Boltzmann transport equation (BTE) is an ideal tool to describe the multiscale phonon transport phenomena, which are critical to applications like microelectronics cooling. Numerically solving phonon BTE is extremely computationally challenging due to the high dimensionality of such problems, especially when mode-resolved properties are considered. In this work, we demonstrate the use of physics-informed neural networks (PINNs) to efficiently solve phonon BTE for multiscale thermal transport problems with the consideration of phonon dispersion and polarization. In particular, a PINN framework is devised to predict the phonon energy distribution by minimizing the residuals of governing equations and boundary conditions, without the need for any labeled training data. Moreover, geometric parameters, such as the characteristic length scale, are included as a part of the input to PINN, which enables learning BTE solutions in a parametric setting. The effectiveness of the present scheme is demonstrated by solving a number of phonon transport problems in different spatial dimensions (from 1D to 3D). Compared to existing numerical BTE solvers, the proposed method exhibits superiority in efficiency and accuracy, showing great promises for practical applications, such as the thermal design of electronic devices.

玻尔兹曼输运方程（BTE）是描述多尺度声子输运现象的理想工具，这对于微电子冷却等应用至关重要。由于此类问题的高维性，特别是在考虑模式解析性质时，数值求解声子BTE的计算极具挑战性。在这项工作中，我们演示了使用物理信息神经网络（PINN）来有效解决声子BTE的多尺度热输运问题，同时考虑了声子的色散和极化。特别是，设计了一个PINN框架，通过使控制方程和边界条件的残差最小化来预测声子能量分布，而无需任何标记的训练数据。而且，几何参数，例如特征长度标尺，包括作为PINN输入的一部分，从而可以在参数设置中学习BTE解决方案。通过解决不同空间维度（从1D到3D）中的许多声子传输问题，证明了本方案的有效性。与现有的数值BTE求解器相比，所提出的方法在效率和精度上均具有优势，对电子设备的热设计等实际应用具有广阔的前景。