Fabian Duddeck

C. Bach, L. Song, T. Erhart et al.

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on Galerkin projection sometimes exhibit much larger stable time step sizes than their unreduced counterparts. This work provides a detailed theoretical analysis of this phenomenon for structural mechanics. We first show that many desirable system matrix properties are preserved by the Galerkin projection. Next, we prove that the eigenvalues of the linearized Galerkin reduced-order system separate the eigenvalues of the linearized original system. Assuming non-negative Rayleigh damping and a time integration using the popular central difference method, we further prove that the theoretical linear stability time step of the ROM is in fact always larger than or equal to the critical time step of its corresponding full-order model. We also give mathematical expressions for computing the stable time step size. Finally, we show that under certain conditions this increase in the stability time step even extends to some hyper-reduction methods. The findings can be used to compute numerical stability time step sizes for the integration of nonlinear ROMs in structural mechanics, and to speed up simulations by permitting the use of larger time steps.

Paolo Ascia, Elena Raponi, Thomas Bäck et al.

Bayesian optimization is a powerful tool for solving real-world optimization tasks under tight evaluation budgets, making it well-suited for applications involving costly simulations or experiments. However, many of these tasks are also characterized by the presence of expensive constraints whose analytical formulation is unknown and often defined in high-dimensional spaces where feasible regions are small, irregular, and difficult to identify. In such cases, a substantial portion of the optimization budget may be spent just trying to locate the first feasible solution, limiting the effectiveness of existing methods. In this work, we present a Feasibility-Driven Trust Region Bayesian Optimization (FuRBO) algorithm. FuRBO iteratively defines a trust region from which the next candidate solution is selected, using information from both the objective and constraint surrogate models. Our adaptive strategy allows the trust region to shift and resize significantly between iterations, enabling the optimizer to rapidly refocus its search and consistently accelerate the discovery of feasible and good-quality solutions. We empirically demonstrate the effectiveness of FuRBO through extensive testing on the full BBOB-constrained COCO benchmark suite and other physics-inspired benchmarks, comparing it against state-of-the-art baselines for constrained black-box optimization across varying levels of constraint severity and problem dimensionalities ranging from 2 to 60.