# PINN Solving of Poisson's Equation on Poisson (Loss Metrics)

Source: [PINN Solving of Poisson's Equation on Poisson (Loss Metrics)](<https://www.sota2.com/research/sota/pinn-solving-of-poisson-s-equation-on-poisson-loss-metrics>)

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

Data updated: 2026-05-20T09:24:16.871Z

Evaluation of Physics-Informed Neural Networks (PINNs) applied to solving the Poisson equation on the Poisson dataset, reporting specific loss components including overall validation L2 error, PDE residual loss, and boundary condition (BC) loss.

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 Poisson's equation with PINNs |
| Dataset (including any stated split) | Poisson |
| Metric | Validation L2 Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 4 of 4 |
| 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

- [Validation L2 Error](<https://www.sota2.com/research/sota/pinn-solving-of-poisson-s-equation-on-poisson-loss-metrics.md?metric=Validation%20L2%20Error>): Lower is better; unit: SCALAR.

- [PDE Residual Loss](<https://www.sota2.com/research/sota/pinn-solving-of-poisson-s-equation-on-poisson-loss-metrics.md?metric=PDE%20Residual%20Loss>): Lower is better; unit: SCALAR.

- [BC Loss](<https://www.sota2.com/research/sota/pinn-solving-of-poisson-s-equation-on-poisson-loss-metrics.md?metric=BC%20Loss>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Validation L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| StableGrad | 0.000026 | Not recorded | 6a0d402bf984739ed6737909 |
| StableGrad | 0.000038 | Not recorded | 6a0d402bf984739ed6737909 |
| Vanilla | 0.000059 | Not recorded | 6a0d402bf984739ed6737909 |
| Vanilla | 0.000065 | Not recorded | 6a0d402bf984739ed6737909 |

### StableGrad

Validation L2 Error: 0.000026. Result ID: 6a0d7cdcfbc373592c05cd32.

[Reporting paper](<https://www.sota2.com/research/paper/6a0d402bf984739ed6737909.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0d402bf984739ed6737909.md>)

Recorded evaluation configuration: {"Depth":"6"}. This record does not assert independent reproduction.

### StableGrad

Validation L2 Error: 0.000038. Result ID: 6a0d7cdcfbc373592c05cd34.

[Reporting paper](<https://www.sota2.com/research/paper/6a0d402bf984739ed6737909.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0d402bf984739ed6737909.md>)

Recorded evaluation configuration: {"Depth":"12"}. This record does not assert independent reproduction.

### Vanilla

Validation L2 Error: 0.000059. Result ID: 6a0d7cdcfbc373592c05cd33.

[Reporting paper](<https://www.sota2.com/research/paper/6a0d402bf984739ed6737909.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa55761e209131ce9946db.md>)

Recorded evaluation configuration: {"Depth":"12"}. This record does not assert independent reproduction.

### Vanilla

Validation L2 Error: 0.000065. Result ID: 6a0d7cdcfbc373592c05cd31.

[Reporting paper](<https://www.sota2.com/research/paper/6a0d402bf984739ed6737909.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa55761e209131ce9946db.md>)

Recorded evaluation configuration: {"Depth":"6"}. This record does not assert independent reproduction.

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