Academic Journal
Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities.
| Title: | Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities. |
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| Authors: | Yu T; The Artificial Intelligence Center Skolkovo Institute of Science and Technology, Skolkovo, Russia; Artificial Intelligence Research Institute, Moscow, Russia., Qiu J; Department of Mathematics, Southern University of Science and Technology, Shenzhen, China., Yang J; Department of Mathematics, Southern University of Science and Technology, Shenzhen, China; National Center for Applied Mathematics Shenzhen (NCAMS), Southern University of Science and Technology, Shenzhen, China; SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China. Electronic address: yangj7@sustech.edu.cn., Oseledets I; The Artificial Intelligence Center Skolkovo Institute of Science and Technology, Skolkovo, Russia; Artificial Intelligence Research Institute, Moscow, Russia. |
| Source: | Neural networks : the official journal of the International Neural Network Society [Neural Netw] 2026 Oct; Vol. 202, pp. 109033. Date of Electronic Publication: 2026 Apr 24. |
| Publication Type: | Journal Article |
| Language: | English |
| Journal Info: | Publisher: Pergamon Press Country of Publication: United States NLM ID: 8805018 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1879-2782 (Electronic) Linking ISSN: 08936080 NLM ISO Abbreviation: Neural Netw Subsets: MEDLINE |
| Imprint Name(s): | Original Publication: New York : Pergamon Press, [c1988- |
| MeSH Terms: | Neural Networks, Computer*, Multilayer Perceptrons ; Algorithms |
| 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 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. The codes are public at https://github.com/DUCH714/SincKAN. (Copyright © 2026 Elsevier Ltd. All rights reserved.) |
| Competing Interests: | Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. |
| Contributed Indexing: | Keywords: Computational physics; Kolmogorov-Arnold networks; Partial differential equations; Physics-informed neural networks |
| Entry Date(s): | Date Created: 20260430 Date Completed: 20260718 Latest Revision: 20260718 |
| Update Code: | 20260718 |
| DOI: | 10.1016/j.neunet.2026.109033 |
| PMID: | 42061189 |
| Database: | MEDLINE |
| ISSN: | 1879-2782 |
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| DOI: | 10.1016/j.neunet.2026.109033 |