Physics-informed neural networks for solving time-dependent mode-resolved phonon Boltzmann transport equation

Jiahang Zhou, Ruiyang Li & Tengfei Luo

npj Computational Materials 9: 212 (2023)

doi.org/10.1038/s41524-023-01165-7

Published online: 25 November 2023

编辑概述

释放神经网络的力量：解决声子输运问题

随着半导体技术的微型化发展，微电子器件的热管理变得前所未有的关键。尤其是在大功率电子器件的微型化封装中，微纳尺度的热分析对于了解和预测焦耳热效应、进行热封装的设计和改进显得尤为必要。尽管傅立叶定律在宏观尺度上广泛应用于热传导的分析，但当长度尺度小于声子平均自由程或时间尺度短于平均声子弛豫时间时，这一定律并不适用于准确描述热输运。与之相反，玻尔兹曼输运方程（BTE）可以准确地描述微纳尺度下的能量输运，但是求解这一高度非线性微积分方程非常耗费计算资源。该研究提出了使用机器学习的方法来求解声子BTE，并且验证了这一方法在解决微纳尺度传热问题中的准确性和高效性。 

来自美国圣母大学航空航天和机械工程系的罗腾飞教授团队，使用物理信息神经网络（PINN），通过优化残差来获得时变声子BTE的近似解，并且与现有的数值方法进行对比，验证了PINN方法的有效性。区别于其他数值方法，该方法不需要进行网格划分和数值差分，因为神经网络在反向传播的过程中可以利用链式法则进行求导运算。另外，和数据驱动型的神经网络相比，训练PINN不需要任何数据标签。在完成训练后，PINN可以在数秒内完成对时变温度场的预测。该研究展示了PINN在微纳尺度下瞬态热输运中的应用，有助于微电子器件的设计和优化。

Editorial Summary

Unleashing the Power of Neural Networks: Solving the Phonon Transport Problem

With the miniaturization of semiconductor technology, thermal management of microelectronic devices has become unprecedentedly crucial. Particularly, in the miniaturized packaging of high-power electronic devices, micro- /nanoscale thermal analysis is essential for understanding and predicting the Joule heating effect, as well as for designing and improving thermal packaging. Despite the widespread application of Fourier's law in the macroscopic analysis of heat conduction, this law is not applicable for accurately describing heat transport when the length scale is smaller than the phonon mean free path or when the time scale is shorter than the average phonon relaxation time. Instead, the Boltzmann transport equation (BTE) accurately describes energy transport at the micro-/nanoscale, but solving this highly nonlinear integro-differential equation demands significant computational resources.

This study proposes the use of machine learning to solve the phonon BTE and validates the accuracy and efficiency of this method in addressing micro-/nanoscale heat transfer problems. A team led by Prof. Tengfei Luo from the Department of Aerospace and Mechanical Engineering at the University of Notre Dame, utilizes physics-informed neural networks (PINNs) to approximate solution for the time-dependent mode-resolved phonon BTE by minimizing residuals. The effectiveness of the PINN method is validated through comparisons with existing numerical methods. Unlike other numerical approaches, this method eliminates the need for mesh generation and numerical differencing, as neural networks leverage the chain rule to calculate derivatives during backpropagation. Additionally, unlike data-driven approaches, PINN does not require any data labels. After training, PINN can predict the time-varying temperature field within seconds. This study demonstrates the application of PINN in solving transient heat transport at the micro-/nanoscale, contributing to the design and optimization of microelectronic devices.