# Forward mapping on 2D Heat Equation 16 x 16 finite element mesh (test) Source: [Forward mapping on 2D Heat Equation 16 x 16 finite element mesh (test)]() Collection index: [llms.txt]() Data updated: 2026-05-04T07:56:04.252Z Evaluation of models performing forward mapping for the 2D Heat Equation solved on a 16x16 finite element mesh, measured by average relative 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 | Forward mapping | | Dataset (including any stated split) | 2D Heat Equation 16 x 16 finite element mesh (test) | | Metric | Average Relative Error | | Unit | PERCENT | | Direction | Lower is better | | Results loaded | 14 of 14 | | 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 - [Average Relative Error](): Lower is better; unit: PERCENT. ## Recorded results | Method | Average Relative Error | Result date | Report paper | | --- | --- | --- | --- | | nOPO | 1.09 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN | 1.22 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN | 1.57 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN-Full | 2.12 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO | 2.73 | Not recorded | 68fa48ee1e209131ce9335e5 | | nOPO | 2.9 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO | 3.94 | Not recorded | 68fa48ee1e209131ce9335e5 | | nPOP | 3.99 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcPOP | 3.99 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO-Full | 4.21 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO-Full | 4.56 | Not recorded | 68fa48ee1e209131ce9335e5 | | nPOP | 5.3 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcPOP | 5.3 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN-Full | 8.8 | Not recorded | 68fa48ee1e209131ce9335e5 | ### nOPO Average Relative Error: 1.09. Result ID: 69f850ff47f34ce924dbcae1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### TAEN Average Relative Error: 1.22. Result ID: 69f850ff47f34ce924dbcae9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### TAEN Average Relative Error: 1.57. Result ID: 69f850ff47f34ce924dbcae8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### TAEN-Full Average Relative Error: 2.12. Result ID: 69f850ff47f34ce924dbcaeb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### mcOPO Average Relative Error: 2.73. Result ID: 69f850ff47f34ce924dbcae4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### nOPO Average Relative Error: 2.9. Result ID: 69f850ff47f34ce924dbcae0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcOPO Average Relative Error: 3.94. Result ID: 69f850ff47f34ce924dbcae5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### nPOP Average Relative Error: 3.99. Result ID: 69f850ff47f34ce924dbcade. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcPOP Average Relative Error: 3.99. Result ID: 69f850ff47f34ce924dbcae2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcOPO-Full Average Relative Error: 4.21. Result ID: 69f850ff47f34ce924dbcae6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcOPO-Full Average Relative Error: 4.56. Result ID: 69f850ff47f34ce924dbcae7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### nPOP Average Relative Error: 5.3. Result ID: 69f850ff47f34ce924dbcadf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### mcPOP Average Relative Error: 5.3. Result ID: 69f850ff47f34ce924dbcae3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### TAEN-Full Average Relative Error: 8.8. Result ID: 69f850ff47f34ce924dbcaea. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.