# Inverse Mapping on 2D Heat Equation 16 x 16 finite element mesh (test) Source: [Inverse Mapping on 2D Heat Equation 16 x 16 finite element mesh (test)]() Collection index: [llms.txt]() Data updated: 2026-05-04T07:56:04.218Z Evaluation of models performing inverse mapping (parameter estimation) on the 2D Heat Equation defined over 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 | Inverse 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 | 16 of 16 | | 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 | | --- | --- | --- | --- | | Tik | 44.99 | Not recorded | 68fa48ee1e209131ce9335e5 | | Tik | 44.99 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN | 45.03 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN-Full | 45.03 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN | 45.23 | Not recorded | 68fa48ee1e209131ce9335e5 | | TAEN-Full | 45.23 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO | 46.32 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO-Full | 46.32 | Not recorded | 68fa48ee1e209131ce9335e5 | | nOPO | 50.18 | Not recorded | 68fa48ee1e209131ce9335e5 | | nPOP | 80.48 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcPOP | 87.6 | Not recorded | 68fa48ee1e209131ce9335e5 | | nPOP | 100.18 | Not recorded | 68fa48ee1e209131ce9335e5 | | nOPO | 107.55 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcPOP | 107.99 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO | 108.28 | Not recorded | 68fa48ee1e209131ce9335e5 | | mcOPO-Full | 108.28 | Not recorded | 68fa48ee1e209131ce9335e5 | ### Tik Average Relative Error: 44.99. Result ID: 69f850ff47f34ce924dbcadc. [Reporting paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### Tik Average Relative Error: 44.99. Result ID: 69f850ff47f34ce924dbcadd. [Reporting paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### TAEN Average Relative Error: 45.03. Result ID: 69f850ff47f34ce924dbcad9. [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: 45.03. Result ID: 69f850ff47f34ce924dbcadb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### TAEN Average Relative Error: 45.23. Result ID: 69f850ff47f34ce924dbcad8. [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: 45.23. Result ID: 69f850ff47f34ce924dbcada. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcOPO Average Relative Error: 46.32. Result ID: 69f850ff47f34ce924dbcad5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### mcOPO-Full Average Relative Error: 46.32. Result ID: 69f850ff47f34ce924dbcad7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### nOPO Average Relative Error: 50.18. Result ID: 69f850ff47f34ce924dbcad1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### nPOP Average Relative Error: 80.48. Result ID: 69f850ff47f34ce924dbcacf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### mcPOP Average Relative Error: 87.6. Result ID: 69f850ff47f34ce924dbcad3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"100"}. This record does not assert independent reproduction. ### nPOP Average Relative Error: 100.18. Result ID: 69f850ff47f34ce924dbcace. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### nOPO Average Relative Error: 107.55. Result ID: 69f850ff47f34ce924dbcad0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcPOP Average Relative Error: 107.99. Result ID: 69f850ff47f34ce924dbcad2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of training samples":"1"}. This record does not assert independent reproduction. ### mcOPO Average Relative Error: 108.28. Result ID: 69f850ff47f34ce924dbcad4. [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: 108.28. Result ID: 69f850ff47f34ce924dbcad6. [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.