SPIKANs: separable physics-informed Kolmogorov–Arnold networks

Journal Article · Mon Sep 22 00:00:00 EDT 2025 · Machine Learning: Science and Technology

DOI:https://doi.org/10.1088/2632-2153/ae05af· OSTI ID:3015493

Jacob, Bruno ^[1]; Howard, Amanda A. ^[1]; Stinis, Panos ^[1]

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1. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov–Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov–Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC05-76RL01830
• OSTI ID: 3015493
• Report Number(s): PNNL-SA--211691
• Journal Information: Machine Learning: Science and Technology, Journal Name: Machine Learning: Science and Technology Journal Issue: 3 Vol. 6; ISSN 2632-2153
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

Kolmogorov-Arnold networks
Physics-informed neural networks
Separable physics-informed neural networks