Physics-informed neural networks for transient diffusion interface problems: Kolmogorov–Arnold networks versus multilayer perceptrons

Hosseini, Vahid Reza; Carraro, Thomas

doi:10.1016/j.cma.2026.119219

Physics-informed neural networks for transient diffusion interface problems: Kolmogorov–Arnold networks versus multilayer perceptrons

Publication date

2026-07-09

Document type

Forschungsartikel

Author

Hosseini, Vahid Reza

Carraro, Thomas

Organisational unit

Angewandte Mathematik

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DOI

10.1016/j.cma.2026.119219

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/24300

Scopus ID

2-s2.0-105044109306

Publisher

Elsevier

Series or journal

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

Periodical volume

461, Part B

Article ID

119219

Peer-reviewed

✅

Part of the university bibliography

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Language

English

Keyword

Battery modeling

Interface problems

Kolmogorov–Arnold networks

Lithium-ion batteries

Physics-informed neural networks

Progressive time marching

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Abstract

Physics-informed neural networks (PINNs) remain challenging for transient interface problems with discontinuous coefficients, sharp interfacial gradients, and multiple temporal scales. In this work, we develop a PINN framework for transient diffusion interface problems with physically consistent interface conditions and compare multilayer perceptron (MLP) architectures with several radial-basis-function Kolmogorov–Arnold network (RBF–KAN) variants.The novelty of the proposed framework lies in a trainable-center RBF–KAN approximation enriched by low-degree polynomial components and embedded in a progressive expanding-time-domain PINN formulation for transient diffusion interface problems. The RBF–KAN models use trainable centers and are considered both with and without polynomial enrichment, allowing us to assess the effects of localized adaptive approximation and polynomial augmentation on accuracy and parameter efficiency. Training starts on a short time interval and is successively extended to larger temporal domains, allowing the localized approximation space to adapt as the space–time domain is enlarged. This strategy is compared with a time-domain-decomposition approach.The methods are assessed on transient diffusion interface benchmarks with analytical reference solutions, including a battery-inspired model with discontinuous diffusion coefficients, rapid transient decay, and convergence to steady state. The results show that RBF–KANs alone do not uniformly outperform MLP-based PINNs. Instead, the best accuracy and parameter efficiency are obtained when localized RBF–KAN approximation is combined with polynomial enrichment, trainable centers, and the progressive expanding-time-domain strategy. This conclusion is further supported by a component-wise analysis, which shows that the interaction between approximation space and temporal training strategy is critical for the considered transient interface problems.

Description

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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Published version

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