pdebench-fno-audit/fno-weights

PDEBench FNO Re-evaluation: Model Weights

Pre-trained model checkpoints from "The Unrealized Potential of Fourier Neural Operators: A Systematic Re-evaluation of PDEBench Baselines" (NeurIPS 2026 E&D Track submission).

Files

File	Test	PDE	nRMSE	Improvement
test_01_best_model.pt	1	Advection β=1.0	4.68e-3	2.07×
test_02_best_model.pt	2	Burgers ν=0.1	1.41e-3	2.05×
test_03_best_model.pt	3	1D Diff-React ν=0.5	1.23e-3	1.13×
test_04_best_model.pt	4	Burgers ν=0.001	1.08e-2	2.69×
test_05_best_model.pt	5	1D Comp NS η=ζ=0.01	1.56e-2	6.08×
test_06_best_model.pt	6	1D Comp NS Shock	1.32e-2	3.57×
test_07_best_model.pt	7	Advection β=0.1	3.29e-3	2.34×
test_08_best_model.pt	8	Advection β=0.4	4.60e-3	2.18×
test_09_best_model.pt	9	Advection β=4.0	4.65e-3	1.44×
test_10_best_model.pt	10	Burgers ν=0.01	4.16e-3	1.87×
test_11_best_model.pt	11	Burgers ν=1.0	4.32e-3	0.93× (miss)
test_13_best_model.pt	13	1D Diff-React ν=2.0	3.45e-4	2.03×
test_16_best_model.pt	16	Diff-Sorp	9.95e-4	1.71×
test_17_best_model.pt	17	1D Comp NS η=ζ=0.1	6.76e-3	10.05×
test_19_best_model.pt	19	1D Comp NS Inv Rand	3.00e-2	4.00×
test_20_best_model.pt	20	1D Comp NS Inv Outg	2.36e-1	28.44×
test_21_best_model.pt	21	Darcy β=0.01	2.67e-1	9.36×
test_22_best_model.pt	22	Darcy β=0.1	1.18e-1	1.87×
test_23_best_model.pt	23	Darcy β=1.0	2.77e-2	2.31×
test_24_best_model.pt	24	Darcy β=10.0	1.15e-2	1.04×
test_25_best_model.pt	25	Darcy β=100.0	9.50e-3	0.67× (miss)
test_26_best_model.pt	26	2D Diff-React	2.74e-3	43.75×
test_27_best_model.pt	27	2D SWE	1.89e-3	2.33×
test_29_best_model.pt	29	2D Comp CFD M=0.1, η=ζ=0.01	1.86e-2	9.13×
test_29_M01_Eta01_best_model.pt	29 (supp.)	2D Comp CFD M=0.1, η=ζ=0.1	5.31e-2	6.78×
test_29_M10_Eta001_best_model.pt	29 (supp.)	2D Comp CFD M=1.0, η=ζ=0.01	5.19e-2	1.85×
test_29_M10_Eta01_best_model.pt	29 (supp.)	2D Comp CFD M=1.0, η=ζ=0.1	4.17e-2	2.35×
test_28_best_model.pt	28 (exploratory)	2D Incompressible NS, Re≈1000	2.46e-1	1.05×

The supp. entries are three additional 2D CFD configurations beyond the headline 24, used in the OmniArch contextual comparison. Test 28 is the exploratory 2D incompressible NS analysis (vorticity-Poisson FNO; see paper Section 8); its baseline (0.2574) comes from the OmniArch reproduction of the PDEBench FNO baseline.

Seed-variance ablation (seed_ablation/)

Two additional training seeds (123, 456) for four borderline rows:

File	Test	nRMSE (per-timestep)
seed_ablation/test_11_seed123_best_model.pt	11	4.51e-3
seed_ablation/test_11_seed456_best_model.pt	11	4.23e-3
seed_ablation/test_24_seed123_best_model.pt	24	1.15e-2
seed_ablation/test_24_seed456_best_model.pt	24	1.11e-2
seed_ablation/test_25_seed123_best_model.pt	25	1.10e-2
seed_ablation/test_25_seed456_best_model.pt	25	1.17e-2
seed_ablation/test_26_seed123_best_model.pt	26	2.90e-3
seed_ablation/test_26_seed456_best_model.pt	26	2.98e-3

The seed-42 weights for the same rows are at the headline paths (test_NN_best_model.pt).

Usage

import torch
from standalone.models import FNO1d_AR  # from the code repo

model = FNO1d_AR(nc=1, modes=12, width=32, init_step=5, n_layers=4)
model.load_state_dict(torch.load("test_13_best_model.pt", weights_only=True))

Baselines

All improvement factors computed against PDEBench FNO (arXiv:2210.07182v7).