--- 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/