# Autoregressive PDE rollout on Navier-Stokes cylinder wake (T = 6.75)

Source: [Autoregressive PDE rollout on Navier-Stokes cylinder wake (T = 6.75)](<https://www.sota2.com/research/sota/autoregressive-pde-rollout-on-navier-stokes-cylinder-wake-t-6-75>)

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

Data updated: 2026-04-09T23:28:00.788Z

Evaluation of autoregressive models for time-series forecasting (rollout) on the Navier-Stokes cylinder wake simulation data at time T=6.75, measured by relative errors in velocity components (ux, uy) and pressure (p).

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 PDE rollout |
| Dataset (including any stated split) | Navier-Stokes cylinder wake (T = 6.75) |
| Metric | Relative Error (ux) |
| Unit | SCALAR |
| 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

- [Relative Error (ux)](<https://www.sota2.com/research/sota/autoregressive-pde-rollout-on-navier-stokes-cylinder-wake-t-6-75.md?metric=Relative%20Error%20(ux)>): Lower is better; unit: SCALAR.

- [Relative Error (uy)](<https://www.sota2.com/research/sota/autoregressive-pde-rollout-on-navier-stokes-cylinder-wake-t-6-75.md?metric=Relative%20Error%20(uy)>): Lower is better; unit: SCALAR.

- [Relative Error (p)](<https://www.sota2.com/research/sota/autoregressive-pde-rollout-on-navier-stokes-cylinder-wake-t-6-75.md?metric=Relative%20Error%20(p)>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative Error (ux) | Result date | Report paper |
| --- | --- | --- | --- |
| AE-ViT | 0.0276 | Not recorded | 69d732777d0172140ec76a6f |
| AE + 1D transformer | 0.1391 | Not recorded | 69d732777d0172140ec76a6f |
| DL-ROM | 0.4147 | Not recorded | 69d732777d0172140ec76a6f |
| ViT | 0.433 | Not recorded | 69d732777d0172140ec76a6f |

### AE-ViT

Relative Error (ux): 0.0276. Result ID: 69d835e547f34ce924bfef73.

[Reporting paper](<https://www.sota2.com/research/paper/69d732777d0172140ec76a6f.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69d732777d0172140ec76a6f.md>)

Recorded evaluation configuration: {"one-step prediction":"true"}. This record does not assert independent reproduction.

### AE + 1D transformer

Relative Error (ux): 0.1391. Result ID: 69d835e547f34ce924bfef76.

[Reporting paper](<https://www.sota2.com/research/paper/69d732777d0172140ec76a6f.md>)

Recorded evaluation configuration: {"one-step prediction":"true"}. This record does not assert independent reproduction.

### DL-ROM

Relative Error (ux): 0.4147. Result ID: 69d835e547f34ce924bfef75.

[Reporting paper](<https://www.sota2.com/research/paper/69d732777d0172140ec76a6f.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa59e21e209131ce9baf24.md>)

Recorded evaluation configuration: {"one-step prediction":"false"}. This record does not assert independent reproduction.

### ViT

Relative Error (ux): 0.433. Result ID: 69d835e547f34ce924bfef74.

[Reporting paper](<https://www.sota2.com/research/paper/69d732777d0172140ec76a6f.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6a0b1e209131cea25b04.md>)

[Implementation](<https://github.com/google-research/vision_transformer>)

Recorded evaluation configuration: {"one-step prediction":"true"}. This record does not assert independent reproduction.

Page 1 of 1. This is an index page, not the full collection.