SpectraNet

Parameter-efficient autoregressive spectral U-Net for PDE surrogates.

SpectraNet bridges spectral operator learning and U-Net hierarchies through a Residual-Target Spectral Block and a Semigroup-Consistency Loss. On the canonical Navier–Stokes ν = 10⁻⁵ benchmark it reaches 0.0822 test L² with 2,040,705 parameters — 2.33× fewer than canonical FNO (4.75 M, L² = 0.1024) at ≈20 % lower error. The architectural advantage transports to 5 of 6 additional dataset/regime combinations and strengthens at higher resolution (native 128²: SpectraNet 0.0724 vs FNO 0.3080).

The accompanying paper is Bridging Spectral Operator Learning and U-Net Hierarchies: SpectraNet for Stable Autoregressive PDE Surrogates (Hernández Noguera, Ferdaus, Ioup, Abdelguerfi, Simeonov; 2026). The compiled PDF is at paper/paper.pdf.

Quick start

# install
pip install -e .

# canonical reproduction (NS ν = 1e-5, 64², ~100 min on a single H100)
python scripts/train_spectranet.py \
       --config configs/spectranet_ns_v1e5.yaml \
       --data_root ./data
# → prints best_test_l2 ≈ 0.0822

# eval-only path (uses shipped pretrained weights)
python scripts/eval_long_horizon.py \
       --ckpt   checkpoints/spectranet_ns_v1e5_canonical_best.pt \
       --model_kind ar2d

Repository layout

Path	Purpose
spectranet/	Installable Python package: the SpectraNet model, spectral and KAN layers, data loaders, losses, utilities.
scripts/	One trainer (train_spectranet.py) for SpectraNet across all 7 datasets, one trainer (train_baseline.py) for the 17 baselines, four eval scripts (eval_{lipschitz,long_horizon,resolution_transfer,cross_viscosity}.py), the persistence floor, the in-house 128² generator, and the figure-regeneration scripts under scripts/figures/.
baselines/	Adapter scripts that wire each third-party operator library to our gold-standard protocol, plus install_baselines.sh that git clones the upstream repos at pinned commits.
timing/	GPU + CPU inference-timing harness used to produce Figure 4 and the timing-section appendix.
configs/	One YAML per canonical run (per-dataset SpectraNet config + per-baseline config).
results/	Canonical CSVs that back every table and figure in the paper (leaderboard, cross-PDE, multi-seed, Lipschitz, long-horizon, resolution transfer, …).
figures/	The exact PDF figures embedded in the paper, regenerable from results/ via scripts/figures/.
checkpoints/	Pretrained weights for the canonical SpectraNet on every dataset, the decorated-head ablation variant, the bottleneck-widened sanity check, the canonical FNO, and the canonical Transformer.
data/	Pointer-only README. The in-house native-128² dataset is hosted on Zenodo (see docs/ARTIFACTS.md); other datasets are public — see docs/DATA.md for download instructions.
paper/paper.pdf	The compiled paper PDF.
tests/	Smoke tests you can run without an H100 or a full dataset (param-count, imports, eval).
slurm/	H100 sbatch templates for cluster reproduction.
docs/	REPRODUCING.md (paper-claim → command map), DATA.md, BASELINES.md, ARCHITECTURE.md, ARTIFACTS.md.

Reproducing every paper number

Read docs/REPRODUCING.md. It maps every table and figure in the paper to the exact command sequence that regenerates the underlying CSV and the rendered PDF.

Datasets

• Navier–Stokes ν = 10⁻⁵, 10⁻⁴, 10⁻³ at 64²: public, from the FNO release (Li et al., 2020). See docs/DATA.md for the download URL.
• Shallow Water, Diffusion–Reaction: public, from PDEBench. See docs/DATA.md.
• Active Matter: public, from The Well. See docs/DATA.md.
• Navier–Stokes ν = 10⁻⁵ at 128²: in-house. Hosted on Zenodo — see docs/ARTIFACTS.md for the DOI. Equivalently, the dataset is regenerable bit-identically by running scripts/generate_ns_128.py (~6 hours on a single H100); provenance and protocol are documented in docs/DATA.md.

Baselines

The 17 baseline operators come from eight upstream repositories (NSL, CNO, FactFormer, GNOT, KoopmanLab, OFormer, ONO, Transolver). To respect upstream licenses we do not vendor their code; instead, run bash baselines/install_baselines.sh to clone each at the pinned commit we used. Our adapter scripts in baselines/ns_*.py then wire each operator to the gold-standard training protocol described in the paper.

Citation

@misc{hernandez2026spectranet,
  title  = {Bridging Spectral Operator Learning and U-Net Hierarchies:
            {SpectraNet} for Stable Autoregressive {PDE} Surrogates},
  author = {Hern{\'a}ndez Noguera, Enrique and Ferdaus, Md Meftahul and
            Ioup, Elias and Abdelguerfi, Mahdi and Simeonov, Julian},
  year   = {2026},
  url    = {https://github.com/Enrikkk/spectranet}
}

License

MIT. See LICENSE.

Authors

• Enrique Hernández Noguera¹ · ehernan8@uno.edu
• Md Meftahul Ferdaus¹ · mferdaus@uno.edu
• Elias Ioup²
• Mahdi Abdelguerfi¹
• Julian Simeonov²

¹ University of New Orleans, New Orleans, LA, USA ² Naval Research Laboratory, Stennis Space Center, MS, USA