Complex dynamics on the one-dimensional quantum droplets via time piecewise PINNs

The dynamics of one-dimensional quantum droplets and the landing applications of deep learning are recent research hotspots. In this work, we propose a novel time piecewise physics-informed neural networks (PINNs) to study complex dynamics on the one-dimensional quantum droplets by solving the corresponding amended Gross-Pitaevskii equation. The training effect of this network model in the long time domain is far better than that of the conventional PINNs, and each of its subnetworks is independent and highly adjustable. By using time piecewise PINNs with scarce training points, we not only study intrinsic modulation of single droplet and collision between two droplets, but also excite the breathers on droplet background. Intriguingly, we obtain an interference pattern from training result of collision between two droplets, which is a significant feature of the interplay of coherent matter waves. The numerical results showcase that different parameters may lead to completely different dynamic behaviors under the same initial condition in a nonlinear non-integrable system. Our results provide the significant guidance for intrinsic modulation of single droplet, droplet collision and breathers excitation via deep learning technology.