# SPDE Solving (xi to u) on Additive Stochastic Ginzburg-Landau (test)

Source: [SPDE Solving (xi to u) on Additive Stochastic Ginzburg-Landau (test)](<https://www.sota2.com/research/sota/spde-solving-xi-to-u-on-additive-stochastic-ginzburg-landau-test>)

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

Data updated: 2026-02-26T06:01:57.484Z

Evaluation of models solving the Additive Stochastic Ginzburg-Landau equation with homogeneous Dirichlet boundary conditions on the test set, specifically focusing on the mapping from stochastic forcing term (xi) to the solution (u), 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 SPDE (xi to u) |
| Dataset (including any stated split) | Additive stochastic Ginzburg-Landau equation with homogeneous Dirichlet boundary conditions (test) |
| Metric | Relative L2 Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 2 of 2 |
| 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/spde-solving-xi-to-u-on-additive-stochastic-ginzburg-landau-test.md?metric=Relative%20L2%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| NSPDE | 0.008 | Not recorded | 68fa6d851e209131cea3a59b |
| FNO | 0.023 | Not recorded | 68fa6d851e209131cea3a59b |

### NSPDE

Relative L2 Error: 0.008. Result ID: 698fb7c63a6c314849fb5c0a.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6d851e209131cea3a59b.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6d851e209131cea3a59b.md>)

Recorded evaluation configuration: {"Boundary conditions":"homogeneous Dirichlet","N (Sample size/Resolution)":"1000"}. This record does not assert independent reproduction.

### FNO

Relative L2 Error: 0.023. Result ID: 698fb7c63a6c314849fb5c09.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6d851e209131cea3a59b.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bb81e209131ce9cac33.md>)

Recorded evaluation configuration: {"Boundary conditions":"homogeneous Dirichlet","N (Sample size/Resolution)":"1000"}. This record does not assert independent reproduction.

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