PDE-OBS benchmark · PartialObs-PDEBench

One manuscript, controlled claims

This repository now treats PDE-OBS: A Controlled Partial-Observation Benchmark for PDE Dynamics as the only manuscript in scope. Its contribution is the dataset design, task/split/metric protocol, anchor leaderboard, difficulty analysis, and one-line tooling. Semantic-ID, large world-model, and foundation-model method claims are separate work.

Implementation status: machine-verifiable protocol, one-line generation/training/inference/evaluation/presets, strict storage and split checks, anchor configs, per-sample failure records, Linux server instructions, and SeaWulf workflows are checked in.

Scientific release status: the bundled numerical solvers are compact development references, not convergence-validated paper ground truth. A paper release must pass the numerical-validation gate against trusted high-resolution solvers and publish that report with the data manifest and exact Git revision.

Seven tasks, honest status

Executable field tasks

Sparse recovery, forward prediction, inverse prediction, and time-dependent rollout/world modeling run end to end.

Lightweight anchor protocols

Semantic retrieval and solver routing expose baseline APIs/metrics; foundation transfer is a protocol/component scaffold. They are not advertised as new completed methods.

Official views are IID plus boundary, setting, parameter, combination, mask, and time-horizon OOD. The paper contract requires 15 difficulty analyses, including spectral, scaling, ambiguity, routing, and qualitative failure studies.

Factorized dataset

Equations

Darcy, Poisson, Helmholtz, heat, reaction-diffusion, Burgers, and Navier-Stokes.

Boundary protocols

Dirichlet/no-slip, Neumann/free-slip, periodic, and family-conditioned mixed/Robin/obstacle.

Condition settings

Three GRFs, two Fourier mixtures, blobs, blocks, a level set, a dipole/vortex pair, and a front/ring/shock.

Physical regimes

Low, medium, and high family-specific parameters, stored explicitly in sample metadata.

The full design contains 280 macro cases and 560,000 balanced samples. Nested tiny, debug, signal, medium, and full tiers let the same commands scale from unit tests to a paper campaign.

Partial observations and OOD evaluation

The main 128×128 training view contains exactly 500 observed spatial points. Evaluation covers random 1%, 3%, 5%, and 10% observations, regular grids, missing blocks, lines, boundary-only sensors, and clustered sensors. Official views include IID, boundary-, setting-, parameter-, combination-, mask-, and time-horizon OOD tests.

Matched-mask training protocol

The primary IID recovery table trains every normal operator baseline independently for each PDE family and each observation protocol. Its training mask equals its evaluation mask; checkpoints are not reused across masks. All nine masks are deterministic views of the same physical HDF5 records, so this policy does not create nine copies of the dataset.

Nine observation views

Random 1%, 3%, 5%, and 10%; regular grid; missing block; line sensors; boundary sensors; and clustered sensors.

Method-specific reuse

RBF requires no fit. Gappy POD fits one training-only basis per PDE. DiffusionPDE and FunDPS use one frozen upstream prior per compatible PDE distribution and vary only the observation operator at inference.

Separate secondary test: training on random 3% and testing the other eight masks remains the mask-transfer/OOD analysis. It is not a substitute for the nine separately trained matched-mask IID rows.

Campaign size and ten-day planning scenario

Scenario	Result cells	Preparation jobs	Interpretation
Medium, all 10 slots x 7 PDEs x 9 masks	630	511-525 with PINN/PINO at 3 seeds	Recommended complete comparison after adapters and pilots
Full hybrid anchors	231	84	RBF/POD on all masks; five heavier anchors on random 1%, random 3%, and missing block

Medium contains 140,000 records (20,000 per PDE, approximately 14,000 per PDE in the optimizer split). Full contains 560,000 records (80,000 per PDE, exactly 56,000 training records per PDE). The quoted 12-A6000 GPU-hour ranges are unmeasured planning assumptions, not SeaWulf/A100 runtime promises; every platform needs a measured pilot.

Executable status: this repository currently provides RBF and compact-reference U-Net/FNO/CNO adapters. Gappy POD, DeepONet, PINN/PINO, Transolver/GNOT, DiffusionPDE, and FunDPS remain explicit integration targets. The Builder shows their counts and blockers but does not fabricate commands for them. A single all-boundary Navier-Stokes checkpoint also requires a standardized state representation because periodic data store vorticity while bounded cases store velocity.

Open the complete observation-training and compute protocol.

Run from Git

git clone https://github.com/ru1ch3n/PartialObs--PDEBench.git
cd PartialObs--PDEBench
python -m pip install -e ".[train,test]"
pdeobs doctor
pdeobs protocol --check
pdeobs generate --tier signal --root ./data --num-workers 8
pdeobs train --task sparse_recovery --model fno \
  --data ./data/pdeobs_signal --split iid --mask random_3pct \
  --output runs/fno_sparse_recovery

See the benchmark-paper contract, numerical/data protocol, numerical-validation gate, method extension guide, generate a tailored configuration in the interactive Benchmark Builder, or use the Linux and SeaWulf quick starts.