id int64 0 2M | kind stringclasses 3
values | split stringclasses 1
value | gt int64 1 1 | mask int64 1 1 | source int64 1 1 | bc int64 0 0 | meta int64 1 1 | available_budgets stringclasses 1
value | complete_expected int64 1 1 |
|---|---|---|---|---|---|---|---|---|---|
0 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
1 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
2 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
3 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
4 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
5 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
6 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
7 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
8 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
9 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
10 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
11 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
12 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
13 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
14 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
15 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
16 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
17 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
18 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
19 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
20 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
21 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
22 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
23 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
24 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
25 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
26 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
27 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
28 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
29 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
30 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
31 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
32 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
33 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
34 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
35 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
36 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
37 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
38 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
39 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
40 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
41 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
42 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
43 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
44 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
45 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
46 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
47 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
48 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
49 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
50 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
51 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
52 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
53 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
54 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
55 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
56 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
57 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
58 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
59 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
60 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
61 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
62 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
63 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
64 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
65 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
66 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
67 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
68 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
69 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
70 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
71 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
72 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
73 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
74 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
75 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
76 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
77 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
78 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
79 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
80 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
81 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
82 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
83 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
84 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
85 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
86 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
87 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
88 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
89 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
90 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
91 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
92 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
93 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
94 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
95 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
96 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
97 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
98 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
99 | laplace | expanded_pool | 1 | 1 | 1 | 0 | 1 | 1 2 4 8 16 32 | 1 |
PDEZoo: 2D and 3D elliptic PDE datasets
This dataset accompanies MC² and provides manufactured PDE specifications, analytic solution fields, domain masks, source fields, and multi-budget Walk-on-Spheres estimates. The 2D and 3D collections are separate named subsets within one dataset repository.
Release status: uploading. Inventories and the archive plan describe the staged collection; only archives listed in uploaded_shards.jsonl have been verified on the Hub. See release_status.json for progress. Downloadable tensor data are being added incrementally. Real-geometry payloads remain held for license review. The synthetic dataset uses CC BY 4.0 and release code uses MIT.
Collections
| Subset | Manifest cases | Cases complete at all expected budgets | Resolution | Stored budgets |
|---|---|---|---|---|
2d_original |
100,000 | 100,000 | 256² | 1, 2, 4, 8, 16, 32 |
2d_test |
5,000 | 4,946 | 256² | 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072 |
2d_unseen_atoms |
500 | 500 | 256² | 8, 16, 32, 64, 128, 256, 512, 1024 |
3d_analytic_train |
20,000 | 20,000 | 64³ | 1, 2, 4, 8, 16, 32 |
3d_analytic_test |
500 | 500 | 64³ | 8, 32, 128 |
3d_real_train |
8,000 | 6,517 | 64³ | 1, 2, 4, 8, 16, 32 |
3d_real_test |
500 | 500 | 64³ | 8, 32, 128 |
3d_implicit_test |
400 | 400 | 64³ | 8, 32, 128 |
2d_expanded |
2,000,000 | 2,000,000 | 256² | 1, 2, 4, 8, 16, 32 |
“Complete” here means that the required field and budget filenames were present, not that every tensor was finite or every solve converged. Archive checksums are verified during packaging. Pilot validation checks representative tensor shapes and finite values within masks. Full numerical validation of every tensor has not been performed.
Reproducing the paper splits
The headline 2D model uses 2d_original, with 95,041 training and 4,959 validation cases. 2d_expanded is a separate 2M generated pool and is not the training set used for the headline model. Case IDs must be namespaced by subset.
The 2D test manifest contains 5,000 cases. Forty-nine have no stored WoS solutions, and five additional cases lack some high-budget solutions. Availability is explicit per case; do not silently treat missing budgets as zero-valued fields.
The 3D analytic pool contains 20,000 cases, split 19,000/1,000 for training/validation. Real-geometry training has 8,000 declared cases on 1,600 meshes, but only 117 of its 1,600 biharmonic cases have stored solutions. The other 1,483 remain specification/ground-truth records. Fine-tuning also filters masks with fewer than 100 interior voxels, leaving 6,108 usable training and 318 validation cases in the real-data component. See the eligibility manifest for per-case records.
Real-geometry test data contain five problems on each of 100 meshes. Training/test mesh IDs are disjoint. Case-level training/validation splits do not imply geometry-disjoint validation. The implicit test collection contains 200 gyroid and 200 blended-blob problems and omits biharmonic.
Loading
The Hugging Face configurations expose lightweight case inventories. They do not automatically materialize the tensor archives. Use its inventory to select cases and shard_plan.jsonl to locate the corresponding archive. Download the selected archive with huggingface_hub.hf_hub_download, then use the supplied loader:
from huggingface_hub import hf_hub_download
from load_shard import load_case
archive = hf_hub_download(
repo_id="ethanhibiscus/PDEZoo", repo_type="dataset",
filename="data/3d_implicit_test/000/000000.tar.gz",
)
sample = load_case(archive, case_id=0, budget=8)
u = sample["gt"]
noisy = sample["noisy"]
mask = sample["masks"] > 0.5
Use Python 3.10+ and PyTorch with weights_only=True support. Tensor bytes are preserved from the evaluation data. No normalization or clipping is applied by the release tooling. Always use the domain mask for metrics. See SCHEMA.md for file conventions, equations, splits and missing-data semantics.
Attribution and real-model geometry
Real-model geometry originates from Thingi10K. Original authors, model IDs, license strings and source links are retained under attribution/. These assets have heterogeneous licenses, including non-commercial and no-derivatives terms. No blanket synthetic-data license should be applied to those assets. Raw STL files are not bundled in this preparation; meshes/<file_id>.stl is a portable external dependency.
The geometry implementation centers the mesh bounding box and scales its longest side to 1.8. Use the accompanying PDEZoo-3D implementation to reproduce geometric queries rather than treating a voxel mask as an exact surface.
Known numerical limitations
Finite walk caps, shell termination and source interpolation can introduce numerical bias. Stored 2D biharmonic solves include a finite inner-walk cap. Increasing the walk budget alone does not remove all approximation error. Resolution and thin geometry also affect the represented fields. The data are not a claim that every stored WoS field has converged.
License
The original synthetic PDEZoo dataset is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Copyright 2026 Ethan Hsu. See LICENSE for the full terms.
Please attribute the dataset to Ethan Hsu, link to this repository and the license, and indicate any changes as required by CC BY 4.0.
Accompanying original release code is licensed separately under MIT.
Third-party geometry and real-geometry assets retain their applicable source terms; this grant does not relicense them. Real-geometry payloads remain on hold for redistribution review.
- Downloads last month
- 2,141