# PDE solving on Korteweg-de Vries (KdV) 1-D (test) Source: [PDE solving on Korteweg-de Vries (KdV) 1-D (test)]() Collection index: [llms.txt]() Data updated: 2026-02-26T06:01:58.454Z Evaluation of model performance on solving the 1D Korteweg-de Vries (KdV) Partial Differential Equation using the test set, measured by 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 | PDE solving | | Dataset (including any stated split) | Korteweg-de Vries (KdV) 1-D (test) | | Metric | Relative L2 Error | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 32 of 32 | | 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. - [MSE](): Lower is better; unit: SCALAR. ## Recorded results | Method | Relative L2 Error | Result date | Report paper | | --- | --- | --- | --- | | ATHENA | 0.00000221 | Not recorded | 6931156bd6b0dd3342933a19 | | \[65\] | 0.000006 | Not recorded | 6931156bd6b0dd3342933a19 | | MWT Leg | 0.00338 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00375 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00389 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00393 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00418 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00604 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00675 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00712 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00715 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00769 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.0122 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.0124 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.0125 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.0125 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.0126 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0414 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0425 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0429 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0447 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0557 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0695 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0699 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0721 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.076 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0789 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.1296 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.1345 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.1355 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.1363 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.1515 | Not recorded | 68fa58891e209131ce9af110 | ### ATHENA Relative L2 Error: 0.00000221. Result ID: 69998d485698665ec4ff8664. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Benchmark Type":"Agents"}. This record does not assert independent reproduction. ### \[65\] Relative L2 Error: 0.000006. Result ID: 69998d485698665ec4ff8663. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Benchmark Type":"Human"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00338. Result ID: 698ba3387a967eddb77038e8. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"64"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00375. Result ID: 698ba3387a967eddb77038e9. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"128"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00389. Result ID: 698ba3387a967eddb77038ec. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00393. Result ID: 698ba3387a967eddb77038eb. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00418. Result ID: 698ba3387a967eddb77038ea. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00604. Result ID: 698ba3387a967eddb77038ef. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00675. Result ID: 698ba3387a967eddb77038f1. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00712. Result ID: 698ba3387a967eddb77038ee. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"128"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00715. Result ID: 698ba3387a967eddb77038ed. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"64"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00769. Result ID: 698ba3387a967eddb77038f0. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.0122. Result ID: 698ba3387a967eddb77038f5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.0124. Result ID: 698ba3387a967eddb77038f3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"128"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.0125. Result ID: 698ba3387a967eddb77038f2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"64"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.0125. Result ID: 698ba3387a967eddb77038f4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.0126. Result ID: 698ba3387a967eddb77038f6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0414. Result ID: 698ba3387a967eddb77038fe. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0425. Result ID: 698ba3387a967eddb77038ff. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0429. Result ID: 698ba3387a967eddb77038fc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"64"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0447. Result ID: 698ba3387a967eddb7703900. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0557. Result ID: 698ba3387a967eddb77038fd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"128"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0695. Result ID: 698ba3387a967eddb7703903. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0699. Result ID: 698ba3387a967eddb7703904. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0721. Result ID: 698ba3387a967eddb7703905. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.076. Result ID: 698ba3387a967eddb7703902. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"128"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0789. Result ID: 698ba3387a967eddb7703901. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"64"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.1296. Result ID: 698ba3387a967eddb77038f7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"64"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.1345. Result ID: 698ba3387a967eddb77038fa. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.1355. Result ID: 698ba3387a967eddb77038f9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.1363. Result ID: 698ba3387a967eddb77038fb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.1515. Result ID: 698ba3387a967eddb77038f8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"128"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.