  Machine learning methods have found novel application areas in various
disciplines as they offer low-computational cost solutions to complex problems.
Recently, metasurface design has joined among these applications, and neural
networks enabled significant improvements within a short period of time.
However, there are still outstanding challenges that needs to be overcome.
Here, we propose a data pre-processing approach based on the governing laws of
the physical problem to eliminate dimensional mismatch between high dimensional
optical response and low dimensional feature space of metasurfaces. We train
forward and inverse models to predict optical responses of cylindrical
meta-atoms and to retrieve their geometric parameters for a desired optical
response, respectively. Our approach provides accurate prediction capability
even outside the training spectral range. Finally, using our inverse model, we
design and demonstrate a focusing metalens as a proof-of-concept application,
thus validating the capability of our proposed approach. We believe our method
will pave the way towards practical learning-based models to solve more
complicated photonic design problems.
