A Surrogate-Based Adaptive Sampling Approach for Electromagnetic Problems

Black-box optimization problems arise in many real-world applications, where the objective function is unknown or computationally expensive to evaluate. In electromagnetic engineering, optimization tasks often involve complex structures and materials, making direct analytical solutions infeasible. These problems are further complicated by high-dimensional search spaces, the need for numerous simulations, and the absence of explicit derivative information. Gradient-based optimization methods are often impractical due to the lack of gradients and high evaluation costs. Even derivative-free optimization (DFO) techniques may struggle with efficiency in high dimensions. To address these challenges, we implement a surrogate-based adaptive sampling DFO approach that refines a surrogate model while optimizing black-box electromagnetic problems. We focus on deterministic black-box functions with noise-free evaluations. Our methodology is demonstrated in two case studies: optimizing the reflection coefficient in a partially filled waveguide and the transmission properties of a multilayered dielectric filter. We compare our method against Monte Carlo, Polynomial Chaos, Genetic Algorithms, and Particle Swarm Optimization. We confirm that our approach achieves a better solution while maintaining high accuracy in the surrogate model, with significantly fewer simulations. For the waveguide problem, our method achieved a best value of 0.1325 using only 168 simulations, compared to 0.1374 with 100 million Monte Carlo samples and 0.1469 with 9180 Polynomial Chaos evaluations. In the filter case, we obtained 1.7113 GHz using 240 simulations, outperforming the 1.7682 GHz result from 5370 Polynomial Chaos samples. These results demonstrate a simulation cost reduction of over 95%–98%, while achieving improved optimization performance.