“Super-efficient gradient estimation technique,” Recent advances in efficient adjoint sensitivity analysis and its application in metamaterial design

Computer-aided design (CAD) tools in electromagnetics allow accurate modeling of the preferred responses. We can adjust a desired response by conducting an optimization algorithm. This requisite the gradient estimation of structures with respect to potentially N number of optimizable parameters. In conventional gradient estimation methods, the number of required simulations scales linearly with N. Adjoint variable method (AVM) is an extremely efficient sensitivity analysis method that estimates the gradients with respect to the all N parameters by conducting only 2 simulations, regardless of N. We have developed AVM method for gradient analysis of anisotropic and dispersive anisotropic structures. Then, we applied it in wideband inversely invisibility cloak design for 2-D and 3-D structures at optical and microwave frequency regions. In those examples, our algorithm accelerates the gradient estimation over 1400 and 12 500 times per iteration, respectively, compared to the conventional methods. This advanced optimization based metamaterial cloak design to 3-D arbitrary shape objects and optical frequency region which was not feasible before. For the next step, we are planning to extend this efficient gradient estimation algorithm to the state of the art machine learning techniques and recently introduced continuous neural networks such as neural ordinary differential equations (ODE-Net).