Rapid inverse design of microwave devices with scattering matrices

Inverse design (InvDes) combines simulation and optimization to algorithmically discover physical device layouts beyond conventional intuition. However, typical InvDes approaches require hundreds or thousands of simulations and numerous initializations to adequately explore complex design spaces. This computational burden is especially pronounced in metallic microwave-frequency devices, which involve highly nonconvex optimization landscapes and demand computationally expensive, high-resolution full-wave electromagnetic simulations. Here, we introduce a significantly accelerated inverse design method tailored for microwave-frequency devices. Our approach leverages rigorous full-wave simulations to precompute scattering parameters of small, simple elements, which are subsequently combined to form larger devices during optimization. This scattering-matrix-based approach enables simulations that are approximately $10\phantom{\rule{0.1em}{0ex}}000$ times faster and use approximately $100$--$10\phantom{\rule{0.1em}{0ex}}000$ times less memory than conventional full-wave methods, while maintaining high accuracy. Coupling this accelerated simulator with an adaptive random search optimization algorithm allows rapid, thorough exploration of highly nonconvex design spaces. We demonstrate the effectiveness and versatility of our method by efficiently designing a range of commonly used microwave devices, including couplers, power splitters, phase shifters, impedance-matching circuits, and demultiplexers.