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.
