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<p>During the freezing of frozen soil, the processes of temperature migration, moisture redistribution, and ice-water phase transitions are intricately interrelated, leading to governing equations characterized by pronounced nonlinearity and competing constraints. Conventional numerical approaches generally depend on grid discretization and nonlinear iterative schemes, whereas traditional physics-informed neural networks (PINNs) often encounter challenges such as loss term trade-offs and difficulties in optimizing over extended time steps when applied to strongly coupled phase-change phenomena. To overcome these limitations, this study introduces a Physical Information Extreme Learning Machine (PIELM) framework for simulating the coupled water-heat dynamics in frozen soils. By utilizing spatiotemporal coordinates as inputs and temperature and saturation as outputs, the proposed method employs a fixed stochastic hidden layer mapping alongside analytical derivative computations to systematically integrate initial conditions, Dirichlet and Neumann boundary conditions, experimental anchor points, and partial differential equation (PDE) residuals into a unified weighted linear system. Concurrently, Picard iteration is applied to linearize nonlinear closed-form expressions, including the ice-to-water ratio, diffusion coefficient, and hydraulic conductivity. Validation against clay freezing experimental data demonstrates that the comprehensive PIELM approach accurately reconstructs the final moisture content distribution and the temporal evolution of the hydrothermal field, achieving a root mean square error (RMSE) of 0.387% in moisture content prediction. This performance surpasses that of baseline PINN models and various thawing simulations. Analysis of the melting process reveals that experimental anchor points serve as critical constraints for stabilizing the final moisture profile; PDE constraints ensure the continuity of moisture and temperature fields; boundary condition weights directly influence boundary adherence; and the hydrothermal coupling mechanism significantly affects localized thermal and moisture responses. Furthermore, comparisons of computational time indicate that PIELM substantially reduces training costs under equivalent hardware configurations. A stochastic feature sensitivity analysis identifies 540 hidden layer nodes as optimal, balancing accuracy, stability, and computational efficiency. The findings of this research offer a novel physics-informed computational strategy for rapid prediction, assimilation of experimental data, and engineering-scale simulation of coupled water-heat processes during frozen soil phase transitions.</p>

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A physics-informed extreme learning machine for efficient linearized simulation of hydrothermal coupling during phase change in frozen soils

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Shangjiu Meng,
  • Mingwei Hai,
  • Miao Wang,
  • Zhiyuan Sun,
  • Bin Zhou

摘要

During the freezing of frozen soil, the processes of temperature migration, moisture redistribution, and ice-water phase transitions are intricately interrelated, leading to governing equations characterized by pronounced nonlinearity and competing constraints. Conventional numerical approaches generally depend on grid discretization and nonlinear iterative schemes, whereas traditional physics-informed neural networks (PINNs) often encounter challenges such as loss term trade-offs and difficulties in optimizing over extended time steps when applied to strongly coupled phase-change phenomena. To overcome these limitations, this study introduces a Physical Information Extreme Learning Machine (PIELM) framework for simulating the coupled water-heat dynamics in frozen soils. By utilizing spatiotemporal coordinates as inputs and temperature and saturation as outputs, the proposed method employs a fixed stochastic hidden layer mapping alongside analytical derivative computations to systematically integrate initial conditions, Dirichlet and Neumann boundary conditions, experimental anchor points, and partial differential equation (PDE) residuals into a unified weighted linear system. Concurrently, Picard iteration is applied to linearize nonlinear closed-form expressions, including the ice-to-water ratio, diffusion coefficient, and hydraulic conductivity. Validation against clay freezing experimental data demonstrates that the comprehensive PIELM approach accurately reconstructs the final moisture content distribution and the temporal evolution of the hydrothermal field, achieving a root mean square error (RMSE) of 0.387% in moisture content prediction. This performance surpasses that of baseline PINN models and various thawing simulations. Analysis of the melting process reveals that experimental anchor points serve as critical constraints for stabilizing the final moisture profile; PDE constraints ensure the continuity of moisture and temperature fields; boundary condition weights directly influence boundary adherence; and the hydrothermal coupling mechanism significantly affects localized thermal and moisture responses. Furthermore, comparisons of computational time indicate that PIELM substantially reduces training costs under equivalent hardware configurations. A stochastic feature sensitivity analysis identifies 540 hidden layer nodes as optimal, balancing accuracy, stability, and computational efficiency. The findings of this research offer a novel physics-informed computational strategy for rapid prediction, assimilation of experimental data, and engineering-scale simulation of coupled water-heat processes during frozen soil phase transitions.