# Operator Regression on Advection-Diffusion-Reaction (ADR) PDE (50 unseen operators)

Source: [Operator Regression on Advection-Diffusion-Reaction (ADR) PDE (50 unseen operators)](<https://www.sota2.com/research/sota/operator-regression-on-advection-diffusion-reaction-adr-pde-50-unseen-operators>)

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

Data updated: 2026-02-26T05:59:55.540Z

Evaluation of models performing Operator Regression on the Advection-Diffusion-Reaction (ADR) PDE dataset, specifically focusing on 50 unseen operators, measured by Root Mean Square Error (RMSE).

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 | Operator Regression |
| Dataset (including any stated split) | Advection-Diffusion-Reaction (ADR) PDE (50 unseen operators) |
| Metric | RMSE |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 3 of 3 |
| 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

- [RMSE](<https://www.sota2.com/research/sota/operator-regression-on-advection-diffusion-reaction-adr-pde-50-unseen-operators.md?metric=RMSE>): Lower is better; unit: SCALAR.

## Recorded results

| Method | RMSE | Result date | Report paper |
| --- | --- | --- | --- |
| Transducer | 0.000239 | Not recorded | 68fa6f711e209131cea459d1 |
| FNO | 0.000296 | Not recorded | 68fa6f711e209131cea459d1 |
| DeepONet | 0.0202 | Not recorded | 68fa6f711e209131cea459d1 |

### Transducer

RMSE: 0.000239. Result ID: 6990beae3a6c31484902eea2.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6f711e209131cea459d1.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6f711e209131cea459d1.md>)

Recorded evaluation configuration: {"TIME (S)":"3.10e-3","GFLOPS":"1.06e-1","Number of examples (n)":50,"Optimization strategy":"pre-trained"}. This record does not assert independent reproduction.

### FNO

RMSE: 0.000296. Result ID: 6990beae3a6c31484902eea0.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6f711e209131cea459d1.md>)

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

Recorded evaluation configuration: {"TIME (S)":"1.72e2","GFLOPS":"1.68e2","Number of examples (n)":50,"Optimization strategy":"optimized from scratch"}. This record does not assert independent reproduction.

### DeepONet

RMSE: 0.0202. Result ID: 6990beae3a6c31484902eea1.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6f711e209131cea459d1.md>)

Recorded evaluation configuration: {"TIME (S)":"7.85e1","GFLOPS":"1.54e2","Number of examples (n)":50,"Optimization strategy":"optimized from scratch"}. This record does not assert independent reproduction.

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