  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 fuzzy structure of microcosmos. Recently, hybrid neural structures raised
intense attention, resulting in various intelligent systems with far-reaching
influence. Here, we propose a probability-density-based deep learning paradigm
for the fuzzy design of functional meta-structures. In contrast to other
inverse design methods, our probability-density-based neural network can
efficiently evaluate and accurately capture all plausible meta-structures in a
high-dimensional parameter space. Local maxima in probability density
distribution correspond to the most likely candidates to meet the desired
performances. We verify this universally adaptive approach in but not limited
to acoustics by designing multiple meta-structures for each targeted
transmission spectrum, with experiments unequivocally demonstrating the
effectiveness and generalization of the inverse design.

Machine Learning