SGON (Sheaf-Glue Operator Network)

This repo contains an SGON-style operator learning prototype for the Darcy 1D dataset. It represents the solution using local patch coefficients and decodes with a partition of unity.

For fixed sensors on a fixed 1D grid, we found that adding a small 1D convolutional backbone over the input (--u_backbone) substantially improves accuracy.

Quickstart:

1. Create a virtualenv and install deps.
2. Run the training script.

Install:

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Recommended training config (fixed sensors):

python scripts/train_darcy1d_sgon.py \
  --multiscale --n_patches_coarse 8 --n_patches_mid 16 --n_patches 32 \
  --glue_mode poly --poly_k 3 \
  --attention_pool \
  --u_backbone

Noise/accuracy evaluation:

python scripts/eval_noise.py \
  --models sgon deeponet \
  --ckpts <sgon_best.pt> <deeponet_best.pt> \
  --labels SGON DeepONet \
  --noise_levels 0.0 0.02 0.04 0.06 0.08 0.1 \
  --n_eval 1024 \
  --batch_size 256 \
  --plot

Finding (no noise): on Data/darcy_1d_data/darcy_1d_dataset_501 with sensor_size=64 and n_eval=1024, we observed:

Model	Test rel L2 (mean)	Test MSE (mean)
SGON (--u_backbone)	1.55e-3	3.79e-8
DeepONet	4.19e-3	3.22e-7