Sinc Kolmogorov-Arnold Network and Its Applications on Physics-informed Neural Networks
For researchers using KANs or physics-informed neural networks, this work offers a modest improvement in representation accuracy for smooth and singular functions.
The paper introduces Sinc interpolation into Kolmogorov-Arnold Networks (KANs) to improve function approximation and physics-informed neural network performance, achieving better results in nearly all tested examples.
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.