# Operator Learning on PDEBench CNS (η=0.1, ζ=0.01) Source: [Operator Learning on PDEBench CNS (η=0.1, ζ=0.01)]() Collection index: [llms.txt]() Data updated: 2026-05-18T08:19:40.589Z Evaluation of models performing Operator Learning on the PDEBench CNS dataset subset, using parameters η=0.1 and ζ=0.01, typically measured by 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=0.01) | | Metric | L2 Relative Error | | 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](): Lower is better; unit: SCALAR. ## Recorded results | Method | L2 Relative Error | Result date | Report paper | | --- | --- | --- | --- | | AOT-POT-M | 0.00323 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-S | 0.00356 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-T | 0.00388 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-M | 0.00903 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-M | 0.00947 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-M | 0.00954 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-S | 0.00965 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-S | 0.0118 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-M | 0.0121 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-S | 0.0126 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-M | 0.0129 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | AOT-POT-T | 0.013 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-T | 0.0131 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-T | 0.0138 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-S | 0.0181 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-S | 0.0188 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | Oformer | 0.0205 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | MoE-POT-T | 0.0215 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | DPOT-T | 0.022 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | GNOT | 0.0341 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | GK-T | 0.0366 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | FFNO | 0.0452 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | FNO-m | 0.076 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | FNO | 0.17 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | | UNet | 0.357 | Not recorded | 6a0a9ce7dbc836b87d82b2a5 | ### AOT-POT-M L2 Relative Error: 0.00323. Result ID: 6a0acb9447f34ce924f0da85. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"124M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### AOT-POT-S L2 Relative Error: 0.00356. Result ID: 6a0acb9447f34ce924f0da84. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"31M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### AOT-POT-T L2 Relative Error: 0.00388. Result ID: 6a0acb9447f34ce924f0da83. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-M L2 Relative Error: 0.00903. Result ID: 6a0acb9447f34ce924f0da82. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"288M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### DPOT-M L2 Relative Error: 0.00947. Result ID: 6a0acb9447f34ce924f0da7f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"122M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### AOT-POT-M L2 Relative Error: 0.00954. Result ID: 6a0acb9447f34ce924f0da7c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"124M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### AOT-POT-S L2 Relative Error: 0.00965. Result ID: 6a0acb9447f34ce924f0da7b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"31M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### MoE-POT-S L2 Relative Error: 0.0118. Result ID: 6a0acb9447f34ce924f0da81. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"90M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-M L2 Relative Error: 0.0121. Result ID: 6a0acb9447f34ce924f0da79. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"288M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### DPOT-S L2 Relative Error: 0.0126. Result ID: 6a0acb9447f34ce924f0da7e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"30M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### DPOT-M L2 Relative Error: 0.0129. Result ID: 6a0acb9447f34ce924f0da76. [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: 0.013. Result ID: 6a0acb9447f34ce924f0da7a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### MoE-POT-T L2 Relative Error: 0.0131. Result ID: 6a0acb9447f34ce924f0da80. [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: 0.0138. Result ID: 6a0acb9447f34ce924f0da7d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Fine-tuned"}. This record does not assert independent reproduction. ### MoE-POT-S L2 Relative Error: 0.0181. Result ID: 6a0acb9447f34ce924f0da78. [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: 0.0188. Result ID: 6a0acb9447f34ce924f0da75. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"30M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### Oformer L2 Relative Error: 0.0205. Result ID: 6a0acb9447f34ce924f0da72. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.9M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### MoE-POT-T L2 Relative Error: 0.0215. Result ID: 6a0acb9447f34ce924f0da77. [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: 0.022. Result ID: 6a0acb9447f34ce924f0da74. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"7M","Evaluation Protocol":"Zero-shot"}. This record does not assert independent reproduction. ### GNOT L2 Relative Error: 0.0341. Result ID: 6a0acb9447f34ce924f0da71. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Params":"1.8M","Evaluation Protocol":"Individually trained"}. This record does not assert independent reproduction. ### GK-T L2 Relative Error: 0.0366. Result ID: 6a0acb9447f34ce924f0da70. [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: 0.0452. Result ID: 6a0acb9447f34ce924f0da6f. [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: 0.076. Result ID: 6a0acb9447f34ce924f0da73. [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: 0.17. Result ID: 6a0acb9447f34ce924f0da6d. [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: 0.357. Result ID: 6a0acb9447f34ce924f0da6e. [Reporting paper]() [Method origin paper]() [Implementation]() Recorded evaluation configuration: {"Params":"25M","Evaluation Protocol":"Individually trained"}. 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