# Fractional Poisson Equation Solving on Unit Ball (d=3, test) Source: [Fractional Poisson Equation Solving on Unit Ball (d=3, test)]() Collection index: [llms.txt]() Data updated: 2026-06-26T08:57:33.017Z Evaluation of models solving the fractional Poisson equation on a 3D Unit Ball, utilizing the exact solution defined by (1 - \|\|x\|\|^2)^(1+alpha/2), measured on the test split. 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 | Solving fractional Poisson equations | | Dataset (including any stated split) | fPE on Unit Ball (d=3, u\_exact = (1 - \|\|x\|\|^2)^(1+alpha/2)) 1.0 (test) | | Metric | Relative L2 Error (Test) | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 10 of 10 | | 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 (Test)](): Lower is better; unit: SCALAR. ## Recorded results | Method | Relative L2 Error (Test) | Result date | Report paper | | --- | --- | --- | --- | | fTNN | 0.000356 | Not recorded | 6a3e079e206542251d7cb557 | | fTNN | 0.000397 | Not recorded | 6a3e079e206542251d7cb557 | | QE-MC-fPINN | 0.00118 | Not recorded | 6a3e079e206542251d7cb557 | | QE-MC-fPINN | 0.00174 | Not recorded | 6a3e079e206542251d7cb557 | | fPINN | 0.00502 | Not recorded | 6a3e079e206542251d7cb557 | | fPINN | 0.00559 | Not recorded | 6a3e079e206542251d7cb557 | | Improved MC-fPINN | 0.00766 | Not recorded | 6a3e079e206542251d7cb557 | | MC-fPINN | 0.0137 | Not recorded | 6a3e079e206542251d7cb557 | | Improved MC-fPINN | 0.435 | Not recorded | 6a3e079e206542251d7cb557 | | MC-fPINN | 0.811 | Not recorded | 6a3e079e206542251d7cb557 | ### fTNN Relative L2 Error (Test): 0.000356. Result ID: 6a3e3efafbc373592c60a4cf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### fTNN Relative L2 Error (Test): 0.000397. Result ID: 6a3e3efafbc373592c60a4ce. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### QE-MC-fPINN Relative L2 Error (Test): 0.00118. Result ID: 6a3e3efafbc373592c60a4cd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### QE-MC-fPINN Relative L2 Error (Test): 0.00174. Result ID: 6a3e3efafbc373592c60a4cc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### fPINN Relative L2 Error (Test): 0.00502. Result ID: 6a3e3efafbc373592c60a4ca. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### fPINN Relative L2 Error (Test): 0.00559. Result ID: 6a3e3efafbc373592c60a4cb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### Improved MC-fPINN Relative L2 Error (Test): 0.00766. Result ID: 6a3e3efafbc373592c60a4c8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### MC-fPINN Relative L2 Error (Test): 0.0137. Result ID: 6a3e3efafbc373592c60a4c6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### Improved MC-fPINN Relative L2 Error (Test): 0.435. Result ID: 6a3e3efafbc373592c60a4c9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### MC-fPINN Relative L2 Error (Test): 0.811. Result ID: 6a3e3efafbc373592c60a4c7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.