Npj Comput. Mater.: 释放神经网络的力量：解决声子输运问题

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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方法的准确性和高效性。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。

Fig.1 PINN框架。使用Net1和Net2分别近似平衡态和非平衡态的声子能量分布。神经网络的输入分别是坐标x (x, y, z) ,固体角度s,波数k, 极化方式p和时间t。

作者使用PINN模型求解了一维和二维的时变声子BTE，并且与数值方法的结果进行了对比。值得注意的是，对模型的训练可以在参数空间中进行，使得训练好的模型能够预测在参数空间中的任意值下的声子能量分布。

该研究展示了PINN在微纳尺度下瞬态热输运中的应用。使用PINN进行温度场的快速预测，有助于微电子器件的设计和优化。

Fig.2 PINN求解一维瞬态热光栅问题。a. 在一维硅薄膜上施加正弦初始温度分布，且两侧为周期性边界条件。b-d. PINN预测的温度变化幅值与解析解对比。

Fig.3 PINN求解二维方形区域内的传热问题。a. 方形区域采用等温边界条件，且上边的温度分布呈高斯分布，用于模拟电子器件中的过热点。b-e. 不同时间下的温度分布。f. 温度分布在扩散极限与傅立叶导热定律的结果吻合。

该文近期发表于npj Computational Materials 9：212(2023)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。

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

Jiahang Zhou, Ruiyang Li & Tengfei Luo

The phonon Boltzmann transport equation (BTE) is a powerful tool for modeling and understanding micro-/nanoscale thermal transport in solids, where Fourier's law can fail due to non-diffusive effect when the characteristic length/time is comparable to the phonon mean free path/relaxation time. However, numerically solving phonon BTE can be computationally costly due to its high dimensionality, especially when considering mode-resolved phonon properties and time dependency. In this work, we demonstrate the effectiveness of physics-informed neural networks (PINNs) in solving time-dependent mode-resolved phonon BTE. The PINNs are trained by minimizing the residual of the governing equations, and boundary/initial conditions to predict phonon energy distributions, without the need for any labeled training data. The results obtained using the PINN framework demonstrate excellent agreement with analytical and numerical solutions. Moreover, after offline training, the PINNs can be utilized for online evaluation of transient heat conduction, providing instantaneous results, such as temperature distribution. It is worth noting that the training can be carried out in a parametric setting, allowing the trained model to predict phonon transport in arbitrary values in the parameter space, such as the characteristic length. This efficient and accurate method makes it a promising tool for practical applications such as the thermal management design of microelectronics.