Sinc Kolmogorov-Arnold Network and Its Applications on Physics-informed Neural Networks

TL;DR

This paper introduces Sinc Kolmogorov-Arnold Networks (SincKANs), utilizing Sinc interpolation as learnable activation functions, demonstrating improved performance in function approximation and physics-informed neural network applications.

Contribution

It presents a novel use of Sinc interpolation within Kolmogorov-Arnold Networks, offering an effective alternative for representing functions with smoothness or singularities.

Findings

SincKANs outperform other methods in various experiments

Sinc interpolation effectively models functions with singularities

Improved results in physics-informed neural network applications

Abstract

In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to multilayer perceptron. Many different function representations have already been tried, but we show that Sinc interpolation proposes a viable alternative, since it is known in numerical analysis to represent well both smooth functions and functions with singularities. This is important not only for function approximation but also for the solutions of partial differential equations with physics-informed neural networks. Through a series of experiments, we show that SincKANs provide better results in almost all of the examples we have considered.