# Solving fractional Poisson equations on fPE on Unit Ball (d=3, u\_exact = (1 - \|\|x\|\|^2)^(alpha/2)) 1.0 (test) Source: [Solving fractional Poisson equations on fPE on Unit Ball (d=3, u\_exact = (1 - \|\|x\|\|^2)^(alpha/2)) 1.0 (test)]() Collection index: [llms.txt]() Data updated: 2026-06-26T08:57:33.085Z Evaluation of models solving the fractional Poisson equation on a 3D Unit Ball, using the exact solution defined by (1 - \|\|x\|\|^2)^(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)^(alpha/2)) 1.0 (test) | | Metric | Relative L2 Test 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 Test Error](): Lower is better; unit: SCALAR. ## Recorded results | Method | Relative L2 Test Error | Result date | Report paper | | --- | --- | --- | --- | | fTNN | 0.000158 | Not recorded | 6a3e079e206542251d7cb557 | | fTNN | 0.000374 | Not recorded | 6a3e079e206542251d7cb557 | | QE-MC-fPINN | 0.03 | Not recorded | 6a3e079e206542251d7cb557 | | QE-MC-fPINN | 0.0307 | Not recorded | 6a3e079e206542251d7cb557 | | Improved MC-fPINN | 0.188 | Not recorded | 6a3e079e206542251d7cb557 | | Improved MC-fPINN | 0.265 | Not recorded | 6a3e079e206542251d7cb557 | | MC-fPINN | 0.443 | Not recorded | 6a3e079e206542251d7cb557 | | fPINN | 0.495 | Not recorded | 6a3e079e206542251d7cb557 | | MC-fPINN | 0.857 | Not recorded | 6a3e079e206542251d7cb557 | | fPINN | 1.3 | Not recorded | 6a3e079e206542251d7cb557 | ### fTNN Relative L2 Test Error: 0.000158. Result ID: 6a3e3efafbc373592c60a4e3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### fTNN Relative L2 Test Error: 0.000374. Result ID: 6a3e3efafbc373592c60a4e2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### QE-MC-fPINN Relative L2 Test Error: 0.03. Result ID: 6a3e3efafbc373592c60a4e1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### QE-MC-fPINN Relative L2 Test Error: 0.0307. Result ID: 6a3e3efafbc373592c60a4e0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### Improved MC-fPINN Relative L2 Test Error: 0.188. Result ID: 6a3e3efafbc373592c60a4dd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### Improved MC-fPINN Relative L2 Test Error: 0.265. Result ID: 6a3e3efafbc373592c60a4dc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### MC-fPINN Relative L2 Test Error: 0.443. Result ID: 6a3e3efafbc373592c60a4da. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### fPINN Relative L2 Test Error: 0.495. Result ID: 6a3e3efafbc373592c60a4de. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.5"}. This record does not assert independent reproduction. ### MC-fPINN Relative L2 Test Error: 0.857. Result ID: 6a3e3efafbc373592c60a4db. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"alpha":"1.9"}. This record does not assert independent reproduction. ### fPINN Relative L2 Test Error: 1.3. Result ID: 6a3e3efafbc373592c60a4df. [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.