Physics and Data-driven Acceleration of Phonon Dynamics Calculations in Ultrahigh Thermal Conductivity Materials

The first-principles solution of the transient Peierls-Boltzmann transport equation (PBE) is computationally challenging due to its high dimensionality, even with the linearized collision matrix. Here, we present a data-driven method to accelerate the solution of the linearized PBE (LPBE) by implementing a low-rank representation of the collision matrix, without compromising accuracy. Our findings indicate that only the eigenvectors associated with small eigenvalues play a significant role in thermal transport, thus allowing us to reduce the problem's dimensionality by excluding the less important eigenvectors without affecting the solution. This technique enables efficient exploration of both Fourier and non-Fourier transport regimes, particularly at low temperatures, where the required dimension of the problem to achieve convergence of the solution is prohibitively large. We demonstrate the effectiveness of this approach by investigating various transport regimes at 100K in diamond, the material with the highest known thermal conductivity.