Session: 17-15-01: Society-Wide Micro/Nano Poster Forum

Paper Number: 99938

99938 - Physics-Informed Neural Networks for Solving Multiscale Time-Dependent Phonon Boltzmann Transport Equation 

The phonon Boltzmann transport equation (BTE) is a vital tool for modeling multiscale phonon transport, and it has been proved to be capable of precisely solving heat conduction problems in sub-micron geometries. Compared to Fourier’s law, phonon BTE can overcome the shortcoming of not being able to capture ballistic-diffusive heat conduction when the characteristic lengths are comparable 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. In our previous studies, physis-informed neural networks (PINNs) have been successfully applied to predict stationary phonon BTE solutions, which exhibit superior efficiency and accuracy. In this study, transient thermal transport is our primary concern. We use PINNs to solve phonon BTE for multiscale time-dependent thermal transport problems efficiently and precisely. In particular, a PINN framework composed of two sub-DNNs 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. The sub-DNNs share the identical structure of 8 hidden layers with 50 neurons per layer. With phonon energy distribution predicted by the PINN, temperature distribution and heat flux can be obtained both in the spatial and time domains. In addition, geometric parameters, such as characteristic length scale, are also considered part of the input to PINN, which makes our model capable of predicting heat distribution in different length scales.

 

Furthermore, 1D cross-plane phonon transport, 2D in-plane phonon transport, 2D square phonon transport, and 3D cuboid phonon transport problems are studied under our PINN framework, and the results show excellent agreement with numerical solutions. Moreover, our PINN framework is also shown to be far more efficient compared with existing numerical phonon BTE solvers. Unlike numerical phonon BTE solvers that solve phonon BTE iteratively on numerous nodes or cells, the PINNs framework can learn the high-dimensional solution by minimizing phonon BTE residuals on a fair number of collocation points without any labeled training data. After offline training, PINN is able to be used for online evaluation for 1D to 3D transient heat conduction problems and produce the predicted results (i.e., temperature distribution and heat flux at any time and any position) in a few seconds. 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.

Presenting Author: Jiahang Zhou University of Notre Dame

Presenting Author Biography: Jiahang Zhou is currently a Ph.D. student in the Department of Aerospace and<br/>Mechanical Engineering, University of Notre Dame. He obtained his bachelor&#39;s degree in Energy<br/>and Power Engineering at Xi&#39;an Jiaotong University. His research interest covers machine<br/>learning and nanoscale thermal transport.

Authors:

Jiahang Zhou University of Notre Dame
Ruiyang Li University of Notre Dame
Tengfei Luo University of Notre Dame