Data-driven Surrogate Modeling of Structural Dynamical Systems via Latent Space Representations

Abstract

Numerical simulations provide powerful predictive capabilities to analyze the dynamic behavior of complex systems but suffer from high computational costs, limiting applicability in multi-query, real-time, or resource-constrained scenarios. This motivates the development of surrogate models—efficient approximations emulating high-fidelity simulations with reduced overhead. This thesis focuses on non-intrusive, data-driven surrogate modeling approaches that integrate classical numerical methods with modern Machine Learning (ML) techniques, thereby harnessing the synergy between scientific principles and data-driven technologies. The introduced framework combines model order reduction and ML concepts, constructing compact, low-dimensional latent representations where complex system dynamics can be efficiently learned and predicted. Various strategies for identifying suitable coordinate representations and modeling latent dynamics are explored, including black-box approximations and system identification yielding interpretable equations. Applications range from simple academic cases to complex multi-body and finite element models, including coupled simulations and nonlinear contact scenarios. Key contributions include systematic benchmarking of dimensionality reduction techniques, multi-resolution modeling for multi-scale phenomena, structure-preserving discovery methods, and a generative reduced-order modeling framework with embedded uncertainty quantification. These approaches enable computationally efficient, accurate, interpretable surrogate models deployable in real-time settings, broadening numerical simulation accessibility in science and engineering.