rfx: An End-to-End Differentiable 3-D FDTD Simulator for RF and Microwave Engineering

Abstract

Gradient-based inverse design is standard in computational photonics but rare in radio frequency (RF) and microwave engineering, where optimization still relies on derivative-free metaheuristics. We present rfx, a GPU-accelerated 3-D finite-difference time-domain (FDTD) simulator, written in JAX, in which the entire simulation—from time stepping and absorbing boundaries to port extraction and the near-to-far-field (NTFF) transform—forms a single differentiable graph. One reverse-mode automatic-differentiation (AD) pass returns the gradient of RF observables— $S$ -parameters, directivity—with respect to all design variables at a few times the cost of a forward solve, independent of their number; this backward pass is the discrete adjoint of the FDTD recursion, assembled automatically rather than hand-derived per objective. Forward accuracy is validated against closed-form References and a four-solver patch cross-validation including CST; the AD gradient is verified against central finite differences for every smooth observable class. Three examples of increasing dimensionality (one to 2883 design cells)—a microstrip notch filter, a waveguide taper, and a beam-steering superstrate—drive $S$ -parameter and far-field objectives directly; openEMS corroborates the optimized notch and steered beam. On the 30-variable taper, particle-swarm and genetic search at an equal-or-larger solve budget trail the gradient by at least 11.6 dB, and one backward pass returns all 2883 beam-steering cell sensitivities. Reoptimized at fabrication resolution, the taper matches—does not beat—a discretized Klopfenstein design. The designs exercise continuous permittivity and relaxed metal; free-form metal topology and conformal PEC remain open. The contribution is a differentiable formulation of RF observables, realized as an open-source simulator; sensitivity analysis and model calibration follow from the same gradient.