Multi-Fidelity Structural Optimization for Shock-Driven Fluid--Structure Interaction Problems

We investigate structural optimization problems that require repeated evaluations through fully coupled fluid--structure interaction (FSI) simulations, with a focus on shock-driven flows characterized by sharp discontinuities in fluid state variables and material properties, and substantial transient structural deformations. The optimization is undertaken using a gradient-free genetic algorithm (GA). To limit the number of costly FSI simulations typically required in GA-based structural optimization, we introduce an online multi-fidelity framework that selectively replaces the fluid sub-problem with a lightweight surface-pressure surrogate, while retaining the full-fidelity structural dynamics model throughout. The surrogate is constructed on-the-fly from previously computed interface pressures using a nearest-neighbor search and a local interpolation method. At the same time, a separate Gaussian process regression model is trained online to estimate the surrogate error and predictive uncertainty. Using these metrics, we automatically decide, for each candidate design, whether a coupled FSI simulation is required. The effectiveness of the proposed method is demonstrated through a case study involving the shape optimization of a cantilever panel impacted by incoming shock waves. The findings show that the multi-fidelity approach substantially reduces computational cost, offering an overall $4\times$ speedup, while achieving accuracy comparable to a baseline GA-based optimization that relies exclusively on high-fidelity FSI evaluations.