Open Access

ARTICLE

Spectral-Integrated Neural Networks for Transient Heat Conduction in Thin-Walled Structures

Ting Gao¹, Chengze Shang², Juan Wang^1,*, Yan Gu^3,*

1 School of Mathematics and Statistics, Qingdao University, Qingdao, China
2 Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, UK
3 Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, China

* Corresponding Authors: Juan Wang. Email: ; Yan Gu. Email:

(This article belongs to the Special Issue: Machine Learning, Data-Driven and Novel Approaches in Computational Mechanics)

Computer Modeling in Engineering & Sciences 2026, 146(2), 7 https://doi.org/10.32604/cmes.2026.077949

Received 20 December 2025; Accepted 29 January 2026; Issue published 26 February 2026

Abstract

An efficient data-driven numerical framework is developed for transient heat conduction analysis in thin-walled structures. The proposed approach integrates spectral time discretization with neural network approximation, forming a spectral-integrated neural network (SINN) scheme tailored for problems characterized by long-time evolution. Temporal derivatives are treated through a spectral integration strategy based on orthogonal polynomial expansions, which significantly alleviates stability constraints associated with conventional time-marching schemes. A fully connected neural network is employed to approximate the temperature-related variables, while governing equations and boundary conditions are enforced through a physics-informed loss formulation. Numerical investigations demonstrate that the proposed method maintains high accuracy even when large time steps are adopted, where standard numerical solvers often suffer from instability or excessive computational cost. Moreover, the framework exhibits strong robustness for ultrathin configurations with extreme aspect ratios, achieving relative errors on the order of 10⁻⁵ or lower. These results indicate that the SINN framework provides a reliable and efficient alternative for transient thermal analysis of thin-walled structures under challenging computational conditions.

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Keywords

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