In recent decades, the main focus of computer modeling has been on supporting the design and development of engineering prototyes, but it is now ubiquitous in non-traditional areas such as medical rehabilitation. Conventional modeling approaches like the finite element~(FE) method are computationally costly when dealing with complex models, making them of limited use for purposes like real-time simulation or deployment on low-end hardware, if the model at hand cannot be simplified in a useful manner. Consequently, non-traditional approaches such as surrogate modeling using data-driven model order reduction are used to make complex high-fidelity models more widely available anyway. They often involve a dimensionality reduction step, in which the high-dimensional system state is transformed onto a low-dimensional subspace or manifold, and a regression approach to capture the reduced system behavior. While most publications focus on one dimensionality reduction, such as principal component analysis~(PCA) (linear) or autoencoder (nonlinear), we consider and compare PCA, kernel PCA, autoencoders, as well as variational autoencoders for the approximation of a structural dynamical system. In detail, we demonstrate the benefits of the surrogate modeling approach on a complex FE model of a human upper-arm. We consider both the models deformation and the internal stress as the two main quantities of interest in a FE context. By doing so we are able to create a computationally low cost surrogate model which captures the system behavior with high approximation quality and fast evaluations.

翻译：近几十年来，计算机建模的主要焦点已转向支持工程原型的设计与开发，但如今其在医疗康复等非传统领域也日益普及。传统建模方法（如有限元法）在处理复杂模型时计算成本高昂，若无法有效简化模型，其在实时仿真或低端硬件部署等场景中的适用性将受到限制。因此，采用数据驱动模型降阶等非传统替代建模方法，能够使复杂高保真模型更广泛地应用于实际场景。这类方法通常包含两个步骤：首先通过降维技术将高维系统状态映射至低维子空间或流形，随后采用回归方法捕捉降阶后的系统行为。尽管多数研究聚焦于单一降维方法（如主成分分析（线性）或自编码器（非线性）），本文则对主成分分析、核主成分分析、自编码器及变分自编码器在结构动力学系统近似中的表现进行了系统比较。具体而言，我们以人体上臂的复杂有限元模型为例，展示了替代建模方法的优势。在有限元框架下，将模型变形与内应力作为两个关键关注量。通过该方法，我们成功构建了计算成本低廉的替代模型，该模型能以高近似精度快速评估系统行为。