This paper introduces a novel approach that combines proper orthogonal decomposition (POD) with thermodynamics‐based artificial neural networks (TANNs) to capture the macroscopic behavior of complex inelastic systems and derive macro‐elements 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, nonlinear 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 macro‐element for a geotechnical system involving a monopile in a clay layer subjected to horizontal loading. Eventually, the projection operators directly obtained via POD are exploited 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.

中文翻译：

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用于岩土力学中材料多尺度建模和宏观元素推导的 POD-TANN 方法


本文介绍了一种新颖的方法，该方法将适当的正交分解 （POD） 与基于热力学的人工神经网络 （TANN） 相结合，以捕获复杂非弹性系统的宏观行为并推导出地质力学中的宏观元素。该方法利用 POD 从微观状态信息中提取宏观内部状态变量，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与 POD 的分层性质相结合，可以再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。该方法通过日益复杂的应用程序进行了验证，证明了其重现高保真仿真数据的能力。提出的应用包括连续非弹性代表性晶胞的均质化，以及为岩土工程系统推导宏元，该系统涉及承受水平载荷的粘土层中的单桩。最终，利用通过 POD 直接获得的投影算子来轻松重建微观场。结果表明，POD-TANN 方法不仅在再现所研究的本构响应方面提供了准确性，而且还降低了计算成本，使其成为非均质非弹性岩土力学系统多尺度建模的实用工具。