用深度学习求解二维量子液滴及波传播，支持多阱势场下的对称性破缺。
Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning
- 采用迭代神经网络求解二维量子液滴稳态解，再用物理信息网络追踪其演化。
- 在双阱势场下实现自发对称性破缺，生成多组分量子液滴结构。
- 方法可推广至其他非线性物理模型的波动力学研究，适合计算物理与量子模拟方向读者。
本文提出一种系统性的深度学习方法，用于求解二维（2D）稳态量子液滴（QDs）并研究其在含Lee-Huang-Yang修正和两类势场的改进型Gross-Pitaevskii方程中的波传播特性。首先，利用初值迭代神经网络（IINN）算法求解二维稳态量子液滴的方程解；随后将所得稳态解作为初始条件，输入物理信息神经网络（PINNs），以探索其在特定时空区域内的演化行为。特别地，考虑两种势场：二维四阱高斯势和PT对称的谐振子-高斯势，前者引发自发对称性破缺，后者促进多组分量子液滴的形成。该深度学习方法亦可拓展应用于其他非线性物理模型的波传播研究。
原文摘要 · Abstract (English)
In this paper, we develop a systematic deep learning approach to solve two-dimensional (2D) stationary quantum droplets (QDs) and investigate their wave propagation in the 2D amended Gross-Pitaevskii equation with Lee-Huang-Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network (IINN) algorithm for 2D stationary quantum droplets of stationary equations. Then the learned stationary QDs are used as the initial value conditions for physics-informed neural networks (PINNs) to explore their evolutions in the some space-time region. Especially, we consider two types of potentials, one is the 2D quadruple-well Gaussian potential and the other is the PT-symmetric HO-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multi-component QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models.
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