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A comprehensive analysis of physics-informed neural networks for solving one-way coupled problems.

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Title: A comprehensive analysis of physics-informed neural networks for solving one-way coupled problems.
Authors: Kamil, Hamza1,2 (AUTHOR), Soulaïmani, Azzeddine2 (AUTHOR) abdelaziz.beljadid@um6p.ma, Beljadid, Abdelaziz1,3 (AUTHOR) beljadid@mit.edu
Source: Computers & Mathematics with Applications. Jun2026, Vol. 212, p166-189. 24p.
Subjects: Sequential learning, Transfer of training, Fluid-structure interaction, Thermodynamics, Electric heating
Abstract: Physics-informed neural networks (PINNs) offer efficient solvers for differential equations. However, their performance often degrades when applied to complex problems, particularly in multiphysics modeling. In this study, we focus on one-way coupled models, where each equation depends only on the outputs of preceding ones. Such structures frequently arise in thermo-mechanics coupling, fluid-structure interaction, electro-thermal processes, and multispecies transport. We examine why standard PINNs struggle on one-way coupled systems. When all equations are trained simultaneously, the network tends to ignore the inherent one-way causal structure due to spectral bias, leading to biased learning and poor convergence. We analyze these issues using the neural tangent kernel, the loss landscape, the distribution of back-propagated gradients, gradient conflict, and the resulting ill-conditioning. To address these challenges, we introduce PINN strategies that explicitly preserve the one-way causal order, including sequential training, transfer learning, and other causality-aware variants. Numerical experiments on benchmark problems demonstrate that the proposed approaches preserve one-way causality and improve both accuracy and training efficiency compared to standard PINNs. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 193498709
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  Data: <searchLink fieldCode="DE" term="%22Sequential+learning%22">Sequential learning</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+of+training%22">Transfer of training</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid-structure+interaction%22">Fluid-structure interaction</searchLink><br /><searchLink fieldCode="DE" term="%22Thermodynamics%22">Thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+heating%22">Electric heating</searchLink>
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  Data: Physics-informed neural networks (PINNs) offer efficient solvers for differential equations. However, their performance often degrades when applied to complex problems, particularly in multiphysics modeling. In this study, we focus on one-way coupled models, where each equation depends only on the outputs of preceding ones. Such structures frequently arise in thermo-mechanics coupling, fluid-structure interaction, electro-thermal processes, and multispecies transport. We examine why standard PINNs struggle on one-way coupled systems. When all equations are trained simultaneously, the network tends to ignore the inherent one-way causal structure due to spectral bias, leading to biased learning and poor convergence. We analyze these issues using the neural tangent kernel, the loss landscape, the distribution of back-propagated gradients, gradient conflict, and the resulting ill-conditioning. To address these challenges, we introduce PINN strategies that explicitly preserve the one-way causal order, including sequential training, transfer learning, and other causality-aware variants. Numerical experiments on benchmark problems demonstrate that the proposed approaches preserve one-way causality and improve both accuracy and training efficiency compared to standard PINNs. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.camwa.2026.03.037
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      – Code: eng
        Text: English
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        PageCount: 24
        StartPage: 166
    Subjects:
      – SubjectFull: Sequential learning
        Type: general
      – SubjectFull: Transfer of training
        Type: general
      – SubjectFull: Fluid-structure interaction
        Type: general
      – SubjectFull: Thermodynamics
        Type: general
      – SubjectFull: Electric heating
        Type: general
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      – TitleFull: A comprehensive analysis of physics-informed neural networks for solving one-way coupled problems.
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            NameFull: Soulaïmani, Azzeddine
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            – D: 15
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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