Near Real-time Full-wave Inverse Design of Electromagnetic Devices

TL;DR

The paper tackles the heavy computational burden of inverse design for electromagnetic devices by introducing the Precomputed Numerical Green Function (PNGF) method, which precomputes a numerical Green's function for the static parts of the design and evaluates candidate designs with a low-dimensional linear system in the optimization region. By combining direct binary search or other sparse-update optimizers with a Woodbury-based low-rank update, PNGF achieves linear-time objective evaluations and substantial speedups (up to ~16,000×) over conventional full-wave solvers, while maintaining high accuracy. The approach is extended to generalized materials, supports gradient-based optimization, and adapts to multiple discretizations including FD, MoM, and potential future DIELECTRIC implementations. Demonstrations on three devices—a broadband substrate antenna, a switched-beam antenna, and a substrate-integrated waveguide transition—show both large computational savings and experimental validation, underscoring PNGF's potential for ultrafast, practical inverse design without the need for training data.

Abstract

Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic devices require computationally expensive and time-consuming full-wave electromagnetic simulation at each iteration or generation of large datasets for training neural-network surrogate models. This work introduces the Precomputed Numerical Green Function method, an approach for ultrafast electromagnetic inverse design. The static components of the design are incorporated into a numerical Green function obtained from a single fully-parallelized precomputation step, reducing the cost of evaluating candidate designs during optimization to only being proportional to the size of the region under modification. A low-rank matrix update technique is introduced that further decreases the cost of the method to milliseconds per iteration without any approximations or compromises in accuracy. This method is shown to have linear time complexity, reducing the total runtime for an inverse design by several orders of magnitude compared to using conventional electromagnetics solvers. The design examples considered demonstrate speedups of up to 16,000x, shortening the design process from multiple days to weeks down to minutes. The approach enables practical and ultrafast design of complex structures that are prohibitively time-consuming for prior inverse design methods.

Figures (11)

• Figure 1: Current equivalence principle applied to pixelated electromagnetic devices. (a) Example discretization of a representative structure with planar optimization region, where each voxel is a finite-difference Yee cell and each tile comprises the faces of $3 \times 3$ cells; (b) Process to replace an arbitrary arrangement of metallic tiles with equivalent current densities that satisfy boundary conditions and produce identical fields; (c) Concept of a numerical Green's function matrix, allowing equivalent current densities and corresponding fields to be found for arbitrary configurations of the optimization region to satisfy boundary conditions. For simplicity, tiles in (b) and (c) are shown as comprising one voxel each, but in practice, multiple voxels constitute a tile.
• Figure 2: Precomputed numerical Green function optimization with direct binary search. (a) Numerical Green function matrix $G$ allowing candidate designs $P$ to be evaluated by solving a linear system of only $N_{opt}$ unknowns; (b) Process of direct binary search optimization with the PNGF method; (c) Tile flip yielding a low-rank update to the PNGF system matrix, which is performed with the Woodbury matrix identity in this work. For simplicity, tiles are shown as comprising 2x2 voxels each, whereas tiles generally encompass more voxels in practice. The illustration of $G$ at the right of (a) is a simplified representation with one unknown per voxel.
• Figure 3: Runtime performance of the precomputed numerical Green function method. (a) Simulation environment for benchmarking objective function evaluation using PNGF, where the optimization region is populated with tiles ($3 \times 3$ voxels each) in a checkerboard pattern; (b) Performance of PNGF compared to full-wave electromagnetic solvers versus simulation environment size with a fixed optimization region ($0.5\lambda \times 0.5\lambda$), where PNGF is constant-time; (c) Performance of PNGF versus optimization region size for a fixed simulation environment ($3\lambda \times 3\lambda$), demonstrating linear runtime with respect to the optimization region size. Note the 128-core times appear sublinear since the larger size problems better utilize all of the available CPU cores.
• Figure 4: Broadband 30GHz substrate antenna. (a) Antenna design with indicated dimensions; (b) Simulated $S_{11}$ with HFSS and FDTD with values from the final iteration of PNGF; (c) Simulated radiation patterns at frequencies spanning the bandwidth in linear scale relative to an ideal isotropic radiator; (d) Evolution of objective function during inverse design.
• Figure 5: Reconfigurable switched-beam antenna for 5G cellular applications. (a) 30GHz design with indicated dimensions; (b) Fabricated scaled 6GHz antenna with feed and 2.92mm connector on measurement setup; (c) Simulated and measured $S_{11}$ of 6GHz design with the switch open and closed; (d) Simulated and measured radiation patterns of 6GHz design with the switch open and closed at $\phi = 90^\circ$ (yz plane), in linear scale relative to an ideal isotropic radiator; (e) Evolution of objective function during inverse design. The measured pattern is normalized to the maximum gain of the simulation results. A slight deviation in the simulated $S_{11}$ and patterns with HFSS and FDTD arises because the connector is not modeled in the FDTD simulation; HFSS simulation without the connector demonstrates excellent agreement with FDTD.