# Integro-Differential Equation Solving on Volterra IDEs

Source: [Integro-Differential Equation Solving on Volterra IDEs](<https://www.sota2.com/research/sota/integro-differential-equation-solving-on-volterra-ides>)

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

Data updated: 2026-02-26T06:01:57.318Z

Evaluation of model performance on solving Integro-Differential Equations using the Volterra IDEs dataset, measured by Relative L2 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 | Integro-Differential Equation Solving |
| Dataset (including any stated split) | Volterra IDEs |
| Metric | Relative L2 Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 2 of 2 |
| 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/integro-differential-equation-solving-on-volterra-ides.md?metric=Relative%20L2%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| DCGD (Center) | 0.0011 | Not recorded | 68fa5cd41e209131ce9d489b |
| A-PINN | 0.0068 | Not recorded | 68fa5cd41e209131ce9d489b |

### DCGD (Center)

Relative L2 Error: 0.0011. Result ID: 698bb81d7a967eddb770d8d7.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5cd41e209131ce9d489b.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5cd41e209131ce9d489b.md>)

[Implementation](<https://github.com/youngsikhwang/Dual-Cone-Gradient-Descent>)

Recorded evaluation configuration: {"integrated\_with":"A-PINN \[9\]"}. This record does not assert independent reproduction.

### A-PINN

Relative L2 Error: 0.0068. Result ID: 698bb81d7a967eddb770d8d6.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5cd41e209131ce9d489b.md>)

Recorded evaluation configuration: {"baseline":"true"}. This record does not assert independent reproduction.

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