# PINN Performance on Helmholtz Equation Source: [PINN Performance on Helmholtz Equation]() Collection index: [llms.txt]() Data updated: 2026-05-20T09:24:16.911Z Evaluation of Physics-Informed Neural Networks (PINNs) performance when solving the Helmholtz Partial Differential Equation, measured by solution error (L2), PDE residual loss, and boundary condition adherence. 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 Helmholtz equation with PINNs | | Dataset (including any stated split) | Helmholtz | | 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](): Lower is better; unit: SCALAR. - [PDE Loss](): Lower is better; unit: SCALAR. - [BC Loss](): Lower is better; unit: SCALAR. ## Recorded results | Method | Validation L2 Error | Result date | Report paper | | --- | --- | --- | --- | | StableGrad | 0.0023 | Not recorded | 6a0d402bf984739ed6737909 | | StableGrad | 0.0031 | Not recorded | 6a0d402bf984739ed6737909 | | Vanilla | 0.0046 | Not recorded | 6a0d402bf984739ed6737909 | | Vanilla | 0.0065 | Not recorded | 6a0d402bf984739ed6737909 | ### StableGrad Validation L2 Error: 0.0023. Result ID: 6a0d7cdcfbc373592c05cd38. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Depth":"12"}. This record does not assert independent reproduction. ### StableGrad Validation L2 Error: 0.0031. Result ID: 6a0d7cdcfbc373592c05cd36. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Depth":"6"}. This record does not assert independent reproduction. ### Vanilla Validation L2 Error: 0.0046. Result ID: 6a0d7cdcfbc373592c05cd35. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Depth":"6"}. This record does not assert independent reproduction. ### Vanilla Validation L2 Error: 0.0065. Result ID: 6a0d7cdcfbc373592c05cd37. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Depth":"12"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.