# Solving Fractional Advection-Diffusion Equations on ADE 2D Case A2 (T=100)

Source: [Solving Fractional Advection-Diffusion Equations on ADE 2D Case A2 (T=100)](<https://www.sota2.com/research/sota/solving-fractional-advection-diffusion-equations-on-ade-2d-case-a2-t-100>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-26T08:57:33.115Z

Evaluation of models solving the 2D time-space fractional Advection-Diffusion Equation (Case A2, T=100 simulation), measured using 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 time-space fractional Advection-Diffusion Equations |
| Dataset (including any stated split) | Time-space fractional ADE 2D case A2 T=100 (long-time simulation) |
| Metric | Relative L2 Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 5 of 5 |
| 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](<https://www.sota2.com/research/sota/solving-fractional-advection-diffusion-equations-on-ade-2d-case-a2-t-100.md?metric=Relative%20L2%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| fTNN | 0.0001889 | Not recorded | 6a3e079e206542251d7cb557 |
| QE-MC-fPINN | 0.006208 | Not recorded | 6a3e079e206542251d7cb557 |
| fPINN | 0.04066 | Not recorded | 6a3e079e206542251d7cb557 |
| MC-fPINN | 0.1001 | Not recorded | 6a3e079e206542251d7cb557 |
| Improved MC-fPINN | 0.2321 | Not recorded | 6a3e079e206542251d7cb557 |

### fTNN

Relative L2 Error: 0.0001889. Result ID: 6a3e3efafbc373592c60a4e8.

[Reporting paper](<https://www.sota2.com/research/paper/6a3e079e206542251d7cb557.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a3e079e206542251d7cb557.md>)

Recorded evaluation configuration: {"Time Horizon (T)":"100","Simulation Type":"long-time"}. This record does not assert independent reproduction.

### QE-MC-fPINN

Relative L2 Error: 0.006208. Result ID: 6a3e3efafbc373592c60a4e7.

[Reporting paper](<https://www.sota2.com/research/paper/6a3e079e206542251d7cb557.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5cd61e209131ce9d4a53.md>)

Recorded evaluation configuration: {"Time Horizon (T)":"100","Simulation Type":"long-time"}. This record does not assert independent reproduction.

### fPINN

Relative L2 Error: 0.04066. Result ID: 6a3e3efafbc373592c60a4e6.

[Reporting paper](<https://www.sota2.com/research/paper/6a3e079e206542251d7cb557.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa405e1e209131ce8f2fa7.md>)

Recorded evaluation configuration: {"Time Horizon (T)":"100","Simulation Type":"long-time","implementation":"DeepXDE","discretization":"L1 scheme and Grünwald–Letnikov"}. This record does not assert independent reproduction.

### MC-fPINN

Relative L2 Error: 0.1001. Result ID: 6a3e3efafbc373592c60a4e4.

[Reporting paper](<https://www.sota2.com/research/paper/6a3e079e206542251d7cb557.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5cd61e209131ce9d4a53.md>)

Recorded evaluation configuration: {"Time Horizon (T)":"100","Simulation Type":"long-time"}. This record does not assert independent reproduction.

### Improved MC-fPINN

Relative L2 Error: 0.2321. Result ID: 6a3e3efafbc373592c60a4e5.

[Reporting paper](<https://www.sota2.com/research/paper/6a3e079e206542251d7cb557.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5cd61e209131ce9d4a53.md>)

Recorded evaluation configuration: {"Time Horizon (T)":"100","Simulation Type":"long-time"}. This record does not assert independent reproduction.

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