---
license: mit
tags:
  - fno
  - neural-operator
  - pdebench
  - pde
  - scientific-ml
---

# 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

```python
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).