Re-discovering adjoint sensitivities: Toward field-based analysis

Computing the derivatives of the scattering parameters of microwave devices with respect to shape and material parameters is a problem of significant interest in high-frequency computer-aided design. The pioneering work of Bandler, Monaco, Tiberio and others in the late 1960s and the early 1970s brought about the circuit-based sensitivity analysis of microwave networks. Here, we discuss some of the recent developments in adjoint sensitivities including field-based sensitivities, transient adjoint sensitivities, and adjoint-based neural networks. Two examples illustrate these approaches.