Differentiable Phonon Simulations To Optimize Thermal Transport in Nanostructures

Abstract

We introduce a methodology for large-scale optimization of non-Fourier thermal transport in nanostructures, based upon the forward and adjoint phonon Boltzmann transport equation (BTE) and density-based topology optimization. To this end, we also develop the transmission interpolation model (TIM), an interface-based method that allows for smooth interpolation between void and solid regions. We first use our approach to tailor the effective thermal conductivity tensor of a periodic nanomaterial; then, we maximize classical phonon size effects under constrained diffusive transport, obtaining more than a four-fold degradation in the thermal conductivity with respect to commonly-employed configurations. Our method enables systematic optimization of materials for heat management and conversion, and, more broadly, the design of devices where diffusive transport is not valid.