# Autoregressive Forecasting on Kuramoto-Sivashinsky (KS) equation (LPSDA protocol, test)

Source: [Autoregressive Forecasting on Kuramoto-Sivashinsky (KS) equation (LPSDA protocol, test)](<https://www.sota2.com/research/sota/autoregressive-forecasting-on-kuramoto-sivashinsky-ks-equation-lpsda-protocol-test>)

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

Data updated: 2026-05-19T13:33:11.753Z

Evaluation of Autoregressive Forecasting performance on the Kuramoto-Sivashinsky (KS) equation using the in-distribution LPSDA protocol on the test set, measured by Normalized Mean Squared Error (NMSE).

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 | Autoregressive Forecasting |
| Dataset (including any stated split) | Kuramoto-Sivashinsky (KS) equation in-distribution LPSDA protocol (test) |
| Metric | NMSE |
| Unit | PERCENT |
| Direction | Lower is better |
| Results loaded | 4 of 4 |
| 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

- [NMSE](<https://www.sota2.com/research/sota/autoregressive-forecasting-on-kuramoto-sivashinsky-ks-equation-lpsda-protocol-test.md?metric=NMSE>): Lower is better; unit: PERCENT.

## Recorded results

| Method | NMSE | Result date | Report paper |
| --- | --- | --- | --- |
| PACE-FNO (AR) | 0.03 | Not recorded | 6a0bef1adbc836b87d82cb4d |
| PACE-FNO (AR) | 0.08 | Not recorded | 6a0bef1adbc836b87d82cb4d |
| FNO (AR) | 0.09 | Not recorded | 6a0bef1adbc836b87d82cb4d |
| FNO (AR) | 0.1 | Not recorded | 6a0bef1adbc836b87d82cb4d |

### PACE-FNO (AR)

NMSE: 0.03. Result ID: 6a0c6555fbc373592c042b3f.

[Reporting paper](<https://www.sota2.com/research/paper/6a0bef1adbc836b87d82cb4d.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0bef1adbc836b87d82cb4d.md>)

Recorded evaluation configuration: {"Symmetry (Sym.)":"windowed g1 + PACE g2–g3","Architecture":"m=20, w=64, 4 layers, 20 frames","Number of training samples":"512"}. This record does not assert independent reproduction.

### PACE-FNO (AR)

NMSE: 0.08. Result ID: 6a0c6555fbc373592c042b3e.

[Reporting paper](<https://www.sota2.com/research/paper/6a0bef1adbc836b87d82cb4d.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0bef1adbc836b87d82cb4d.md>)

Recorded evaluation configuration: {"Symmetry (Sym.)":"windowed g1 + structured g2–g3","Architecture":"m=20, w=64, 4 layers, 1 frame","Number of training samples":"512"}. This record does not assert independent reproduction.

### FNO (AR)

NMSE: 0.09. Result ID: 6a0c6555fbc373592c042b3d.

[Reporting paper](<https://www.sota2.com/research/paper/6a0bef1adbc836b87d82cb4d.md>)

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

Recorded evaluation configuration: {"Symmetry (Sym.)":"g1g2g3","Architecture":"m=32, w=256, 5 layers, 20 frames","Number of training samples":"512"}. This record does not assert independent reproduction.

### FNO (AR)

NMSE: 0.1. Result ID: 6a0c6555fbc373592c042b3c.

[Reporting paper](<https://www.sota2.com/research/paper/6a0bef1adbc836b87d82cb4d.md>)

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

Recorded evaluation configuration: {"Symmetry (Sym.)":"-","Architecture":"m=32, w=256, 5 layers, 20 frames","Number of training samples":"512"}. This record does not assert independent reproduction.

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