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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.02339 |
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| _version_ | 1866910734180417536 |
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| author | Song, Jin Yan, Zhenya |
| author_facet | Song, Jin Yan, Zhenya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning Song, Jin Yan, Zhenya Machine Learning Mathematical Physics Pattern Formation and Solitons Computational Physics Optics 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. |
| title | Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning |
| topic | Machine Learning Mathematical Physics Pattern Formation and Solitons Computational Physics Optics |
| url | https://arxiv.org/abs/2409.02339 |