Fluid Dynamics Simulation on Navier-Stokes (NS) nu=10^-5 at 64x64 unified-protocol (test)
2.84Relative L2 Error (Test)Transformer (NSL, full softmax)
Evaluation Results
| Method | Links | |
|---|---|---|
| Transformer (NSL, full softmax)Params=4.38 M, Provenance=Wu et al. [2024b]2026.05 | 2.84 | |
| SpectraNet, M=20Params=5.37 M, Provenance=this work (J19), M=202026.05 | 7.87 | |
| SpectraNet, M=16Params=3.60 M, Provenance=this work (J18), M=162026.05 | 7.92 | |
| SpectraNet (headline)Params=2.04 M, Provenance=this work (J23)2026.05 | 8.22 | |
| SpectraNet, w=32 + residual, seed 0Params=2.12 M, Provenance=this work (J14), Width=32, Config=residual, Seed=02026.05 | 8.36 | |
| SpectraNet, w=48 plainParams=4.78 M, Provenance=this work (3190), Width=48, Config=plain2026.05 | 8.36 | |
| SpectraNet, w=32 + spectral envelopeParams=2.12 M, Provenance=this work (J24), Width=32, Config=spectral envelope2026.05 | 8.49 | |
| SpectraNet, w=32 + residual, seed 1Params=2.12 M, Provenance=this work (J3222), Width=32, Config=residual, Seed=12026.05 | 8.5 | |
| SpectraNet, w=32 + grouped channel-mixing MLPParams=1.97 M, Provenance=this work (J21), Width=32, Config=grouped channel-mixing MLP2026.05 | 8.54 | |
| SpectraNet, w=64 plainParams=8.49 M, Provenance=this work (3199), Width=64, Config=plain2026.05 | 8.69 | |
| SpectraNet, w=32 + disk truncationParams=2.12 M, Provenance=this work (J20), Width=32, Config=disk truncation2026.05 | 8.93 | |
| SpectraNet, w=20 plainParams=0.83 M, Provenance=this work (3187), Width=20, Config=plain2026.05 | 9.41 | |
| SpectraNet, 3D-spectral variantParams=8.57 M, Provenance=this work (3188)2026.05 | 10.06 | |
| FNO seed 0Params=4.75 M, Provenance=Li et al. [2021], Seed=02026.05 | 10.24 | |
| FNO seed 1Params=4.75 M, Provenance=Li et al. [2021] (seed 1), Seed=12026.05 | 10.69 | |
| Galerkin TransformerParams=4.39 M, Provenance=Cao [2021]2026.05 | 10.97 | |
| U-FNOParams=39.38 M, Provenance=Wen et al. [2022]2026.05 | 12.18 | |
| U-Net (NSL)Params=276.96 M, Provenance=Wu et al. [2024b]2026.05 | 13.87 | |
| FactFormerParams=3.47 M, Provenance=Li et al. [2023b]2026.05 | 16.39 | |
| U-NOParams=50.80 M, Provenance=Rahman et al. [2023]2026.05 | 16.97 | |
| SpectraNet, single-shot variantParams=14.49 M, Provenance=this work (3123)2026.05 | 19.42 | |
| MWTParams=0.08 M, Provenance=Gupta et al. [2021]2026.05 | 19.44 | |
| LSMParams=19.20 M, Provenance=Wu et al. [2023]2026.05 | 19.51 | |
| OFormerParams=0.55 M, Provenance=Li et al. [2023a]2026.05 | 21.62 | |
| TransolverParams=11.20 M, Provenance=Wu et al. [2024a]2026.05 | 22.47 | |
| F-FNOParams=0.16 M, Provenance=Tran et al. [2023]2026.05 | 23.31 | |
| GNOTParams=1.23 M, Provenance=Hao et al. [2023]2026.05 | 23.62 | |
| KNO2dParams=0.26 M, Provenance=Xiong et al. [2024]2026.05 | 30.92 | |
| CNOParams=2.03 M, Provenance=Raonic et al. [2023]2026.05 | 32.59 | |
| ONOParams=0.12 M, Provenance=Xiao et al. [2024]2026.05 | 34.43 | |
| Persistence (trivial floor)Params=0, Provenance=this work2026.05 | 74.81 |