# Inverse Solving on Darcy

Source: [Inverse Solving on Darcy](<https://www.sota2.com/research/sota/inverse-solving-on-darcy>)

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

Data updated: 2026-06-30T09:02:47.908Z

Evaluation of models performing Inverse Solving on the Darcy dataset, measured by Mean Squared Error (MSE) and PDE 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 | Inverse Solving |
| Dataset (including any stated split) | Darcy |
| Metric | MSE |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 5 of 5 |
| 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

- [MSE](<https://www.sota2.com/research/sota/inverse-solving-on-darcy.md?metric=MSE>): Lower is better; unit: SCALAR.

- [PDE Error](<https://www.sota2.com/research/sota/inverse-solving-on-darcy.md?metric=PDE%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | MSE | Result date | Report paper |
| --- | --- | --- | --- |
| PIDDM | 0.236 | Not recorded | 68fa5d841e209131ce9dae42 |
| D-Flow | 0.428 | Not recorded | 68fa5d841e209131ce9dae42 |
| DiffusionPDE | 0.456 | Not recorded | 68fa5d841e209131ce9dae42 |
| PIDM | 0.468 | Not recorded | 68fa5d841e209131ce9dae42 |
| ECI | 0.545 | Not recorded | 68fa5d841e209131ce9dae42 |

### PIDDM

MSE: 0.236. Result ID: 6a43861dfbc373592c9523c4.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5d841e209131ce9dae42.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5d841e209131ce9dae42.md>)

Recorded evaluation configuration: {"NFE":"0.080"}. This record does not assert independent reproduction.

### D-Flow

MSE: 0.428. Result ID: 6a43861dfbc373592c9523c7.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5d841e209131ce9dae42.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa74361e209131cea60753.md>)

Recorded evaluation configuration: {"NFE":"5.000"}. This record does not assert independent reproduction.

### DiffusionPDE

MSE: 0.456. Result ID: 6a43861dfbc373592c9523c6.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5d841e209131ce9dae42.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5c821e209131ce9d192e.md>)

[Implementation](<https://jhhuangchloe.github.io/Diffusion-PDE/>)

Recorded evaluation configuration: {"NFE":"0.100"}. This record does not assert independent reproduction.

### PIDM

MSE: 0.468. Result ID: 6a43861dfbc373592c9523c8.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5d841e209131ce9dae42.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa77691e209131cea731c7.md>)

Recorded evaluation configuration: {"NFE":"0.100"}. This record does not assert independent reproduction.

### ECI

MSE: 0.545. Result ID: 6a43861dfbc373592c9523c5.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5d841e209131ce9dae42.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa773a1e209131cea71cfd.md>)

Recorded evaluation configuration: {"NFE":"0.500"}. This record does not assert independent reproduction.

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