Physics-Informed Neural Networks for Solving Phonon Boltzmann Transport Equation

The phonon Boltzmann transport equation (pBTE) has been proven to be capable of precisely predicting heat conduction in sub-micron electronic devices. However, numerically solving pBTE is extremely computationally costly due to its high dimensionality, especially when phonon dispersion and time evolution are considered. In this study, we use physics-informed neural networks (PINNs) to solve pBTE for multiscale non-equilibrium thermal transport problems both efficiently and precisely. In particular, a PINN framework is devised to predict phonon energy distribution by minimizing the residuals of governing equations, boundary conditions, and initial conditions without the need for any labeled training data. With phonon energy distribution predicted by the PINN, temperature and heat flux can be obtained thereby. In addition, geometric parameters, such as characteristic length scale, are also considered as a part of the input to PINN, which makes our model capable of predicting heat distribution in different length scales. Furthermore, 1D to 3D heat conduction problems are studied under our PINN framework, and the results show excellent agreement with numerical and FEM solutions. Moreover, our PINN framework has proved to be far more efficient compared to existing pBTE numerical solvers. With superiorly high efficiency and accuracy, the proposed method shows great promise for practical applications, such as thermal design and thermal management of microelectronic devices.<br/>Besides pBTE, we have also extended the applicability of the PINN framework for modeling coupled electron-phonon (e-ph) transport. <i>e-ph</i> coupling and transport are ubiquitous in modern electronic devices. The coupled electron and phonon Boltzmann transport equations (BTEs) hold great potential for the simulation of thermal transport in metal and semiconductor systems. However, solving the BTEs is often computationally challenging due to their high dimensional complexity and widespan heat carrier properties, hindering large-scale thermal modeling at the device level. In this work, we present a PINN framework for solving the coupled electron and phonon BTEs. Instead of relying on labeled data, the proposed framework directly learns the spatiotemporal solutions (i.e., the electron and phonon distribution functions) within a parameterized space by enforcing physical laws. The efficacy of this framework is demonstrated through its ability to accurately resolve temperature profiles in low-dimensional thermal transport problems and visualize the ultrafast electron and phonon dynamics in laser heating experiments on thin metal films. The results indicate that our approach can accurately describe non-equilibrium <i>e-ph</i> energy transfer with improved efficiency, opening new avenues for the predictive design and optimization of micro- and nanostructures.