ScireX FNO · Darcy flow 2D (physics-only, extra-fields run)

A trained FNO neural operator from the open-source scirex library (JAX/Flax) for the Darcy flow 2D (physics-only, extra-fields run) benchmark. The weights are the last-epoch weights of the run described below and are stored as model.safetensors.

Results

Lower is better, except for Spearman correlations. Figures are those of the ScireX results table and benchmark pages: benchmark page and the GitHub README.

Inputs and outputs

Input: permeability field on an 85 x 85 grid (7,225 points). Output: pressure field on the same grid. 1000 training and 200 test samples. The normalisation statistics are in config.json; the weights are unusable without them.

Training data

Trained on the Darcy flow data of Li et al. (ICLR 2021), Zenodo record 12784353, licensed under CC BY 4.0.

Training

FNO, 2,836,281 real parameters. Complex-aware AdamW, lr 1e-3 halved 4 times over the run, no weight decay, no clipping, batch 20, 100,000 steps. Label-free: trained on the Q4 Ritz energy only, with no solution labels. Normalisation is fitted on the training coefficient fields only. Seed 0, final-epoch weights; no checkpoint is chosen on the test set. The exact Q4 solve of the same formulation has a floor of 0.31% relative L2. This run sees 10k coefficient fields in total (the 1000 released fields plus sampled, unlabelled ones). Training time: ~14 min per run.

Full setup: doc/benchmarks/darcy_physics/results/comparative.md.

How to use

hf download zenteiq-ai/scirex-fno-darcy-physics-extra-fields --local-dir ckpt/scirex-fno-darcy-physics-extra-fields

Evaluate on the Darcy 2D test set as described on the benchmark page. Check your install against sample.safetensors, which holds one test input (input) and the model's expected output (expected_output). config.json holds the model settings and the normalisation statistics.

Reproduce

From a checkout of the GitHub repository at tag v1.0.0:

hf download zenteiq-ai/scirex-fno-darcy-physics-extra-fields --local-dir ckpt/scirex-fno-darcy-physics-extra-fields
python scripts/benchmarks/darcy_physics/infer.py --checkpoint ckpt/scirex-fno-darcy-physics-extra-fields --sample   # no dataset needed
python scripts/benchmarks/darcy_physics/infer.py \
    --checkpoint ckpt/scirex-fno-darcy-physics-extra-fields \
    --data-dir $DATA_ROOT/darcy

$DATA_ROOT is the folder that holds the benchmark datasets (see reproducibility.md).

Results table for this benchmark: comparative.md.

Limitations

Valid only within the trained input ranges of the benchmark data. Not for safety-critical design without separate validation. Bug reports: GitHub Issues.

Other ScireX checkpoints

Same benchmark, other models:

Other Darcy runs of the same model:

• Darcy flow 2D (data-driven): zenteiq-ai/scirex-fno-darcy

Same model, other benchmarks:

Licence and citation

The weights are released under the Apache License 2.0 (see LICENSE; dataset credit in NOTICE). The code is LGPL-3.0. Cite the software through the CITATION.cff in the GitHub repository and the architecture paper:

• FNO: Li et al., ICLR 2021, arXiv:2010.08895