Résumé
The simulation and optimization of complex technical systems often require models that are both sufficiently accurate and computationally efficient. In engineering practice, this balance is difficult to achieve: detailed numerical models provide valuable insight, but they are frequently too costly for repeated evaluations, design optimization, uncertainty studies, or real-time applications.
In this contribution, I will discuss how mathematical methods from model order reduction, system identification, and machine learning can be transferred into practical engineering workflows for structural dynamical systems. The focus is not on replacing physics-based models, but on using data-driven latent space representations to construct surrogate models that remain connected to the underlying mechanical problem.
Several strategies are considered, ranging from black-box latent models to structure-aware identification approaches, including port-Hamiltonian formulations. Particular attention is given to practical issues that arise in technical applications: high-dimensional simulation data, limited or noisy training sets, black-box industrial solvers, multi-physics effects, and the need for reliable predictions beyond isolated benchmark examples.
The methods are illustrated using application-oriented examples such as crash simulations, multiphysics disc-brake models, and further structural and fluid-dynamical systems. The aim is to show how recent mathematical developments can support engineers in analyzing, accelerating, and optimizing complex technical systems while maintaining interpretability and physical plausibility.
