Jahani-Nasab Mahyar, Bijarchi Mohamad Ali
Center of Excellence in Energy Conservation (CEEC), Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
Sci Rep. 2024 Oct 11;14(1):23836. doi: 10.1038/s41598-024-74711-y.
This research introduces an accelerated training approach for Vanilla Physics-Informed Neural Networks (PINNs) that addresses three factors affecting the loss function: the initial weight state of the neural network, the ratio of domain to boundary points, and the loss weighting factor. The proposed method involves two phases. In the initial phase, a unique loss function is created using a subset of boundary conditions and partial differential equation terms. Furthermore, we introduce preprocessing procedures that aim to decrease the variance during initialization and choose domain points according to the initial weight state of various neural networks. The second phase resembles Vanilla-PINN training, but a portion of the random weights are substituted with weights from the first phase. This implies that the neural network's structure is designed to prioritize the boundary conditions, subsequently affecting the overall convergence. The study evaluates the method using three benchmarks: two-dimensional flow over a cylinder, an inverse problem of inlet velocity determination, and the Burger equation. Incorporating weights generated in the first training phase neutralizes imbalance effects. Notably, the proposed approach outperforms Vanilla-PINN in terms of speed, convergence likelihood and eliminates the need for hyperparameter tuning to balance the loss function.
本研究介绍了一种针对原始物理信息神经网络（PINNs）的加速训练方法，该方法解决了影响损失函数的三个因素：神经网络的初始权重状态、域点与边界点的比例以及损失加权因子。所提出的方法包括两个阶段。在初始阶段，使用边界条件的一个子集和偏微分方程项创建一个独特的损失函数。此外，我们引入了预处理程序，旨在减少初始化期间的方差，并根据各种神经网络的初始权重状态选择域点。第二阶段类似于原始PINN训练，但一部分随机权重被第一阶段的权重所取代。这意味着神经网络的结构被设计为优先考虑边界条件，从而影响整体收敛。该研究使用三个基准对该方法进行了评估：圆柱体上的二维流动、入口速度确定的反问题以及伯格斯方程。合并在第一训练阶段生成的权重可抵消不平衡效应。值得注意的是，所提出的方法在速度、收敛可能性方面优于原始PINN，并且无需进行超参数调整来平衡损失函数。
