Physics-informed neural networks for modeling mesoscale heat transfer using the Boltzmann transport equation

The phonon Boltzmann transport equation (BTE) is a vital tool for bridging the atomic scale and macroscale heat transfer because it has been proven to be capable of accurately describing phonon transport in the mesoscale. Compared to Fourier's law, phonon BTE can capture the ballistic-diffusive heat conduction when the characteristic lengths are similar to the phonon mean free path. However, numerically solving phonon BTE is extremely computationally costly due to its high dimensionality, especially when phonon dispersion and time evolution are considered. Recently, physicsinformed neural networks (PINNs) have been successfully applied to approximate both stationary and transient phonon BTE solutions, exhibiting superior efficiency and accuracy. Moreover, the PINN scheme can be training data-free and learn the solutions to phonon BTE in parameterized spaces (such as geometric parameters and domain temperature differences), allowing a trained model to quickly evaluate thermal transport of structures with different geometries and under different temperature differences. With high efficiency and accuracy, the PINN technique shows great promise for practical applications, such as thermal design and thermal management of microelectronic devices.