Physics-agnostic inverse design using transfer matrices

Inverse design is an application of machine learning to device design, giving the computer maximal latitude in generating novel structures, learning from their performance, and optimizing them to suit the designer’s needs. Gradient-based optimizers, augmented by the adjoint method to efficiently compute the gradient, are particularly attractive for this approach and have proven highly successful with finite-element and finite-difference physics simulators. Here, we extend adjoint optimization to the transfer matrix method, an accurate and efficient simulator for a wide variety of quasi-1D physical phenomena. We leverage this versatility to develop a physics-agnostic inverse design framework and apply it to three distinct problems, each presenting a substantial challenge for conventional design methods: optics, designing a multivariate optical element for compressive sensing; acoustics, designing a high-performance anti-sonar submarine coating; and quantum mechanics, designing a tunable double-bandpass electron energy filter.