# PDE Modeling on Burgers' Equation various resolutions (val) Source: [PDE Modeling on Burgers' Equation various resolutions (val)]() Collection index: [llms.txt]() Data updated: 2026-02-26T06:01:57.122Z Evaluation of model performance for modeling the Burgers' Equation using data sampled at various resolutions, evaluated on the validation set, typically 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 Modeling | | Dataset (including any stated split) | Burgers' Equation various resolutions (val) | | Metric | Relative L2 Error | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 36 of 36 | | 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 | | --- | --- | --- | --- | | MWT Leg | 0.00178 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00184 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00185 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00185 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00186 | Not recorded | 68fa58891e209131ce9af110 | | MWT Leg | 0.00199 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00289 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00299 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.00324 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.00332 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.00333 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00336 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.00336 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.00346 | Not recorded | 68fa58891e209131ce9af110 | | FNO | 0.00377 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00381 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00395 | Not recorded | 68fa58891e209131ce9af110 | | MWT Cheb | 0.00402 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0189 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.02 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0212 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0217 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0219 | Not recorded | 68fa58891e209131ce9af110 | | LNO | 0.0221 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.0243 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.0355 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.036 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.0364 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.0364 | Not recorded | 68fa58891e209131ce9af110 | | MGNO | 0.0374 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0555 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0594 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0651 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0663 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0666 | Not recorded | 68fa58891e209131ce9af110 | | GNO | 0.0699 | Not recorded | 68fa58891e209131ce9af110 | ### MWT Leg Relative L2 Error: 0.00178. Result ID: 698ba3387a967eddb770390b. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"8192"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00184. Result ID: 698ba3387a967eddb7703908. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00185. Result ID: 698ba3387a967eddb7703907. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00185. Result ID: 698ba3387a967eddb770390a. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"4096"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00186. Result ID: 698ba3387a967eddb7703909. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"2048"}. This record does not assert independent reproduction. ### MWT Leg Relative L2 Error: 0.00199. Result ID: 698ba3387a967eddb7703906. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00289. Result ID: 698ba3387a967eddb7703911. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"8192"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00299. Result ID: 698ba3387a967eddb7703910. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"4096"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.00324. Result ID: 698ba3387a967eddb7703916. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"4096"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.00332. Result ID: 698ba3387a967eddb7703912. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.00333. Result ID: 698ba3387a967eddb7703913. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00336. Result ID: 698ba3387a967eddb770390e. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.00336. Result ID: 698ba3387a967eddb7703917. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"8192"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.00346. Result ID: 698ba3387a967eddb7703915. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"2048"}. This record does not assert independent reproduction. ### FNO Relative L2 Error: 0.00377. Result ID: 698ba3387a967eddb7703914. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00381. Result ID: 698ba3387a967eddb770390d. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00395. Result ID: 698ba3387a967eddb770390f. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"2048"}. This record does not assert independent reproduction. ### MWT Cheb Relative L2 Error: 0.00402. Result ID: 698ba3387a967eddb770390c. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0189. Result ID: 698ba3387a967eddb7703923. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"8192"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.02. Result ID: 698ba3387a967eddb7703922. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"4096"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0212. Result ID: 698ba3387a967eddb770391e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0217. Result ID: 698ba3387a967eddb7703920. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0219. Result ID: 698ba3387a967eddb7703921. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"2048"}. This record does not assert independent reproduction. ### LNO Relative L2 Error: 0.0221. Result ID: 698ba3387a967eddb770391f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.0243. Result ID: 698ba3387a967eddb7703918. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.0355. Result ID: 698ba3387a967eddb7703919. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.036. Result ID: 698ba3387a967eddb770391b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"2048"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.0364. Result ID: 698ba3387a967eddb770391c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"4096"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.0364. Result ID: 698ba3387a967eddb770391d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"8192"}. This record does not assert independent reproduction. ### MGNO Relative L2 Error: 0.0374. Result ID: 698ba3387a967eddb770391a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0555. Result ID: 698ba3387a967eddb7703924. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"256"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0594. Result ID: 698ba3387a967eddb7703925. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"512"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0651. Result ID: 698ba3387a967eddb7703926. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"1024"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0663. Result ID: 698ba3387a967eddb7703927. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"2048"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0666. Result ID: 698ba3387a967eddb7703928. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"4096"}. This record does not assert independent reproduction. ### GNO Relative L2 Error: 0.0699. Result ID: 698ba3387a967eddb7703929. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Resolution (s)":"8192"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.