This paper introduces a novel approach that combines Proper Orthogonal Decomposition (POD) with Thermodynamics-based Artificial Neural Networks (TANN) to capture the macroscopic behavior of complex inelastic systems and derive macroelements in geomechanics. The methodology leverages POD to extract macroscopic Internal State Variables from microscopic state information, thereby enriching the macroscopic state description used to train an energy potential network within the TANN framework. The thermodynamic consistency provided by TANN, combined with the hierarchical nature of POD, allows to reproduce complex, non-linear inelastic material behaviors as well as macroscopic geomechanical systems responses. The approach is validated through applications of increasing complexity, demonstrating its capability to reproduce high-fidelity simulation data. The applications proposed include the homogenization of continuous inelastic representative unit cells and the derivation of a macroelement for a geotechnical system involving a monopile in a clay layer subjected to horizontal loading. Eventually, the projection operators directly obtained via POD, are exploit to easily reconstruct the microscopic fields. The results indicate that the POD-TANN approach not only offers accuracy in reproducing the studied constitutive responses, but also reduces computational costs, making it a practical tool for the multiscale modeling of heterogeneous inelastic geomechanical systems.

翻译：本文提出了一种新颖方法，将本征正交分解（POD）与基于热力学的人工神经网络（TANN）相结合，以捕捉复杂非弹性系统的宏观行为并推导地质力学中的宏观单元。该方法利用POD从微观状态信息中提取宏观内状态变量，从而丰富了用于在TANN框架内训练能量势网络的宏观状态描述。TANN提供的热力学一致性，结合POD的层次化特性，使得该方法能够复现复杂的非线性非弹性材料行为以及宏观地质力学系统响应。通过复杂度递增的应用案例验证了该方法的有效性，证明了其复现高保真仿真数据的能力。所提出的应用包括连续非弹性代表性单元体的均匀化处理，以及针对承受水平荷载的黏土层中单桩岩土系统推导宏观单元。最终，通过POD直接获得的投影算子被用于便捷地重建微观场。结果表明，POD-TANN方法不仅能够精确复现所研究的本构响应，还能显著降低计算成本，使其成为异质非弹性地质力学系统多尺度建模的实用工具。