Machine learning frequency-resolved phonon transport from ultrafast electron diffraction

Developing reliable measurement techniques for frequency-resolved phonon transport is one of the central problems in thermal science and engineering. Significant efforts have been devoted to various laser-based pump-probe techniques; however, their capabilities are limited by several bottlenecks. Here, we present a machine learning-enabled computational framework that can reveal microscopic phonon transport in heterostructures and extract frequency-dependent transport properties. Using the phonon Boltzmann transport equation (BTE) in conjunction with the adjoint-state method and automatic differentiation, we learn the phonon properties that generate a particular ultrafast electron diffraction (UED) signal. This allows us to recover frequency-dependent interface transmission coefficients, the critical incident angle at the interface, and layer-specific emissivity, from which real-time and real-space phonon dynamics can be reconstructed. We demonstrate the validity of our approach on various synthetic data and apply it to experimental measurements of an Au/Si heterostructure. Our work provides a novel approach to explore phonon transport mechanisms at the nanoscale.