Orthogonal Polynomial Kolmogorov–Arnold Networks for physics–informed PDE solving
File(s)
Accepted version
Author(s)
Salluri, Sumith
Shukla, Pancham
Type
Conference Paper
Abstract
Orthogonal Polynomial Kolmogorov–Arnold Networks (OP-KANs) blend the compactness of polynomial bases with neural-network flexibility. We study replacing fully connected networks (FCNs) in Finite-Basis Physics-Informed Networks (FB-PINNs) with OP-KANs for solving PDEs. We use a generalized OP-KAN layer supporting Chebyshev, Legendre, Jacobi, Hermite and any recurrence-defined basis. Our JAX implementation fuses basis evaluation and contraction into one Accelerated Linear Algebra (XLA) kernel, reducing backward floating-point operations (FLOPs) by up to 80% and training time by 50%.
Across a ten-problem benchmark, from 1D harmonic oscillators to the 3D Taylor Green vortex, OP-KANs match or surpass FCN accuracy with roughly 10 fewer parameters. On discontinuous or high-frequency tasks, a two-layer Jacobi-KAN reduces mean relative absolute error by 30% and variance by up to 75% with comparable training time. Scheduled training further lowers peak memory by 65%, enabling single-GPU solutions for problems that exceed memory budget when using FCNs. OP-KANs thus emerge as an efficient, interpretable alternative to FCNs in scientific machine learning, especially when memory or data are scarce.
Across a ten-problem benchmark, from 1D harmonic oscillators to the 3D Taylor Green vortex, OP-KANs match or surpass FCN accuracy with roughly 10 fewer parameters. On discontinuous or high-frequency tasks, a two-layer Jacobi-KAN reduces mean relative absolute error by 30% and variance by up to 75% with comparable training time. Scheduled training further lowers peak memory by 65%, enabling single-GPU solutions for problems that exceed memory budget when using FCNs. OP-KANs thus emerge as an efficient, interpretable alternative to FCNs in scientific machine learning, especially when memory or data are scarce.
Date Issued
2026-01-02
Date Acceptance
2025-08-08
Citation
Lecture Notes in Networks and Systems, 2026, 1727, pp.217-225
ISBN
978-3-032-11515-7
ISSN
2367-3370
Publisher
Springer
Start Page
217
End Page
225
Journal / Book Title
Lecture Notes in Networks and Systems
Volume
1727
Copyright Statement
© 2026 The Author(s), under exclusive license to Springer Nature Switzerland AG. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Source
9th World Conference on Smart Trends in Systems, Security and Sustainability (WorldS4 2025).
Publication Status
Published
Start Date
2025-08-19
Finish Date
2025-08-21
Coverage Spatial
London, UK
Date Publish Online
2026-01-02