# Fluid Dynamics Simulation on Navier-Stokes (NS) nu=10^-5 at 64x64 unified-protocol (test) Source: [Fluid Dynamics Simulation on Navier-Stokes (NS) nu=10^-5 at 64x64 unified-protocol (test)]() Collection index: [llms.txt]() Data updated: 2026-05-12T11:16:04.531Z Evaluation of fluid dynamics simulation performance on the Navier-Stokes dataset configured with viscosity nu=10^-5 and resolution 64x64 under the unified protocol, measured on the test set. A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. | Scope | Recorded value | | --- | --- | | Task | Fluid Dynamics Simulation | | Dataset (including any stated split) | Navier-Stokes (NS) nu=10^-5 at 64x64 unified-protocol (test) | | Metric | Relative L2 Error (Test) | | Unit | PERCENT | | Direction | Lower is better | | Results loaded | 31 of 31 | | Coverage | All results currently returned for this benchmark | Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol. ## Metrics - [Relative L2 Error (Test)](): Lower is better; unit: PERCENT. ## Recorded results | Method | Relative L2 Error (Test) | Result date | Report paper | | --- | --- | --- | --- | | Transformer (NSL, full softmax) | 2.84 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, M=20 | 7.87 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, M=16 | 7.92 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet (headline) | 8.22 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=32 + residual, seed 0 | 8.36 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=48 plain | 8.36 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=32 + spectral envelope | 8.49 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=32 + residual, seed 1 | 8.5 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=32 + grouped channel-mixing MLP | 8.54 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=64 plain | 8.69 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=32 + disk truncation | 8.93 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, w=20 plain | 9.41 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, 3D-spectral variant | 10.06 | Not recorded | 6a02b45bdbc836b87d8249c8 | | FNO seed 0 | 10.24 | Not recorded | 6a02b45bdbc836b87d8249c8 | | FNO seed 1 | 10.69 | Not recorded | 6a02b45bdbc836b87d8249c8 | | Galerkin Transformer | 10.97 | Not recorded | 6a02b45bdbc836b87d8249c8 | | U-FNO | 12.18 | Not recorded | 6a02b45bdbc836b87d8249c8 | | U-Net (NSL) | 13.87 | Not recorded | 6a02b45bdbc836b87d8249c8 | | FactFormer | 16.39 | Not recorded | 6a02b45bdbc836b87d8249c8 | | U-NO | 16.97 | Not recorded | 6a02b45bdbc836b87d8249c8 | | SpectraNet, single-shot variant | 19.42 | Not recorded | 6a02b45bdbc836b87d8249c8 | | MWT | 19.44 | Not recorded | 6a02b45bdbc836b87d8249c8 | | LSM | 19.51 | Not recorded | 6a02b45bdbc836b87d8249c8 | | OFormer | 21.62 | Not recorded | 6a02b45bdbc836b87d8249c8 | | Transolver | 22.47 | Not recorded | 6a02b45bdbc836b87d8249c8 | | F-FNO | 23.31 | Not recorded | 6a02b45bdbc836b87d8249c8 | | GNOT | 23.62 | Not recorded | 6a02b45bdbc836b87d8249c8 | | KNO2d | 30.92 | Not recorded | 6a02b45bdbc836b87d8249c8 | | CNO | 32.59 | Not recorded | 6a02b45bdbc836b87d8249c8 | | ONO | 34.43 | Not recorded | 6a02b45bdbc836b87d8249c8 | | Persistence (trivial floor) | 74.81 | Not recorded | 6a02b45bdbc836b87d8249c8 | ### Transformer (NSL, full softmax) Relative L2 Error (Test): 2.84. Result ID: 6a030be547f34ce924e6c8a8. [Reporting paper]() Recorded evaluation configuration: {"Params":"4.38 M","Provenance":"Wu et al. \[2024b\]"}. This record does not assert independent reproduction. ### SpectraNet, M=20 Relative L2 Error (Test): 7.87. Result ID: 6a030be547f34ce924e6c8a9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"5.37 M","Provenance":"this work (J19)","M":"20"}. This record does not assert independent reproduction. ### SpectraNet, M=16 Relative L2 Error (Test): 7.92. Result ID: 6a030be547f34ce924e6c8aa. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"3.60 M","Provenance":"this work (J18)","M":"16"}. This record does not assert independent reproduction. ### SpectraNet (headline) Relative L2 Error (Test): 8.22. Result ID: 6a030be547f34ce924e6c8ab. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"2.04 M","Provenance":"this work (J23)"}. This record does not assert independent reproduction. ### SpectraNet, w=32 + residual, seed 0 Relative L2 Error (Test): 8.36. Result ID: 6a030be547f34ce924e6c8ac. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"2.12 M","Provenance":"this work (J14)","Width":"32","Config":"residual","Seed":"0"}. This record does not assert independent reproduction. ### SpectraNet, w=48 plain Relative L2 Error (Test): 8.36. Result ID: 6a030be547f34ce924e6c8ad. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"4.78 M","Provenance":"this work (3190)","Width":"48","Config":"plain"}. This record does not assert independent reproduction. ### SpectraNet, w=32 + spectral envelope Relative L2 Error (Test): 8.49. Result ID: 6a030be547f34ce924e6c8ae. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"2.12 M","Provenance":"this work (J24)","Width":"32","Config":"spectral envelope"}. This record does not assert independent reproduction. ### SpectraNet, w=32 + residual, seed 1 Relative L2 Error (Test): 8.5. Result ID: 6a030be547f34ce924e6c8af. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"2.12 M","Provenance":"this work (J3222)","Width":"32","Config":"residual","Seed":"1"}. This record does not assert independent reproduction. ### SpectraNet, w=32 + grouped channel-mixing MLP Relative L2 Error (Test): 8.54. Result ID: 6a030be547f34ce924e6c8b0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.97 M","Provenance":"this work (J21)","Width":"32","Config":"grouped channel-mixing MLP"}. This record does not assert independent reproduction. ### SpectraNet, w=64 plain Relative L2 Error (Test): 8.69. Result ID: 6a030be547f34ce924e6c8b1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"8.49 M","Provenance":"this work (3199)","Width":"64","Config":"plain"}. This record does not assert independent reproduction. ### SpectraNet, w=32 + disk truncation Relative L2 Error (Test): 8.93. Result ID: 6a030be547f34ce924e6c8b2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"2.12 M","Provenance":"this work (J20)","Width":"32","Config":"disk truncation"}. This record does not assert independent reproduction. ### SpectraNet, w=20 plain Relative L2 Error (Test): 9.41. Result ID: 6a030be547f34ce924e6c8b3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"0.83 M","Provenance":"this work (3187)","Width":"20","Config":"plain"}. This record does not assert independent reproduction. ### SpectraNet, 3D-spectral variant Relative L2 Error (Test): 10.06. Result ID: 6a030be547f34ce924e6c8b4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"8.57 M","Provenance":"this work (3188)"}. This record does not assert independent reproduction. ### FNO seed 0 Relative L2 Error (Test): 10.24. Result ID: 6a030be547f34ce924e6c8b5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"4.75 M","Provenance":"Li et al. \[2021\]","Seed":"0"}. This record does not assert independent reproduction. ### FNO seed 1 Relative L2 Error (Test): 10.69. Result ID: 6a030be547f34ce924e6c8b6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"4.75 M","Provenance":"Li et al. \[2021\] (seed 1)","Seed":"1"}. This record does not assert independent reproduction. ### Galerkin Transformer Relative L2 Error (Test): 10.97. Result ID: 6a030be547f34ce924e6c8b7. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"4.39 M","Provenance":"Cao \[2021\]"}. This record does not assert independent reproduction. ### U-FNO Relative L2 Error (Test): 12.18. Result ID: 6a030be547f34ce924e6c8b8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"39.38 M","Provenance":"Wen et al. \[2022\]"}. This record does not assert independent reproduction. ### U-Net (NSL) Relative L2 Error (Test): 13.87. Result ID: 6a030be547f34ce924e6c8b9. [Reporting paper]() Recorded evaluation configuration: {"Params":"276.96 M","Provenance":"Wu et al. \[2024b\]"}. This record does not assert independent reproduction. ### FactFormer Relative L2 Error (Test): 16.39. Result ID: 6a030be547f34ce924e6c8ba. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"3.47 M","Provenance":"Li et al. \[2023b\]"}. This record does not assert independent reproduction. ### U-NO Relative L2 Error (Test): 16.97. Result ID: 6a030be547f34ce924e6c8bb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"50.80 M","Provenance":"Rahman et al. \[2023\]"}. This record does not assert independent reproduction. ### SpectraNet, single-shot variant Relative L2 Error (Test): 19.42. Result ID: 6a030be547f34ce924e6c8bc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"14.49 M","Provenance":"this work (3123)"}. This record does not assert independent reproduction. ### MWT Relative L2 Error (Test): 19.44. Result ID: 6a030be547f34ce924e6c8bd. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"0.08 M","Provenance":"Gupta et al. \[2021\]"}. This record does not assert independent reproduction. ### LSM Relative L2 Error (Test): 19.51. Result ID: 6a030be547f34ce924e6c8be. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"19.20 M","Provenance":"Wu et al. \[2023\]"}. This record does not assert independent reproduction. ### OFormer Relative L2 Error (Test): 21.62. Result ID: 6a030be547f34ce924e6c8bf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"0.55 M","Provenance":"Li et al. \[2023a\]"}. This record does not assert independent reproduction. ### Transolver Relative L2 Error (Test): 22.47. Result ID: 6a030be547f34ce924e6c8c0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"11.20 M","Provenance":"Wu et al. \[2024a\]"}. This record does not assert independent reproduction. ### F-FNO Relative L2 Error (Test): 23.31. Result ID: 6a030be547f34ce924e6c8c1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"0.16 M","Provenance":"Tran et al. \[2023\]"}. This record does not assert independent reproduction. ### GNOT Relative L2 Error (Test): 23.62. Result ID: 6a030be547f34ce924e6c8c2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.23 M","Provenance":"Hao et al. \[2023\]"}. This record does not assert independent reproduction. ### KNO2d Relative L2 Error (Test): 30.92. Result ID: 6a030be547f34ce924e6c8c3. [Reporting paper]() Recorded evaluation configuration: {"Params":"0.26 M","Provenance":"Xiong et al. \[2024\]"}. This record does not assert independent reproduction. ### CNO Relative L2 Error (Test): 32.59. Result ID: 6a030be547f34ce924e6c8c4. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"2.03 M","Provenance":"Raonic et al. \[2023\]"}. This record does not assert independent reproduction. ### ONO Relative L2 Error (Test): 34.43. Result ID: 6a030be547f34ce924e6c8c5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"0.12 M","Provenance":"Xiao et al. \[2024\]"}. This record does not assert independent reproduction. ### Persistence (trivial floor) Relative L2 Error (Test): 74.81. Result ID: 6a030be547f34ce924e6c8c6. [Reporting paper]() Recorded evaluation configuration: {"Params":"0","Provenance":"this work"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.