Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium

Ruiyang Li,Jian-Xun Wang,Eungkyu Lee,Tengfei Luo

doi:10.1038/s41524-022-00712-y

Ruiyang Li, Jian-Xun Wang + Show 2 more

Open Access

https://doi.org/10.1038/s41524-022-00712-y

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Abstract

Phonon Boltzmann transport equation (BTE) is a key tool for modeling multiscale phonon transport, which is critical to the thermal management of miniaturized integrated circuits, but assumptions about the system temperatures (i.e., small temperature gradients) are usually made to ensure that it is computationally tractable. To include the effects of large temperature non-equilibrium, we demonstrate a data-free deep learning scheme, physics-informed neural network (PINN), for solving stationary, mode-resolved phonon BTE with arbitrary temperature gradients. This scheme uses the temperature-dependent phonon relaxation times and learns the solutions in parameterized spaces with both length scale and temperature gradient treated as input variables. Numerical experiments suggest that the proposed PINN can accurately predict phonon transport (from 1D to 3D) under arbitrary temperature gradients. Moreover, the proposed scheme shows great promise in simulating device-level phonon heat conduction efficiently and can be potentially used for thermal design.

Highlights

Multiscale phonon transport from the ballistic limit to the diffusive extreme is ubiquitous in technologically important materials and applications, such as thermoelectrics[1,2] and miniaturized electronic systems like central processing units and flat-panel display[3,4]
Success has been achieved in investigating nanoscale size effects for phonon transport under these assumptions[17–19], the results and conclusions cannot be generalized to the cases with large temperature differences, since the phonon relaxation time or mean free path does depend on the temperature[9,10]
A deep learning-based physics-informed neural network (PINN) model is developed for solving mode-resolved phonon Boltzmann transport equation (BTE) with arbitrary temperature differences

Summary

INTRODUCTION

Multiscale phonon transport from the ballistic limit to the diffusive extreme is ubiquitous in technologically important materials and applications, such as thermoelectrics[1,2] and miniaturized electronic systems like central processing units and flat-panel display[3,4]. Parametric difference learning has been enabled by treating system parameters (e.g., system size) as additional inputs besides mode-resolved phonon properties, providing a significant advantage of investigating effects of parameters like characteristic length scale, which is a key to determining the ballistic and diffusive nature of the phonon transport process. The solution of f can be uniquely determined under certain boundary conditions, stationary mode-resolved phonon BTE with arbitrary temperature difference This scheme uses the temperature-dependent relaxation times and learns the solutions by minimizing the residuals of the governing equations and boundary conditions. Numerical experiments are conducted to validate the model with up to three spatial dimensions We show that both the length scale and boundary temperature difference can be used as input variables to learn BTE solutions in parameterized spaces, so that a single training can enable the model to be used for evaluating thermal transport at any length scale or temperature difference. Each sub-network maps the inputs to a target output, through several layers of neurons

RESULTS

DISCUSSION

METHODS

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