HFS-TransNet: A Hybrid Fixed-Stress Transferable Neural Network for Quasi-Static Biot Poroelasticity
Abstract
The quasi-static Biot system, which governs coupled fluid-solid interactions in poroelastic media, poses significant computational challenges due to its strong coupling and multiscale nature. To address these, we propose a hybrid fixed-stress transferable neural network (HFS-TransNet) method. In HFS-TransNet, a data-driven TransNet module first approximates observed data on an initialization domain to supply a high-quality starting point for the subsequent physics-informed stage, which then drives fixed-stress splitting iterations via TransNet and admits an error bound. After each iteration, a greedy update strategy on a validation domain prevents model degradation and a relative tolerance criterion governs convergence termination. HFS-TransNet thereby inherits the robustness of the fixed-stress splitting scheme, the flexibility of data-driven modeling, and the transferability of TransNet, effectively overcoming the strong coupling and locking instability inherent in the Biot system. Ablation studies and comparisons with FS-FEM and FS-PINN confirm HFS-TransNet's superior performance in capturing multiscale coupled physics across varying physical parameters and boundary conditions. By bridging classical decoupled iterative schemes with hybrid scientific machine learning, HFS-TransNet offers a novel perspective for complex poroelastic simulations, as demonstrated by its successful application to brain edema simulations.
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BibTeX
@misc{shen2026hfstransnet,
title = {{HFS-TransNet: A Hybrid Fixed-Stress Transferable Neural Network for Quasi-Static Biot Poroelasticity}},
author = {Zhequan Shen and Liyong Zhu and Mingchao Cai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04879},
eprint = {2610.04879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04879},
}
RIS
TY - UNPB
TI - HFS-TransNet: A Hybrid Fixed-Stress Transferable Neural Network for Quasi-Static Biot Poroelasticity
AU - Zhequan Shen
AU - Liyong Zhu
AU - Mingchao Cai
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04879
UR - https://arxiv.org/abs/2610.04879
AB - The quasi-static Biot system, which governs coupled fluid-solid interactions in poroelastic media, poses significant computational challenges due to its strong coupling and multiscale nature. To address these, we propose a hybrid fixed-stress transferable neural network (HFS-TransNet) method. In HFS-TransNet, a data-driven TransNet module first approximates observed data on an initialization domain to supply a high-quality starting point for the subsequent physics-informed stage, which then drives fixed-stress splitting iterations via TransNet and admits an error bound. After each iteration, a greedy update strategy on a validation domain prevents model degradation and a relative tolerance criterion governs convergence termination. HFS-TransNet thereby inherits the robustness of the fixed-stress splitting scheme, the flexibility of data-driven modeling, and the transferability of TransNet, effectively overcoming the strong coupling and locking instability inherent in the Biot system. Ablation studies and comparisons with FS-FEM and FS-PINN confirm HFS-TransNet's superior performance in capturing multiscale coupled physics across varying physical parameters and boundary conditions. By bridging classical decoupled iterative schemes with hybrid scientific machine learning, HFS-TransNet offers a novel perspective for complex poroelastic simulations, as demonstrated by its successful application to brain edema simulations.
ER -