datasets
Training and evaluation data, with the modality, task and licence stated up front. Listed live from the Hugging Face Hub.
PDExplBenchPDE_Inverse_Problem_Benchmarking
PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems
This is the official dataset for the paper PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems.
Code: GitHub - ASK-Berkeley/PDEInvBench
Sample Usage
You can use the provided script from the codebase to batch download the data:
pip install huggingface_hub
python3 huggingface_pdeinv_download.py --dataset… See the full description on the dataset page: https://huggingface.co/datasets/DabbyOWL/PDE_Inverse_Problem_Benchmarking.ShallowWater-2DPDEBench-1D
Dataset Card for "PDEBench-1D"
More Information needed
NavierStokes-2Dpde-transformer-ape2dLM-PDE-Save
PINN-Data-Save
combine
cat MOL-LLM/MOL-LLM.tar.part* > MOL-LLM.tar
tar -xvf MOL-LLM.tar
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:… See the full description on the dataset page: https://huggingface.co/datasets/An-onymous/pde-geo.fno-predictions
PDEBench FNO Re-evaluation: Prediction Tensors
Test-set prediction arrays from The Unrealized Potential of Fourier Neural Operators: A Systematic Re-evaluation of PDEBench Baselines (NeurIPS 2026 E&D Track submission).
File layout
For all standard tests (1-27, 29, plus the three supplementary 2D CFD configurations), each .npz file contains:
preds: model predictions, shape [N_test, spatial_dims..., T, nc]
targets: ground truth, same shape
per_sample: per-sample… See the full description on the dataset page: https://huggingface.co/datasets/pdebench-fno-audit/fno-predictions.NavierStokes-2D-conditonedPDEBench_2D_diff-reactlegal:
owner: Takamoto, M et al. (https://darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-2986)
license: cc-by-4.0
data_production:
physics: 2D Diffusion-Reaction
type: simulation
script: Converted to PLAID format for standardized usage; no changes to data content.
num_samples:
train: 1000
storage_backend: hf_datasets
plaid:
version: 0.1.12
This dataset was generated with plaid, we refer to this documentation for additional details on how to extract data… See the full description on the dataset page: https://huggingface.co/datasets/Nionio/PDEBench_2D_diff-react.Burgersstandard-pde-benchmark
🚀 Quick Start: Download Data
The most reliable way to download this benchmark while preserving the recursive folder structure is using the huggingface_hub library.
1. Install requirements
pip install huggingface_hub h5py
2. Download the entire dataset
Run this Python snippet to mirror the full repository to your local machine:
from huggingface_hub import snapshot_download
snapshot_download(
repo_id="kmario23/standard-pde-benchmark"… See the full description on the dataset page: https://huggingface.co/datasets/kmario23/standard-pde-benchmark.AdvectionMaxwell-3Dpd-extended
pd-extended
Summary
PD-Extended is a collection of ~34.7 million image/caption pairs derived from the PD12M and Megalith-CC0 datasets. The image/caption pairs are accompanied with metadata, such as mime type and dimensions, as well as the accompanying CLIP-L14 embeddings. Of note, these images retain their original licensing, and the source_id is available to pair any derived image to its source within the original dataset. All images are paired with synthetic captions… See the full description on the dataset page: https://huggingface.co/datasets/Spawning/pd-extended.LithoBench-PDE
LithoBench-PDE
A benchmark dataset for PDE-based computational lithography simulation, constructed by generating high-fidelity 3D reference simulations for photomasks from the LithoBench dataset. Each sample contains intermediate 2D and 3D field data from the lithography simulation pipeline, providing ground-truth input-output pairs for three PDE learning tasks corresponding to three governing PDEs of photolithography.
PDE Learning Tasks
For each photomask, the… See the full description on the dataset page: https://huggingface.co/datasets/AISDL-SNU/LithoBench-PDE.PDEBench-1D-full
Dataset Card for "PDEBench-1D-full"
More Information needed
staatsblad-synth-nl
Synthetic Dutch from the Belgisch Staatsblad
Diverse, fluent Dutch pretraining text synthesized from
guust-franssens/belgisch-staatsblad
(CC0, Belgian official-gazette filings). Adds Belgium/Flanders coverage to Dutch LM pretraining
mixes, where clean Belgian-Dutch prose is otherwise scarce.
The source text is noisy OCR from scanned PDFs, but its metadata (company, juridical form,
act type, city, date) is clean. A local LLM (google/gemma-2-9b-it)
"launders" the OCR + metadata… See the full description on the dataset page: https://huggingface.co/datasets/pdelobelle/staatsblad-synth-nl.PDEBench-1Dheat1d-pde-dataset
heat1d-pde-dataset
This dataset contains numerical solutions of the 1D heat equation with cooling terms, designed for machine learning applications in scientific computing and physics-informed neural networks.
Dataset Description
Dataset Summary
The dataset consists of spatiotemporal solutions to the 1D heat equation with boundary conditions and a cooling term. Each sample includes initial states, final states (with and without noise), simulation parameters… See the full description on the dataset page: https://huggingface.co/datasets/nick-leland/heat1d-pde-dataset.PDEBench_2D_DarcyFlowExample of usage:
import torch
from plaid.bridges import huggingface_bridge as hfb
from torch.utils.data import DataLoader
def reshape_all(batch: dict[str, torch.Tensor]) -> dict[str, torch.Tensor]:
"""Helper function that reshapes the flattened fields into images of sizes (128, 128)."""
batch["diffusion_coefficient"] = batch["diffusion_coefficient"].reshape(
-1, 128, 128
)
batch["flow"] = batch["flow"].reshape(-1, 128, 128)
return batch
# Load the dataset… See the full description on the dataset page: https://huggingface.co/datasets/Nionio/PDEBench_2D_DarcyFlow.PDEBench_2D_SWElegal:
owner: Takamoto, M et al. (https://darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-2986)
license: cc-by-4.0
data_production:
physics: Shallow Water Equations
type: simulation
script: Converted to PLAID format for standardized usage; no changes to data content.
num_samples:
train: 1000
storage_backend: hf_datasets
plaid:
version: 0.1.12
This dataset was generated with plaid, we refer to this documentation for additional details on how to extract data… See the full description on the dataset page: https://huggingface.co/datasets/Nionio/PDEBench_2D_SWE.pde-controller
Autoformalization and Reasoning for PDE Control
This dataset is used to train PDE-Controller (https://pde-controller.github.io/), a framework that enables large language models (LLMs) to control systems governed by partial differential equations (PDEs).
By training LLMs on this dataset, we can transform informal natural language instructions into formal specifications, and then execute reasoning and planning steps to improve the utility of PDE control.
By bridging the gap between… See the full description on the dataset page: https://huggingface.co/datasets/delta-lab-ai/pde-controller.PDEControl_DPC
PDE Control — TI-DeepONet Training Datasets
Simulation datasets for "Learning to Control PDEs with Differentiable Predictive Control
and Time-Integrated Neural Operators".
📄 Paper: arXiv:2511.08992
💻 Code: github.com/Centrum-IntelliPhysics/PDEControl_DPC
These are the trajectory datasets used to train the TI-DeepONet surrogates. Each file
holds 3000 controlled trajectories generated by a classical numerical solver under randomly
sampled control sequences.
You may not need… See the full description on the dataset page: https://huggingface.co/datasets/Centrum-IntelliPhysics/PDEControl_DPC.1D-Compressible-Navier-StokesPDE5_Inhibitor_Designs_2H42
PDE5 Inhibitor Designs — 2H42 / GA-II
Why this target matters. PDE5 inhibitors are among the most widely prescribed drugs in the world, and the target remains actively pursued in pulmonary arterial hypertension and cardiac indications far beyond its original use.
2,090 small molecules generated de novo by the Technetium TC-43.ai engine (GA-II), conditioned on the catalytic pocket of human cGMP-specific phosphodiesterase 5 (PDE5A), taken from the sildenafil co-crystal 2H42 (2.3… See the full description on the dataset page: https://huggingface.co/datasets/Tc-43/PDE5_Inhibitor_Designs_2H42.ldm_pdes
Text2PDE: Latent Diffusion Models for Accessible Physics Simulation (Pretrained Models and Datasets)
Pretrained Models
The pretrained models are:
- Autoencoders:
- ae_cylinder.ckpt : autoencoder trained to compress cylinder mesh data across 25 timesteps. Does not use GAN or LPIPS.
- ae_ns2D.ckpt: autoencoder trained to compress smoke buoyancy data (48x128x128). Does not use GAN or LPIPS.
- LDMs:
- cylinder flow
- ldm_DiT_FF_cylinder.ckpt: ldm model… See the full description on the dataset page: https://huggingface.co/datasets/ayz2/ldm_pdes.PDExplorer-Bench
ID
is_turbulent
type_non_turbulent
type_turbulent
is_newtonian
powerlaw
carreau
is_dilatant
newtonian_type
is_compressible
type_body_force
is_isothermal
1
0
0
0
1
0
0
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1
0
0
1
2
0
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1
0
0
0
1
0
1
1
3
0
0
0
1
0
0
0
1
1
0
1
4
0
0
0
1
0
0
0
1
1
1
1
5
0
1
0
1
0
0
0
1
0
0
1
6
0
1
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1
0
0
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1
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1
1
7
0
1
0
1
0
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1
1
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1
8
0
1
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1
0
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1
1
1
1
9
0
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0
0
0
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1
10
0
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1
0
0
0
0
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1
11
0
0
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1
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0
0
1
0
1
12
0
0
0
1
0
0
0
0
1
1
1
13
0
0
0
0
0
1
0
0… See the full description on the dataset page: https://huggingface.co/datasets/anonymousneurips12345/PDExplorer-Bench.FSI-pde-dataset
Multi-Physics Fluid-Solid Interaction Dataset
From Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs
How to Download ?from huggingface_hub import snapshot_download
folder_path = snapshot_download(
repo_id="ashiq24/FSI-pde-dataset",
repo_type="dataset",
allow_patterns=["fsi-data/*"]
)
Dataset Description: Fluid-Solid Interaction Simulations (fsi-data)
This dataset contains simulations of fluid dynamics (using the Navier-Stokes… See the full description on the dataset page: https://huggingface.co/datasets/ashiq24/FSI-pde-dataset.