---
license: cc-by-4.0
task_categories:
  - other
tags:
  - partial-differential-equations
  - scientific-machine-learning
  - neural-operators
  - partial-observations
  - benchmark
size_categories:
  - 100K<n<1M
configs:
  - config_name: default
    data_files: data/**/*.h5
---

# PDE-OBS: physical records

Complete numerical solutions for the seven PDE families of the PDE-OBS benchmark, generated by the
solvers in the benchmark's own code. Nothing was downloaded, scraped or converted from another corpus,
and the same specification reproduces the same record.

This repository accompanies an anonymous submission under double-blind review.

## What is here

| Axis | Value |
|---|---|
| PDE families | Darcy, Poisson, Helmholtz (stationary); Heat, reaction–diffusion, Burgers, Navier–Stokes (temporal) |
| Boundary protocols | Dirichlet, Neumann, periodic, Robin with obstacle |
| Condition-field constructions | `smooth_grf`, `medium_grf`, `rough_grf`, `low_frequency_fourier`, `multi_frequency_fourier`, `gaussian_blobs`, `piecewise_blocks`, `threshold_level_set`, `front_ring_shock`, `dipole_vortex_pair` |
| Records | 2,000 per (family, boundary, construction), divided 667 / 667 / 666 across the three physical regimes; 280 such combinations in 840 regime nodes, **560,000 records** in total |
| Resolution | 128 × 128; 1 stored frame for stationary families, 15 equally spaced states for temporal families |
| Format | HDF5 shards, channel-last, float32, gzip level 4. A regime node's 667 or 666 records are written as 200 / 200 / 200 / 67 or 66, so the fourth shard of every node is a short one |
| Size | 3,360 shards, 244 GB, plus per-shard sidecars |

**The paper-evaluated slice** is the subset under `data/<family>/<paper boundary>/smooth_grf/`
(Dirichlet for the stationary families, periodic for the temporal ones): 14,000 records in 84 shards,
6.5 GB with sidecars. Everything else is the rest of the factorial design the benchmark supports.

Each shard stores `condition [N,H,W,1]`, `trajectory [N,T,H,W,1]`, `geometry [N,H,W,1]` and one JSON
metadata string per record carrying its identity, family, boundary, construction, regime, seeds and
stored times. Beside every shard: `.manifest.json` (schema, record count, byte size, SHA-256),
`.sha256`, `.quality.json` (the generation quality gates), and `.metadata.json` / `.metadata.csv`
exports of the per-record metadata.

**Observation masks are not stored here.** They are constructed at access time from the record
identity and the protocol name, which is what lets one physical record serve every observation
pattern. The benchmark code defines the nine frozen views and their exact observed-cell counts.

## How to use it

Two checksum manifests are published in this repository. Both follow the benchmark's release-manifest
v1 contract (schema version 1, one entry per file with its SHA-256, byte size and URL) and both list
the sidecars the loader's verify mode checks against.

| Manifest | Contents | Size |
|---|---|---:|
| `release_manifest.json` | the paper-evaluated slice, 84 shards + 252 sidecars | 6.5 GB |
| `release_manifest_full.json` | the complete corpus, 3,360 shards + 10,080 sidecars | 244 GB |

With the benchmark's downloader, which validates the manifest before fetching, resumes interrupted
files and verifies every file's SHA-256 on arrival:

```bash
pdeobs download --tier full --output ./pdeobs-data \
    --manifest https://huggingface.co/datasets/PDE-OBS/pdeobs-data/resolve/main/release_manifest.json
```

Then build a task instance:

```python
from pdeobs import api

data = api.load_dataset("./pdeobs-data", verify=True)      # checks every shard against its sidecars
obs = api.make_observation("paper:R50")                    # one of the nine frozen views
package, targets = api.inference_input_from_dataset(data, obs, task="recovery")
```

Or fetch the raw files without the benchmark:

```python
from huggingface_hub import snapshot_download
root = snapshot_download("PDE-OBS/pdeobs-data", repo_type="dataset",
                         allow_patterns=["data/poisson/dirichlet/smooth_grf/*"])
```

## Provenance and limits

- Generated by the benchmark's deterministic solvers with seed 20260804; elliptic solves use relative
  tolerance 1e-9 and raise rather than returning a partial solution.
- Every record passed the generation quality gates: all stored values finite, geometry binary error
  ≤ 1e-6, normalized initial-condition / boundary-condition / initial-transition defects
  ≤ 1e-6 / 1e-4 / 5e-6, and a normalized PDE residual ≤ 0.05.
- These are discrete-residual checks. **No independent reference-solution or grid-convergence study
  is included**, so the records are not certified against an external numerical reference.
- The Dirichlet families impose zero values on the outer stored layer of a cell-centered grid; that
  boundary placement is part of the numerical specification and differs from an endpoint-coordinate
  convention.
- Parameter values are unitless numbers on the unit domain; no SI units are assigned.
- Every published shard's SHA-256 equals its `.sha256` sidecar and its entry in the two release manifests;
  all 3,360 were re-hashed before upload and every file was verified on the Hub after upload.

## De-identification

The shards were re-emitted before publication with the generation provenance de-identified: the output
path, interpreter path, host name and scheduler block inside each shard's `spec_json` attribute, the
per-record `git_commit`, and the same fields in every sidecar were replaced by placeholders. The
numerical datasets (`condition`, `trajectory`, `geometry`) were copied chunk by chunk without
recompression and are bit-identical to the generated corpus. Because the attributes changed, the
published shard digests differ from the generation-time ones; `scrub-manifest.json` lists the rewritten
files with their published SHA-256 (the correspondence to the generation-time digests is kept in the
benchmark repository, beside the results). `summary.json` and `summary.quality.json` / `summary.quality.csv`
are the generation-time corpus summary and quality tables with the same fields de-identified, the data-root
label reduced to `numerics-full-t15`, and their shard digests re-pointed to the published files.

## Citation

Anonymous submission under review. Please cite the paper once it is public.