KAN PDE Thesis Code

Implementation accompanying the Master's Thesis “Kolmogorov–Arnold Theorem and Its Applications to Neural Networks”, University of Calabria.

This repository provides the implementation developed for my Master's Thesis in Mathematics.

The project implements a numerical solver for the 1D Fokker–Planck equation using Kolmogorov–Arnold Networks (KAN) within a Dual Physics-Informed Neural Network (Dual-PINN) framework.

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Author

Ugo Giorgio Samuele Campolo University of Calabria

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Description

The implementation includes:

• Kolmogorov–Arnold Network (KAN) architecture
• Dual Physics-Informed Neural Network training strategy
• Boundary–interior specialization
• Numerical solution of the 1D Fokker–Planck partial differential equation

This project accompanies the research work developed during the Master's Thesis in Mathematics.

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Results

Example result for the 1D Fokker–Planck equation:

Best model performance:

• Relative L2 error: 0.027
• L2 accuracy: 97.3%
• Total parameters: 160

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Requirements

Install all dependencies using:

pip install -r requirements.txt

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Run

Execute the main experiment:

python kan_doublepinn.py

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References

[1] Abbas, N., Colao, V., Macrì, D., Spataro, W. (2025). A Multi-Phase Dual-PINN Framework: Soft Boundary–Interior Specialization via Distance-Weighted Priors. arXiv preprint arXiv:2511.23409.

[2] LeBleu, B. (2024). efficient-KAN: An Efficient Implementation of Kolmogorov–Arnold Networks. GitHub Repository. https://github.com/Blealtan/efficient-kan

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Thesis

📄 Kolmogorov–Arnold Theorem and Its Applications to Neural Networks

The full Master's Thesis accompanying this repository is available here:

Download Thesis PDF