Model Order Reduction (MOR) is a core technology for the creation of comprehensive executable Digital Twins, since it efficiently reduces the computational burden of high-fidelity models. When dealing with nonlinear structural Finite Element analyses, several Hyper-Reduction (HR) approaches have been developed to reduce the computational cost. Nonetheless, HR approaches are typically intrusive in nature, posing challenges when it comes to integration into existing (commercial) software. Recently, data driven Non-Intrusive MOR methodologies have been proposed. However, these techniques often suffer from overfitting and violate key physics properties, leading to unstable behavior. This work proposes to use Scientific Machine Learning to reintegrate critical stability-preserving physics properties. It introduces a data-driven, physics-augmented, parametric approach that combines Proper Orthogonal Decomposition (POD) with a Partially Input Convex Neural Network (PICNN) architecture. The proposed method effectively reduces the computational burden associated with parametric static nonlinear elastic structural problems while retaining material consistency, hyper-elasticity, and material stability properties in the Reduced Order Model. Numerical validation on several structural models subjected to geometrical and material nonlinearities under static loading conditions demonstrates the effectiveness of the POD-PICNN approach. Additionally, three different sampling strategies have been compared to assess their impact on the method performance. The results emphasize that physics-augmentation is required, as it inherently embeds essential physical constraints into the neural network architecture, ensuring stable and consistent behavior, while highlighting its potential for dynamic and multiphysics applications.

中文翻译：

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非线性结构有限元公式的非侵入式参数超还原


模型降阶 （MOR） 是创建全面的可执行数字孪生的核心技术，因为它有效地减轻了高保真模型的计算负担。在处理非线性结构有限元分析时，已经开发了几种超还原 （HR） 方法来降低计算成本。尽管如此，人力资源方法通常具有侵入性，在集成到现有（商业）软件时构成了挑战。最近，提出了数据驱动的非侵入式 MOR 方法。然而，这些技术经常出现过拟合并违反关键物理特性，导致行为不稳定。这项工作建议使用科学机器学习来重新整合关键的保稳物理特性。它引入了一种数据驱动、物理增强的参数化方法，该方法将正确正交分解 （POD） 与部分输入凸神经网络 （PICNN） 架构相结合。所提出的方法有效地减轻了与参数化静态非线性弹性结构问题相关的计算负担，同时在降阶模型中保留了材料的一致性、超弹性和材料稳定性属性。在静态载荷条件下对几个受几何和材料非线性影响的结构模型进行数值验证，证明了 POD-PICNN 方法的有效性。此外，还比较了三种不同的采样策略，以评估它们对方法性能的影响。 结果强调物理场增强是必需的，因为它本质上将基本的物理约束嵌入到神经网络架构中，确保稳定一致的行为，同时突出了其在动态和多物理场应用方面的潜力。