  Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type
equations, have been widely used to investigate interfacial dynamic problems.
Designing accurate, efficient, and stable numerical algorithms for solving the
phase field models has been an active field for decades. In this paper, we
focus on using the deep neural network to design an automatic numerical solver
for the Allen-Cahn and Cahn-Hilliard equations by proposing an improved physics
informed neural network (PINN). Though the PINN has been embraced to
investigate many differential equation problems, we find a direct application
of the PINN in solving phase-field equations won't provide accurate solutions
in many cases. Thus, we propose various techniques that add to the
approximation power of the PINN. As a major contribution of this paper, we
propose to embrace the adaptive idea in both space and time and introduce
various sampling strategies, such that we are able to improve the efficiency
and accuracy of the PINN on solving phase field equations. In addition, the
improved PINN has no restriction on the explicit form of the PDEs, making it
applicable to a wider class of PDE problems, and shedding light on numerical
approximations of other PDEs in general.
