  In quantum mechanics, a norm squared wave function can be interpreted as the
probability density that describes the likelihood of a particle to be measured
in a given position or momentum. This statistical property is at the core of
the microcosmos. Meanwhile, machine learning inverse design of materials raised
intensive attention, resulting in various intelligent systems for matter
engineering. Here, inspired by quantum theory, we propose a probabilistic deep
learning paradigm for the inverse design of functional meta-structures. Our
probability-density-based neural network (PDN) can accurately capture all
plausible meta-structures to meet the desired performances. Local maxima in
probability density distribution correspond to the most likely candidates. We
verify this approach by designing multiple meta-structures for each targeted
transmission spectrum to enrich design choices.
