# Root Finding on Lane-Emden differential equation

Source: [Root Finding on Lane-Emden differential equation](<https://www.sota2.com/research/sota/root-finding-on-lane-emden-differential-equation>)

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

Data updated: 2026-02-26T05:26:40.769Z

Evaluation of model performance on finding the roots of the Lane-Emden differential equation, typically measured by Absolute 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 | Root Finding |
| Dataset (including any stated split) | Lane-Emden differential equation |
| Metric | Absolute Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 30 of 30 |
| 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

- [Absolute Error](<https://www.sota2.com/research/sota/root-finding-on-lane-emden-differential-equation.md?metric=Absolute%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Absolute Error | Result date | Report paper |
| --- | --- | --- | --- |
| GEPINN | 1.4e-7 | Not recorded | 68fa5be31e209131ce9cc4ac |
| GEPINN | 1.4e-7 | Not recorded | 68fa5bec1e209131ce9cca99 |
| fKAN | 5.55e-7 | Not recorded | 68fa5be31e209131ce9cc4ac |
| fKAN | 5.55e-7 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Padé\[q/6\]-rKAN | 0.00000486 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Jacobi-rKAN | 0.00000515 | Not recorded | 68fa5bec1e209131ce9cca99 |
| fKAN | 0.00000867 | Not recorded | 68fa5be31e209131ce9cc4ac |
| Padé\[q/6\]-rKAN | 0.00000867 | Not recorded | 68fa5bec1e209131ce9cca99 |
| fKAN | 0.00000867 | Not recorded | 68fa5bec1e209131ce9cca99 |
| fKAN | 0.00000934 | Not recorded | 68fa5be31e209131ce9cc4ac |
| fKAN | 0.00000934 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Padé\[q/6\]-rKAN | 0.0000106 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Jacobi-rKAN | 0.0000288 | Not recorded | 68fa5bec1e209131ce9cca99 |
| fKAN | 0.0000352 | Not recorded | 68fa5be31e209131ce9cc4ac |
| fKAN | 0.0000352 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Padé\[q/6\]-rKAN | 0.0000509 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Jacobi-rKAN | 0.0000712 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Jacobi-rKAN | 0.00024 | Not recorded | 68fa5bec1e209131ce9cca99 |
| fKAN | 0.000297 | Not recorded | 68fa5be31e209131ce9cc4ac |
| fKAN | 0.000297 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Jacobi-rKAN | 0.00157 | Not recorded | 68fa5bec1e209131ce9cca99 |
| GEPINN | 0.00483 | Not recorded | 68fa5be31e209131ce9cc4ac |
| GEPINN | 0.00483 | Not recorded | 68fa5bec1e209131ce9cca99 |
| GEPINN | 0.00893 | Not recorded | 68fa5be31e209131ce9cc4ac |
| GEPINN | 0.00893 | Not recorded | 68fa5bec1e209131ce9cca99 |
| GEPINN | 0.0188 | Not recorded | 68fa5be31e209131ce9cc4ac |
| GEPINN | 0.0188 | Not recorded | 68fa5bec1e209131ce9cca99 |
| Padé\[q/6\]-rKAN | 0.0282 | Not recorded | 68fa5bec1e209131ce9cca99 |
| GEPINN | 0.0508 | Not recorded | 68fa5be31e209131ce9cc4ac |
| GEPINN | 0.0508 | Not recorded | 68fa5bec1e209131ce9cca99 |

### GEPINN

Absolute Error: 1.4e-7. Result ID: 698bb2ec7a967eddb770b473.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

Recorded evaluation configuration: {"m":"0"}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 1.4e-7. Result ID: 698c621637894ef7d9cdfe0e.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

Recorded evaluation configuration: {"Polytropic index (w)":0}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 5.55e-7. Result ID: 698bb2ec7a967eddb770b471.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"m":"3"}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 5.55e-7. Result ID: 698c621637894ef7d9cdfe0c.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":3}. This record does not assert independent reproduction.

### Padé\[q/6\]-rKAN

Absolute Error: 0.00000486. Result ID: 698c621637894ef7d9cdfe04.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":0}. This record does not assert independent reproduction.

### Jacobi-rKAN

Absolute Error: 0.00000515. Result ID: 698c621637894ef7d9cdfdff.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":0}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.00000867. Result ID: 698bb2ec7a967eddb770b46f.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"m":"1"}. This record does not assert independent reproduction.

### Padé\[q/6\]-rKAN

Absolute Error: 0.00000867. Result ID: 698c621637894ef7d9cdfe05.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":1}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.00000867. Result ID: 698c621637894ef7d9cdfe0a.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":1}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.00000934. Result ID: 698bb2ec7a967eddb770b470.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"m":"2"}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.00000934. Result ID: 698c621637894ef7d9cdfe0b.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":2}. This record does not assert independent reproduction.

### Padé\[q/6\]-rKAN

Absolute Error: 0.0000106. Result ID: 698c621637894ef7d9cdfe07.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":3}. This record does not assert independent reproduction.

### Jacobi-rKAN

Absolute Error: 0.0000288. Result ID: 698c621637894ef7d9cdfe01.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":2}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.0000352. Result ID: 698bb2ec7a967eddb770b46e.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"m":"0"}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.0000352. Result ID: 698c621637894ef7d9cdfe09.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":0}. This record does not assert independent reproduction.

### Padé\[q/6\]-rKAN

Absolute Error: 0.0000509. Result ID: 698c621637894ef7d9cdfe06.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":2}. This record does not assert independent reproduction.

### Jacobi-rKAN

Absolute Error: 0.0000712. Result ID: 698c621637894ef7d9cdfe00.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":1}. This record does not assert independent reproduction.

### Jacobi-rKAN

Absolute Error: 0.00024. Result ID: 698c621637894ef7d9cdfe02.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":3}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.000297. Result ID: 698bb2ec7a967eddb770b472.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"m":"4"}. This record does not assert independent reproduction.

### fKAN

Absolute Error: 0.000297. Result ID: 698c621637894ef7d9cdfe0d.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/fKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":4}. This record does not assert independent reproduction.

### Jacobi-rKAN

Absolute Error: 0.00157. Result ID: 698c621637894ef7d9cdfe03.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":4}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.00483. Result ID: 698bb2ec7a967eddb770b474.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

Recorded evaluation configuration: {"m":"1"}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.00483. Result ID: 698c621637894ef7d9cdfe0f.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

Recorded evaluation configuration: {"Polytropic index (w)":1}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.00893. Result ID: 698bb2ec7a967eddb770b475.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

Recorded evaluation configuration: {"m":"2"}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.00893. Result ID: 698c621637894ef7d9cdfe10.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

Recorded evaluation configuration: {"Polytropic index (w)":2}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.0188. Result ID: 698bb2ec7a967eddb770b476.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

Recorded evaluation configuration: {"m":"3"}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.0188. Result ID: 698c621637894ef7d9cdfe11.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

Recorded evaluation configuration: {"Polytropic index (w)":3}. This record does not assert independent reproduction.

### Padé\[q/6\]-rKAN

Absolute Error: 0.0282. Result ID: 698c621637894ef7d9cdfe08.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

[Implementation](<https://github.com/alirezaafzalaghaei/rKAN>)

Recorded evaluation configuration: {"Polytropic index (w)":4}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.0508. Result ID: 698bb2ec7a967eddb770b477.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4ac.md>)

Recorded evaluation configuration: {"m":"4"}. This record does not assert independent reproduction.

### GEPINN

Absolute Error: 0.0508. Result ID: 698c621637894ef7d9cdfe12.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5bec1e209131ce9cca99.md>)

Recorded evaluation configuration: {"Polytropic index (w)":4}. This record does not assert independent reproduction.

Page 1 of 1. This is an index page, not the full collection.