# Learning PDEs on Helmholtz 2D a=10 Source: [Learning PDEs on Helmholtz 2D a=10]() Collection index: [llms.txt]() Data updated: 2026-05-26T09:11:59.295Z Evaluation of models learning Partial Differential Equations (PDEs) on the specific Helmholtz 2D configuration (a=10), measured using 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 | Learning PDEs | | Dataset (including any stated split) | Helmholtz 2D a=10 | | Metric | Relative L2 Error | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 15 of 15 | | 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](): Lower is better; unit: SCALAR. ## Recorded results | Method | Relative L2 Error | Result date | Report paper | | --- | --- | --- | --- | | Hermite-NGP | 0.0000181 | Not recorded | 6a15293cdbd7150506f7e0e3 | | Hermite-NGP | 0.0000529 | Not recorded | 6a15293cdbd7150506f7e0e3 | | PirateNet | 0.000357 | Not recorded | 6a15293cdbd7150506f7e0e3 | | JAX-PI | 0.000576 | Not recorded | 6a15293cdbd7150506f7e0e3 | | PIG | 0.000704 | Not recorded | 6a15293cdbd7150506f7e0e3 | | INGP-FD | 0.00167 | Not recorded | 6a15293cdbd7150506f7e0e3 | | SPINN | 0.00546 | Not recorded | 6a15293cdbd7150506f7e0e3 | | ∂∞-Grid | 0.00607 | Not recorded | 6a15293cdbd7150506f7e0e3 | | PIXEL | 0.0347 | Not recorded | 6a15293cdbd7150506f7e0e3 | | SIREN | 0.0667 | Not recorded | 6a15293cdbd7150506f7e0e3 | | Cubic I-NGP | 2.47 | Not recorded | 6a15293cdbd7150506f7e0e3 | | Hermite-NGP | 3.35 | Not recorded | 6a15293cdbd7150506f7e0e3 | | INGP-FD | 3.66 | Not recorded | 6a15293cdbd7150506f7e0e3 | | ∂∞-Grid | 6.07 | Not recorded | 6a15293cdbd7150506f7e0e3 | | SIREN | 6.67 | Not recorded | 6a15293cdbd7150506f7e0e3 | ### Hermite-NGP Relative L2 Error: 0.0000181. Result ID: 6a1563d7fbc373592c0d0a38. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Model Scale":"Compact (Larger)"}. This record does not assert independent reproduction. ### Hermite-NGP Relative L2 Error: 0.0000529. Result ID: 6a1563d7fbc373592c0d0a37. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Model Scale":"Small"}. This record does not assert independent reproduction. ### PirateNet Relative L2 Error: 0.000357. Result ID: 6a1563d7fbc373592c0d0a39. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### JAX-PI Relative L2 Error: 0.000576. Result ID: 6a1563d7fbc373592c0d0a3a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### PIG Relative L2 Error: 0.000704. Result ID: 6a1563d7fbc373592c0d0a3e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### INGP-FD Relative L2 Error: 0.00167. Result ID: 6a1563d7fbc373592c0d0a3b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### SPINN Relative L2 Error: 0.00546. Result ID: 6a1563d7fbc373592c0d0a3c. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### ∂∞-Grid Relative L2 Error: 0.00607. Result ID: 6a1563d7fbc373592c0d0a3f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### PIXEL Relative L2 Error: 0.0347. Result ID: 6a1563d7fbc373592c0d0a3d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### SIREN Relative L2 Error: 0.0667. Result ID: 6a1563d7fbc373592c0d0a40. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### Cubic I-NGP Relative L2 Error: 2.47. Result ID: 6a1563d7fbc373592c0d0a82. [Reporting paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### Hermite-NGP Relative L2 Error: 3.35. Result ID: 6a1563d7fbc373592c0d0a7e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### INGP-FD Relative L2 Error: 3.66. Result ID: 6a1563d7fbc373592c0d0a7f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### ∂∞-Grid Relative L2 Error: 6.07. Result ID: 6a1563d7fbc373592c0d0a80. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. ### SIREN Relative L2 Error: 6.67. Result ID: 6a1563d7fbc373592c0d0a81. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.