Modern engineering design optimization increasingly relies on surrogate models to reduce the computational cost associated with repeated high-fidelity simulations. While standard Gaussian Processes are widely used, their assumption of stationarity can limit predictive accuracy in problems involving nonlinear material behavior, structural dynamics, or responses that vary across regions of the design space, particularly when only limited training data are available. This study evaluates the potential of deep probabilistic surrogate models, specifically Deep Gaussian Processes (DGPs) and Deep Kernel Learning (DKL), for constrained structural optimization. The work systematically benchmarks DGP and DKL side by side, clarifying their respective strengths and limitations. The approach is first validated on the classical 10-bar truss benchmark and subsequently applied to the optimization of a post-tensioned concrete bridge girder aimed at minimizing environmental impact. The results indicate that both DGP and DKL identify high-quality feasible designs with fewer high-fidelity evaluations, achieve faster convergence than standard GP-based approaches, and exhibit improved consistency across repeated optimization runs. These findings highlight the potential of deep probabilistic surrogates to accelerate structural design by reducing the number of computationally expensive simulations required in practice. • Compares Deep Gaussian Processes and Deep Kernel Learning for structural optimization. • Evaluates accuracy and uncertainty on non-stationary benchmarks. • Demonstrates application to optimization of a 10-bar truss and a bridge girder. • Shows better convergence and robustness than standard GP models. • Provides practical insights on using deep probabilistic surrogates in design.
Røstum et al. (Wed,) studied this question.