# Solving 2D Navier-Stokes equations on TorusVis

Source: [Solving 2D Navier-Stokes equations on TorusVis](<https://www.sota2.com/research/sota/solving-2d-navier-stokes-equations-on-torusvis>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-09T06:49:17.321Z

Evaluation of models on solving 2D Navier-Stokes equations using the TorusVis dataset, measured by Relative l2 error.

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 | Solving 2D Navier-Stokes equations |
| Dataset (including any stated split) | TorusVis |
| Metric | Relative L2 Error |
| Unit | PERCENT |
| Direction | Lower is better |
| Results loaded | 6 of 6 |
| 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](<https://www.sota2.com/research/sota/solving-2d-navier-stokes-equations-on-torusvis.md?metric=Relative%20L2%20Error>): Lower is better; unit: PERCENT.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| SS-NO | 2.18 | Not recorded | 68fa7ba31e209131cea898b7 |
| FFNO | 2.31 | Not recorded | 68fa7ba31e209131cea898b7 |
| Factformer (2D) | 3.37 | Not recorded | 68fa7ba31e209131cea898b7 |
| GKT | 4.04 | Not recorded | 68fa7ba31e209131cea898b7 |
| FNO2D | 4.66 | Not recorded | 68fa7ba31e209131cea898b7 |
| U-Net | 4.74 | Not recorded | 68fa7ba31e209131cea898b7 |

### SS-NO

Relative L2 Error: 2.18. Result ID: 69ae6d436dbb7075b955e9cf.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

Recorded evaluation configuration: {"# Parameters":"369, 665","Resolution":"64 x 64"}. This record does not assert independent reproduction.

### FFNO

Relative L2 Error: 2.31. Result ID: 69ae6d436dbb7075b955e9ce.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6ea81e209131cea412c9.md>)

Recorded evaluation configuration: {"# Parameters":"2, 192, 897","Resolution":"64 x 64"}. This record does not assert independent reproduction.

### Factformer (2D)

Relative L2 Error: 3.37. Result ID: 69ae6d436dbb7075b955e9cb.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa710d1e209131cea4ee4c.md>)

[Implementation](<https://github.com/BaratiLab/FactFormer>)

Recorded evaluation configuration: {"# Parameters":"1, 006, 433","Resolution":"64 x 64"}. This record does not assert independent reproduction.

### GKT

Relative L2 Error: 4.04. Result ID: 69ae6d436dbb7075b955e9cc.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa58a01e209131ce9afbf3.md>)

[Implementation](<https://github.com/scaomath/galerkin-transformer>)

Recorded evaluation configuration: {"# Parameters":"8, 418, 049","Resolution":"64 x 64"}. This record does not assert independent reproduction.

### FNO2D

Relative L2 Error: 4.66. Result ID: 69ae6d436dbb7075b955e9cd.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa581d1e209131ce9ab45d.md>)

Recorded evaluation configuration: {"# Parameters":"67, 197, 700","Resolution":"64 x 64"}. This record does not assert independent reproduction.

### U-Net

Relative L2 Error: 4.74. Result ID: 69ae6d436dbb7075b955e9ca.

[Reporting paper](<https://www.sota2.com/research/paper/68fa7ba31e209131cea898b7.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6df71e209131cea3d06d.md>)

Recorded evaluation configuration: {"# Parameters":"7, 783, 777","Resolution":"64 x 64"}. This record does not assert independent reproduction.

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