Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning
<|reference_start|>Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning: 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.<|reference_end|>
@article{song2024data-driven,
    title={Data-driven 2D stationary quantum droplets and wave propagations in the
  amended GP equation with two potentials via deep neural networks learning},
    author={Jin Song, Zhenya Yan},
    journal={arXiv preprint arXiv:2409.02339},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.02339},
    primaryClass={cs.LG math-ph math.MP nlin.PS physics.comp-ph physics.optics}
}