# 1D linear advection prediction on 1D linear advection in-range (test)

Source: [1D linear advection prediction on 1D linear advection in-range (test)](<https://www.sota2.com/research/sota/1d-linear-advection-prediction-on-1d-linear-advection-in-range-test>)

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

Data updated: 2026-04-13T09:22:46.820Z

Evaluation of models predicting 1D linear advection dynamics using the specified test set, 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 | 1D linear advection prediction |
| Dataset (including any stated split) | 1D linear advection in-range (test) |
| 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/1d-linear-advection-prediction-on-1d-linear-advection-in-range-test.md?metric=Relative%20L2%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| KAPI predictor | 1.166 | Not recorded | 69dc78747d0172140ec78a28 |
| FiLM-HyperPINN | 2.047 | Not recorded | 69dc78747d0172140ec78a28 |
| PI-DeepONet | 2.95 | Not recorded | 69dc78747d0172140ec78a28 |
| KAPI predictor | 4.022 | Not recorded | 69dc78747d0172140ec78a28 |
| FiLM-HyperPINN | 5.581 | Not recorded | 69dc78747d0172140ec78a28 |
| PI-DeepONet | 8.45 | Not recorded | 69dc78747d0172140ec78a28 |

### KAPI predictor

Relative L2 Error: 1.166. Result ID: 69dcb5d047f34ce924c3f2a1.

[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, ν)":"(0.65, 0.04)"}. This record does not assert independent reproduction.

### FiLM-HyperPINN

Relative L2 Error: 2.047. Result ID: 69dcb5d047f34ce924c3f2a2.

[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, ν)":"(0.65, 0.04)"}. This record does not assert independent reproduction.

### PI-DeepONet

Relative L2 Error: 2.95. Result ID: 69dcb5d047f34ce924c3f2a0.

[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, ν)":"(0.50, 0.07)"}. This record does not assert independent reproduction.

### KAPI predictor

Relative L2 Error: 4.022. Result ID: 69dcb5d047f34ce924c3f29e.

[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, ν)":"(0.50, 0.07)"}. This record does not assert independent reproduction.

### FiLM-HyperPINN

Relative L2 Error: 5.581. Result ID: 69dcb5d047f34ce924c3f29f.

[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, ν)":"(0.50, 0.07)"}. This record does not assert independent reproduction.

### PI-DeepONet

Relative L2 Error: 8.45. Result ID: 69dcb5d047f34ce924c3f2a3.

[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, ν)":"(0.65, 0.04)"}. This record does not assert independent reproduction.

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