Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities
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Abstract (arXiv)
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 effectively represent both smooth functions and functions with singularities. This is important not only for function approximation but also for solving the 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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 29 of its 72 references that are in the map. First posted on arXiv 5 Oct 2024.
Builds on
29 of 72 references.
References · 29
- 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
- 2018On the Spectral Bias of Neural Networkscited by 1,321
- 2024KAN: Kolmogorov-Arnold Networkscited by 634
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
- 2016Error bounds for approximations with deep ReLU networkscited by 567
- 2017Solving high-dimensional partial differential equations using deep learningcited by 549
- 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 360
- 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
- 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
- 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
- 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
- 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
17 more
- 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
- 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
- 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 64
- 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
- 2024KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physicscited by 58
- 2021Physics-Informed Neural Networks for AC Optimal Power Flowcited by 52
- 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
- 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
- 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
- 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 33
- 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 31
- 2020Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspectivecited by 22
- 2022Physics-Informed Neural Networks for Quantum Eigenvalue Problemscited by 18
- 2023MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networkscited by 17
- 2024Physics-informed neural networks for parameter learning of wildfire spreadingcited by 6
- 2024Frequency-adaptive Multi-scale Deep Neural Networkscited by 5
- 2024Astral: training physics-informed neural networks with error majorantscited by 1
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