  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.
