School of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.
Chaos. 2023 Jan;33(1):013118. doi: 10.1063/5.0102741.
In the paper, we employ an improved physics-informed neural network (PINN) algorithm to investigate the data-driven nonlinear wave solutions to the nonlocal Davey-Stewartson (DS) I equation with parity-time (PT) symmetry, including the line breather, kink-shaped and W-shaped line rogue wave solutions. Both the PT symmetry and model are introduced into the loss function to strengthen the physical constraint. In addition, since the nonlocal DS I equation is a high-dimensional coupled system, this leads to an increase in the number of output results. The PT symmetry also needs to be learned that is not given in advance, which increases challenges in computing for multi-output neural networks. To address these problems, our objective is to assign various levels of weight to different items in the loss function. The experimental results show that the improved algorithm has better prediction accuracy to a certain extent compared with the original PINN algorithm. This approach is feasible to investigate complex nonlinear waves in a high-dimensional model with PT symmetry.
在本文中，我们采用改进的物理信息神经网络（PINN）算法来研究具有奇偶时间（PT）对称性的非局域 Davey-Stewartson（DS）I 方程的基于数据的非线性波解，包括线呼吸子、扭结形和 W 形线孤波解。PT 对称性和模型都被引入到损失函数中，以加强物理约束。此外，由于非局域 DS I 方程是一个高维耦合系统，这导致输出结果的数量增加。PT 对称性也需要学习，而不是预先给定的，这增加了多输出神经网络计算的挑战。为了解决这些问题，我们的目标是在损失函数中为不同的项分配不同的权重级别。实验结果表明，改进的算法在一定程度上比原始 PINN 算法具有更好的预测精度。这种方法可用于研究具有 PT 对称性的高维模型中的复杂非线性波。
