  We demonstrate optimization of thermal conductance across nanostructures by
developing a method combining atomistic Green's function and Bayesian
optimization. With an aim to minimize and maximize the interfacial thermal
conductance (ITC) across Si-Si and Si-Ge interfaces by means of Si/Ge composite
interfacial structure, the method identifies the optimal structures from
calculations of only a few percent of the entire candidates (over 60,000
structures). The obtained optimal interfacial structures are non-intuitive and
impacting: the minimum-ITC structure is an aperiodic superlattice that realizes
50% reduction from the best periodic superlattice. The physical mechanism of
the minimum ITC can be understood in terms of crossover of the two effects on
phonon transport: as the layer thickness in superlattice increases, the impact
of Fabry-P\'erot interference increases, and the rate of reflection at the
layer-interfaces decreases. Aperiodic superlattice with spatial variation in
the layer thickness has a degree of freedom to realize optimal balance between
the above two competing mechanism. Furthermore, aperiodicity breaks the
constructive phonon interference between the interfaces inhibiting the coherent
phonon transport. The present work shows the effectiveness and advantage of
material informatics in designing nanostructures to control heat conduction,
which can be extended to other interfacial structures.
