# 2D Poisson prediction on 2D Poisson (in-range)

Source: [2D Poisson prediction on 2D Poisson (in-range)](<https://www.sota2.com/research/sota/2d-poisson-prediction-on-2d-poisson-in-range>)

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

Data updated: 2026-04-13T09:22:46.766Z

Evaluation of models performing 2D Poisson prediction on the in-range subset of the 2D Poisson dataset, measured using 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 | 2D Poisson prediction |
| Dataset (including any stated split) | 2D Poisson (in-range) |
| Metric | Relative L2 Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 6 of 6 |
| 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/2d-poisson-prediction-on-2d-poisson-in-range.md?metric=Relative%20L2%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| KAPI predictor | 0.01195 | Not recorded | 69dc78747d0172140ec78a28 |
| PI-DeepONet | 0.01345 | Not recorded | 69dc78747d0172140ec78a28 |
| FiLM-HyperPINN | 0.01657 | Not recorded | 69dc78747d0172140ec78a28 |
| KAPI predictor | 0.02008 | Not recorded | 69dc78747d0172140ec78a28 |
| PI-DeepONet | 0.02946 | Not recorded | 69dc78747d0172140ec78a28 |
| FiLM-HyperPINN | 0.06055 | Not recorded | 69dc78747d0172140ec78a28 |

### KAPI predictor

Relative L2 Error: 0.01195. Result ID: 69dcb5d047f34ce924c3f295.

[Reporting paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

Recorded evaluation configuration: {"Test case (x0, y0, ν)":"(0.45, 0.55, 0.09)"}. This record does not assert independent reproduction.

### PI-DeepONet

Relative L2 Error: 0.01345. Result ID: 69dcb5d047f34ce924c3f297.

[Reporting paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa59711e209131ce9b724b.md>)

Recorded evaluation configuration: {"Test case (x0, y0, ν)":"(0.45, 0.55, 0.09)"}. This record does not assert independent reproduction.

### FiLM-HyperPINN

Relative L2 Error: 0.01657. Result ID: 69dcb5d047f34ce924c3f293.

[Reporting paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa63ee1e209131cea0190e.md>)

[Implementation](<https://github.com/ethanjperez/film>)

Recorded evaluation configuration: {"Test case (x0, y0, ν)":"(0.50, 0.50, 0.07)"}. This record does not assert independent reproduction.

### KAPI predictor

Relative L2 Error: 0.02008. Result ID: 69dcb5d047f34ce924c3f292.

[Reporting paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

Recorded evaluation configuration: {"Test case (x0, y0, ν)":"(0.50, 0.50, 0.07)"}. This record does not assert independent reproduction.

### PI-DeepONet

Relative L2 Error: 0.02946. Result ID: 69dcb5d047f34ce924c3f294.

[Reporting paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa59711e209131ce9b724b.md>)

Recorded evaluation configuration: {"Test case (x0, y0, ν)":"(0.50, 0.50, 0.07)"}. This record does not assert independent reproduction.

### FiLM-HyperPINN

Relative L2 Error: 0.06055. Result ID: 69dcb5d047f34ce924c3f296.

[Reporting paper](<https://www.sota2.com/research/paper/69dc78747d0172140ec78a28.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa63ee1e209131cea0190e.md>)

[Implementation](<https://github.com/ethanjperez/film>)

Recorded evaluation configuration: {"Test case (x0, y0, ν)":"(0.45, 0.55, 0.09)"}. This record does not assert independent reproduction.

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