Our approach is based on interpreting data from the TDTR experiment with ab-initio phonon transport model. Briefly, TDTR is a widely used optical pump-probe technique that is used to characterize thermal properties. In this experiment, a sample consists of a metal transducer film on a substrate. A pulsed laser beam from an ultrafast oscillator is split into a pump and a probe beam. The pump pulse train is modulated at a frequency from 1 to 15 MHz to enable lock-in detection, and is then used to impulsively heat the metal film coated on the sample. The transient temperature decay $Z(t)$ at the surface is detected as a change in optical reflectance by the probe beam.[@Capinski1996]

In the traditional TDTR approach, this transient signal is related to the desired thermal properties by a macroscopic transfer function based on a multilayer heat diffusion model.[@Schmidt2008; @Cahill2014Review] This function maps thermal properties such as substrate thermal conductivity and metal-substrate interface conductance to the TDTR signal, and thus these properties are obtained by varying these parameters until the simulated results match the measured data sets. Put another way, one must solve an inverse problem that links the data sets to the unknown parameters; this calculation 