# Dynamical system modeling on Navier-Stokes (NS) m=4, n=8 (train)

Source: [Dynamical system modeling on Navier-Stokes (NS) m=4, n=8 (train)](<https://www.sota2.com/research/sota/dynamical-system-modeling-on-navier-stokes-ns-m-4-n-8-train>)

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

Data updated: 2026-02-26T05:50:38.913Z

Evaluation of models performing dynamical system modeling on the specific Navier-Stokes configuration defined by m=4 and n=8, using the training split, typically measured using Mean Squared Error (MSE).

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 | Dynamical system modeling |
| Dataset (including any stated split) | Navier-Stokes (NS) m=4, n=8 (train) |
| Metric | MSE |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 7 of 7 |
| 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

- [MSE](<https://www.sota2.com/research/sota/dynamical-system-modeling-on-navier-stokes-ns-m-4-n-8-train.md?metric=MSE>): Lower is better; unit: SCALAR.

## Recorded results

| Method | MSE | Result date | Report paper |
| --- | --- | --- | --- |
| One-Per-Env. | 0.0000056 | Not recorded | 68fa6bd81e209131cea30887 |
| LEADS (Ours) | 0.000103 | Not recorded | 68fa6bd81e209131cea30887 |
| GBML-like | 0.000139 | Not recorded | 68fa6bd81e209131cea30887 |
| FT-NODE | 0.00018 | Not recorded | 68fa6bd81e209131cea30887 |
| LEADS no min. | 0.00032 | Not recorded | 68fa6bd81e209131cea30887 |
| FT-RNN | 0.00074 | Not recorded | 68fa6bd81e209131cea30887 |
| One-For-All | 0.0517 | Not recorded | 68fa6bd81e209131cea30887 |

### One-Per-Env.

MSE: 0.0000056. Result ID: 698ea53dffc3901de09f6baa.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

### LEADS (Ours)

MSE: 0.000103. Result ID: 698ea53dffc3901de09f6baf.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Implementation](<https://github.com/yuan-yin/LEADS>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

### GBML-like

MSE: 0.000139. Result ID: 698ea53dffc3901de09f6bad.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa63861e209131ce9ff3e8.md>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

### FT-NODE

MSE: 0.00018. Result ID: 698ea53dffc3901de09f6bac.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa66cb1e209131cea12502.md>)

[Implementation](<https://www.sota2.com/github.com/rtqichen/torchdiffeq>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

### LEADS no min.

MSE: 0.00032. Result ID: 698ea53dffc3901de09f6bae.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Implementation](<https://github.com/yuan-yin/LEADS>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

### FT-RNN

MSE: 0.00074. Result ID: 698ea53dffc3901de09f6bab.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

### One-For-All

MSE: 0.0517. Result ID: 698ea53dffc3901de09f6ba9.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6bd81e209131cea30887.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa39531e209131ce8c19f2.md>)

Recorded evaluation configuration: {"m":"4","n":"8"}. This record does not assert independent reproduction.

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