用物理神经网络模拟移动热源的瞬态传热，训练更高效。
Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks
- 通过迁移学习实现连续时间步训练，避免网络复杂度上升。
- 在大时间区间内计算温度分布，与有限元法结果吻合良好。
- 适合需要高效模拟移动热源传热的工程场景。
本文采用物理信息神经网络（PINNs）对包含移动热源的传热问题进行数值模拟。为降低计算成本，提出一种新训练方法：通过迁移学习实现连续时间步进。将时间区间划分为若干子区间，使用单个神经网络进行训练，每个时间步的初始条件由前一时间步的解提供。该框架可在不增加网络复杂度的前提下，完成大时间区间的计算。利用该框架估计了均质介质中移动热源的温度分布，结果与传统有限元法对比显示良好一致性。
原文摘要 · Abstract (English)
In this paper, the physics informed neural networks (PINNs) is employed for the numerical simulation of heat transfer involving a moving source. To reduce the computational effort, a new training method is proposed that uses a continuous time-stepping through transfer learning. Within this, the time interval is divided into smaller intervals and a single network is initialized. On this single network each time interval is trained with the initial condition for (n+1)th as the solution obtained at nth time increment. Thus, this framework enables the computation of large temporal intervals without increasing the complexity of the network itself. The proposed framework is used to estimate the temperature distribution in a homogeneous medium with a moving heat source. The results from the proposed framework is compared with traditional finite element method and a good agreement is seen.
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