# Operator Learning on PDEBench CNS (η=0.1, ζ=0.1) Source: [Operator Learning on PDEBench CNS (η=0.1, ζ=0.1)]() Collection index: [llms.txt]() Data updated: 2026-05-18T08:19:40.555Z Evaluation of models performing Operator Learning on the PDEBench CNS dataset, specifically using parameters η=0.1 and ζ=0.1, typically measured using L2RE. 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 | Operator Learning | | Dataset (including any stated split) | PDEBench CNS (η=0.1, ζ=0.1) | | Metric | L2 Relative Error (L2RE) | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 25 of 25 | | 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 - [L2 Relative Error (L2RE)](): Lower is better; unit: SCALAR. ## Recorded results | Method | L2 Relative Error (L2RE) | Result date | Report paper | | --- | --- | --- | --- | | AOT-POT-M | 0.00788 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-M | 0.00826 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-S | 0.00833 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-M | 0.00866 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-T | 0.0088 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-S | 0.00909 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-S | 0.0113 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-S | 0.0119 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-T | 0.012 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-T | 0.0126 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-T | 0.0132 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-S | 0.0145 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-S | 0.0152 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-M | 0.0152 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-M | 0.0158 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-M | 0.0161 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-T | 0.0163 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-T | 0.0174 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | GNOT | 0.0228 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | Oformer | 0.0254 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | GK-T | 0.0274 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | FFNO | 0.162 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | FNO-m | 0.23 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | FNO | 0.36 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | UNet | 0.569 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | ### AOT-POT-M L2 Relative Error (L2RE): 0.00788. Result ID: 6a0acb9447f34ce924f0da63. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"124M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### MoE-POT-M L2 Relative Error (L2RE): 0.00826. Result ID: 6a0acb9447f34ce924f0da60. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"288M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### AOT-POT-S L2 Relative Error (L2RE): 0.00833. Result ID: 6a0acb9447f34ce924f0da62. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"31M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### DPOT-M L2 Relative Error (L2RE): 0.00866. Result ID: 6a0acb9447f34ce924f0da5d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"122M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### AOT-POT-T L2 Relative Error (L2RE): 0.0088. Result ID: 6a0acb9447f34ce924f0da61. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### AOT-POT-S L2 Relative Error (L2RE): 0.00909. Result ID: 6a0acb9447f34ce924f0da6b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"31M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-S L2 Relative Error (L2RE): 0.0113. Result ID: 6a0acb9447f34ce924f0da5f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"90M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### DPOT-S L2 Relative Error (L2RE): 0.0119. Result ID: 6a0acb9447f34ce924f0da5c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"30M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### AOT-POT-T L2 Relative Error (L2RE): 0.012. Result ID: 6a0acb9447f34ce924f0da6a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-T L2 Relative Error (L2RE): 0.0126. Result ID: 6a0acb9447f34ce924f0da5e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"17M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### DPOT-T L2 Relative Error (L2RE): 0.0132. Result ID: 6a0acb9447f34ce924f0da5b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### MoE-POT-S L2 Relative Error (L2RE): 0.0145. Result ID: 6a0acb9447f34ce924f0da68. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"90M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### DPOT-S L2 Relative Error (L2RE): 0.0152. Result ID: 6a0acb9447f34ce924f0da65. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"30M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-M L2 Relative Error (L2RE): 0.0152. Result ID: 6a0acb9447f34ce924f0da69. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"288M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### AOT-POT-M L2 Relative Error (L2RE): 0.0158. Result ID: 6a0acb9447f34ce924f0da6c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"124M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### DPOT-M L2 Relative Error (L2RE): 0.0161. Result ID: 6a0acb9447f34ce924f0da66. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"122M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-T L2 Relative Error (L2RE): 0.0163. Result ID: 6a0acb9447f34ce924f0da67. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"17M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### DPOT-T L2 Relative Error (L2RE): 0.0174. Result ID: 6a0acb9447f34ce924f0da64. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### GNOT L2 Relative Error (L2RE): 0.0228. Result ID: 6a0acb9447f34ce924f0da58. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.8M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### Oformer L2 Relative Error (L2RE): 0.0254. Result ID: 6a0acb9447f34ce924f0da59. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.9M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### GK-T L2 Relative Error (L2RE): 0.0274. Result ID: 6a0acb9447f34ce924f0da57. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"1.6M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### FFNO L2 Relative Error (L2RE): 0.162. Result ID: 6a0acb9447f34ce924f0da56. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.3M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### FNO-m L2 Relative Error (L2RE): 0.23. Result ID: 6a0acb9447f34ce924f0da5a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### FNO L2 Relative Error (L2RE): 0.36. Result ID: 6a0acb9447f34ce924f0da54. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"0.5M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### UNet L2 Relative Error (L2RE): 0.569. Result ID: 6a0acb9447f34ce924f0da55. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"25M","Evaluation Protocol":"Individually trained"}. 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