Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning

TL;DR

This paper introduces a deep learning framework combining iterative neural networks and physics-informed neural networks to solve and analyze 2D quantum droplets and their wave propagation under complex potentials.

Contribution

It presents a novel systematic deep learning approach for 2D stationary quantum droplets and their evolution in amended Gross-Pitaevskii equations with multiple potentials.

Findings

Successful modeling of 2D quantum droplets using deep neural networks

Observation of spontaneous symmetry breaking in potentials

Application of the method to wave propagation in nonlinear models

Abstract

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.