An-onymous/pde-geo

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

.
├── 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

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"]

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

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/