A Cooperative Soft-Hard PINN Framework for Decoupling the Thermoelasticity and Thermal Convection Multiphysics

Physics-informed neural networks (PINNs) often struggle to balance multiple loss terms in thermally coupled multiphysics problems. We propose Cooperative Soft-Hard PINNs (s-hPINN/s-HB-PINN), which apply soft constraints to fields with Neumann conditions while enforcing hard constraints on others to balance exact boundary enforcement with training stability. Validated on thermoelasticity and thermal convection, our method reduces training time by approximately 56%. In thermal convection experiments, incorporating partial data further reduces velocity errors by up to 78% compared to standard PINNs. We subsequently assessed the framework’s robustness against varying relative Gaussian white noise levels and different data sampling locations. The result demonstrate that s-HB-PINN maintains high-fidelity predictions even under noise interference, consistently outperforming baseline methods. This confirms that the proposed collaborative strategy offers a superior trade-off between accuracy, efficiency, and robustness in complex multiphysics environments.

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Publication Details

Journal
Applied Sciences
Published
2026-02-13
DOI
https://doi.org/10.3390/app16041885
Citations
1
Primary Topic
Model Reduction and Neural Networks
Type
article
Field-Weighted Citation Impact
36.90
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article

A Cooperative Soft-Hard PINN Framework for Decoupling the Thermoelasticity and Thermal Convection Multiphysics

Hangzhou Yang, Chuyu Zhou, Pengyu Nan, Guoguo Xin et al.
1 citations
Applied Sciences
Model Reduction and Neural Networks
36.90
article

A Cooperative Soft-Hard PINN Framework for Decoupling the Thermoelasticity and Thermal Convection Multiphysics

Hangzhou Yang, Chuyu Zhou, Pengyu Nan, Guoguo Xin, Yuxin Liu
article en
1 citations

Abstract

Physics-informed neural networks (PINNs) often struggle to balance multiple loss terms in thermally coupled multiphysics problems. We propose Cooperative Soft-Hard PINNs (s-hPINN/s-HB-PINN), which apply soft constraints to fields with Neumann conditions while enforcing hard constraints on others to balance exact boundary enforcement with training stability. Validated on thermoelasticity and thermal convection, our method reduces training time by approximately 56%. In thermal convection experiments, incorporating partial data further reduces velocity errors by up to 78% compared to standard PINNs. We subsequently assessed the framework’s robustness against varying relative Gaussian white noise levels and different data sampling locations. The result demonstrate that s-HB-PINN maintains high-fidelity predictions even under noise interference, consistently outperforming baseline methods. This confirms that the proposed collaborative strategy offers a superior trade-off between accuracy, efficiency, and robustness in complex multiphysics environments.

Applied SciencesVol. 16(4)
Northwest University (CN), QuantumCTek (China) (CN)
Openalex Percentile: Top 1%
Model Reduction and Neural Networks
36.90
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A Cooperative Soft-Hard PINN Framework for Decoupling the Thermoelasticity and Thermal Convection Multiphysics — Hangzhou Yang, Chuyu Zhou, et al. · Applied Sciences (2026) | TGRS Research Map | TGRS