  A key concept underlying the specific functionalities of metasurfaces, i.e.
arrays of subwavelength nanoparticles, is the use of constituent components to
shape the wavefront of the light, on-demand. Metasurfaces are versatile and
novel platforms to manipulate the scattering, colour, phase or the intensity of
the light. Currently, one of the typical approaches for designing a metasurface
is to optimize one or two variables, among a vast number of fixed parameters,
such as various materials' properties and coupling effects, as well as the
geometrical parameters. Ideally, it would require a multi-dimensional space
optimization through direct numerical simulations. Recently, an alternative
approach became quite popular allowing to reduce the computational cost
significantly based on a deep-learning-assisted method. In this paper, we
utilize a deep-learning approach for obtaining high-quality factor (high-Q)
resonances with desired characteristics, such as linewidth, amplitude and
spectral position. We exploit such high-Q resonances for the enhanced
light-matter interaction in nonlinear optical metasurfaces and optomechanical
vibrations, simultaneously. We demonstrate that optimized metasurfaces lead up
to 400+ folds enhancement of the third harmonic generation (THG); at the same
time, they also contribute to 100+ folds enhancement in optomechanical
vibrations. This approach can be further used to realize structures with
unconventional scattering responses.
