# Forward PDE solving on Non-bounded Navier-Stokes full observations

Source: [Forward PDE solving on Non-bounded Navier-Stokes full observations](<https://www.sota2.com/research/sota/forward-pde-solving-on-non-bounded-navier-stokes-full-observations>)

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

Data updated: 2026-02-26T06:01:54.105Z

Evaluation of model performance on solving Partial Differential Equations (PDEs) using the Non-bounded Navier-Stokes full observations dataset, measured by Relative 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 | Forward PDE solving |
| Dataset (including any stated split) | Non-bounded Navier-Stokes full observations |
| Metric | Relative Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 5 of 5 |
| 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 Error](<https://www.sota2.com/research/sota/forward-pde-solving-on-non-bounded-navier-stokes-full-observations.md?metric=Relative%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative Error | Result date | Report paper |
| --- | --- | --- | --- |
| PINO | 0.011 | Not recorded | 68fa5c821e209131ce9d192e |
| FNO | 0.023 | Not recorded | 68fa5c821e209131ce9d192e |
| DiffusionPDE | 0.061 | Not recorded | 68fa5c821e209131ce9d192e |
| DeepONet | 0.256 | Not recorded | 68fa5c821e209131ce9d192e |
| PINNs | 0.273 | Not recorded | 68fa5c821e209131ce9d192e |

### PINO

Relative Error: 0.011. Result ID: 698bb52a7a967eddb770c532.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5aaa1e209131ce9c1a82.md>)

Recorded evaluation configuration: {"Observation":"Full"}. This record does not assert independent reproduction.

### FNO

Relative Error: 0.023. Result ID: 698bb52a7a967eddb770c535.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

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

Recorded evaluation configuration: {"Observation":"Full"}. This record does not assert independent reproduction.

### DiffusionPDE

Relative Error: 0.061. Result ID: 698bb52a7a967eddb770c531.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

[Implementation](<https://jhhuangchloe.github.io/Diffusion-PDE/>)

Recorded evaluation configuration: {"Observation":"Full"}. This record does not assert independent reproduction.

### DeepONet

Relative Error: 0.256. Result ID: 698bb52a7a967eddb770c533.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

Recorded evaluation configuration: {"Observation":"Full"}. This record does not assert independent reproduction.

### PINNs

Relative Error: 0.273. Result ID: 698bb52a7a967eddb770c534.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

Recorded evaluation configuration: {"Observation":"Full"}. This record does not assert independent reproduction.

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