| . |
| ├── README.md |
| ├── CE_Gauss/ |
| │ ├── train.npz |
| │ ├── valid.npz |
| │ └── test.npz |
| │ |
| ├── Darcy/ |
| │ ├── train/ |
| │ │ └── Dataset_polygon_0.{npz,mat} ... Dataset_polygon_199.{npz,mat} |
| │ ├── valid/ |
| │ │ └── Dataset_polygon_200.{npz,mat} ... Dataset_polygon_249.{npz,mat} |
| │ └── test/ |
| │ └── Dataset_polygon_250.{npz,mat} ... Dataset_polygon_299.{npz,mat} |
| └── Poisson/ |
| ├── train/ |
| │ └── PoissonDataset_polygon_0.{npz,mat} ... PoissonDataset_polygon_199.{npz,mat} |
| ├── valid/ |
| │ └── PoissonDataset_polygon_200.{npz,mat} ... PoissonDataset_polygon_249.{npz,mat} |
| └── test/ |
| └── PoissonDataset_polygon_250.{npz,mat} ... PoissonDataset_polygon_299.{npz,mat} |
| ``` |
| |
| Local upload/cache artifacts such as `.cache/`, `*.lock`, or generated cache |
| files are not part of the semantic dataset contents and can be ignored. |
| |
| ## File Formats |
| |
| All core data files are stored as NumPy `.npz` archives. The Darcy and Poisson |
| subsets also include MATLAB `.mat` exports with matching keys for users who |
| prefer MATLAB or SciPy workflows. |
| |
| ### CE_Gauss |
| |
| Files: `CE_Gauss/train.npz`, `CE_Gauss/valid.npz`, `CE_Gauss/test.npz` |
| |
| Main fields: |
| |
| - `u`: float32 array with shape `(B, 80, 16384, 3)`. The first dimension is the |
| number of sequence windows in the split; the 16384 points correspond to a |
| 128 x 128 grid. |
| - `mask`: uint8 array with shape `(B, 80, 16384)`, indicating active spatial |
| domain points. |
| - `sdf`: float32 array with shape `(B, 80, 16384)`, storing signed-distance |
| values for the dynamic geometry. |
| - `t_sample`: float32 array with shape `(B, 80)`, storing sampled times. |
| - `sample_indices`: int32 array with shape `(B, 80)`, storing source time-step |
| indices. |
| - `x`: float32 array with shape `(16384, 2)`, storing 2D coordinates. |
| - `t_full`: float32 array with shape `(10000,)`, storing the full time grid. |
| - `block_ids`, `block_names`, `window_start_indices`, `window_start_offsets`, |
| and `window_stop_indices`: split/window metadata. |
| - `dataset_desc_json` and `resplit_meta_json`: JSON strings describing the |
| dynamic-geometry generation and the split/window construction. |
| |
| Stats file: `CE_Gauss/stats.npz` |
| |
| - `u_mean`, `u_std`: normalization statistics for the three state channels. |
| - `x_min`, `x_max`, `y_min`, `y_max`: coordinate bounds. |
| |
| ### Darcy |
| |
| Files: |
| |
| - `Darcy/{train,valid,test}/Dataset_polygon_*.npz` |
| - `Darcy/{train,valid,test}/Dataset_polygon_*.mat` |
| |
| Each file represents one polygonal geometry. |
| |
| Main fields: |
| |
| - `xx`, `yy`: mesh-node coordinates |
| - `elements`: triangular mesh connectivity |
| - `k_train`, `k_test`: coefficient/permeability fields |
| - `u_train`, `u_test`: scalar solution values |
| - `sdf`: signed-distance values |
| - `holes`: hole metadata |
| |
| The number of mesh nodes and elements varies by geometry. |
| |
| ### Poisson |
| |
| Files: |
| |
| - `Poisson/{train,valid,test}/PoissonDataset_polygon_*.npz` |
| - `Poisson/{train,valid,test}/PoissonDataset_polygon_*.mat` |
| |
| Each file represents one polygonal geometry. |
| |
| Main fields: |
| |
| - `xx`, `yy` |
| - `elements` |
| - `f_train`, `f_test`: source-term fields |
| - `k_train`, `k_test`: coefficient fields |
| - `u_train`, `u_test`: solution values |
| - `sdf` |
| - `holes` |
| |
| Stats file: `Poisson/s3gm_poisson_stats.npz` |
| |
| - `k_mean`, `k_std` |
| - `f_mean`, `f_std` |
| - `sdf_scale` |
| - metadata for coefficient transforms |
| |
| ## Train / Valid / Test Split |
| |
| ### Sequence Subsets |
| |
| | Subset | Split | File | Samples | Temporal length | Shape | |
| | -------- | ----: | -------------------- | ------: | --------------: | ------------------------- | |
| | CE_Gauss | train | `CE_Gauss/train.npz` | 104 | 80 | `(104, 80, 16384, 3)` | |
| | CE_Gauss | valid | `CE_Gauss/valid.npz` | 26 | 80 | `(26, 80, 16384, 3)` | |
| | CE_Gauss | test | `CE_Gauss/test.npz` | 26 | 80 | `(26, 80, 16384, 3)` | |
| |
| ### Static Geometry Subsets |
| |
| | Subset | Split | Geometry IDs | Files | |
| | ------- | ----- | -----------: | ----: | |
| | Darcy | train | 0–199 | 200 | |
| | Darcy | valid | 200–249 | 50 | |
| | Darcy | test | 250–299 | 50 | |
| | Poisson | train | 0–199 | 200 | |
| | Poisson | valid | 200–249 | 50 | |
| | Poisson | test | 250–299 | 50 | |
| |
| ## Usage Notes |
| |
| ### Loading `.npz` files |
| |
| ```python |
| import numpy as np |
| |
| with np.load("CE_Gauss/train.npz", allow_pickle=False) as data: |
| u = data["u"] |
| mask = data["mask"] |
| sdf = data["sdf"] |
| coords = data["x"] |
| ``` |
| |
| ```python |
| with np.load("Darcy/train/Dataset_polygon_0.npz", allow_pickle=False) as data: |
| coords = np.stack([data["xx"], data["yy"]], axis=-1) |
| elements = data["elements"] |
| k = data["k_train"] |
| solution = data["u_train"] |
| ``` |
| |
| ### Loading `.mat` files |
| |
| ```python |
| from scipy.io import loadmat |
| |
| sample = loadmat("Poisson/train/PoissonDataset_polygon_0.mat") |
| xx = sample["xx"] |
| elements = sample["elements"] |
| u_train = sample["u_train"] |
| ``` |
| |
| ## Limitations |
| |
| - This is a simulation dataset, not real-world observational data. |
| - Geometry distributions and generation pipelines are fixed. |
| - Models trained on this dataset may not generalize outside this domain. |
| - Care must be taken to respect train/test splits within each geometry file. |
| - CE_Gauss uses fixed-length temporal windows. |
| |
| ## License |
| |
| This dataset is released under the **Creative Commons Attribution 4.0 |
| International (CC BY 4.0)** license. |
| |
| https://creativecommons.org/licenses/by/4.0/ |
