  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.
