# Solving fractional Poisson equations on fPE on Unit Ball (d=2, v1.0) (test) Source: [Solving fractional Poisson equations on fPE on Unit Ball (d=2, v1.0) (test)]() Collection index: [llms.txt]() Data updated: 2026-06-26T08:57:32.987Z Evaluation of models solving the Fractional Poisson Equation (fPE) on a 2D Unit Ball domain, defined by the specific exact solution u\_exact = (1 - \|\|x\|\|^2)^(1+alpha/2), version 1.0, measured by Relative L2 test 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 | Solving fractional Poisson equations | | Dataset (including any stated split) | fPE on Unit Ball (d=2, u\_exact = (1 - \|\|x\|\|^2)^(1+alpha/2)) 1.0 (test) | | Metric | Relative L2 Error | | 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](): Lower is better; unit: SCALAR. ## Recorded results | Method | Relative L2 Error | Result date | Report paper | | --- | --- | --- | --- | | fTNN | 0.0000022 | Not recorded | 6a3e079e206542251d7cb557 | | fTNN | 0.000017 | Not recorded | 6a3e079e206542251d7cb557 | | fPINN | 0.00112 | Not recorded | 6a3e079e206542251d7cb557 | | QE-MC-fPINN | 0.00133 | Not recorded | 6a3e079e206542251d7cb557 | | QE-MC-fPINN | 0.002 | Not recorded | 6a3e079e206542251d7cb557 | | fPINN | 0.00361 | Not recorded | 6a3e079e206542251d7cb557 | | Improved MC-fPINN | 0.00488 | Not recorded | 6a3e079e206542251d7cb557 | | MC-fPINN | 0.0178 | Not recorded | 6a3e079e206542251d7cb557 | | Improved MC-fPINN | 0.496 | Not recorded | 6a3e079e206542251d7cb557 | | MC-fPINN | 0.531 | Not recorded | 6a3e079e206542251d7cb557 | ### fTNN Relative L2 Error: 0.0000022. Result ID: 6a3e3efafbc373592c60a4c4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### fTNN Relative L2 Error: 0.000017. Result ID: 6a3e3efafbc373592c60a4c5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### fPINN Relative L2 Error: 0.00112. Result ID: 6a3e3efafbc373592c60a4c1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### QE-MC-fPINN Relative L2 Error: 0.00133. Result ID: 6a3e3efafbc373592c60a4c3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### QE-MC-fPINN Relative L2 Error: 0.002. Result ID: 6a3e3efafbc373592c60a4c2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### fPINN Relative L2 Error: 0.00361. Result ID: 6a3e3efafbc373592c60a4c0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### Improved MC-fPINN Relative L2 Error: 0.00488. Result ID: 6a3e3efafbc373592c60a4be. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### MC-fPINN Relative L2 Error: 0.0178. Result ID: 6a3e3efafbc373592c60a4bc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### Improved MC-fPINN Relative L2 Error: 0.496. Result ID: 6a3e3efafbc373592c60a4bf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### MC-fPINN Relative L2 Error: 0.531. Result ID: 6a3e3efafbc373592c60a4bd. [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.