  Deep learning with physics-informed neural networks (PINNs) has emerged as a
highly popular and effective approach for solving partial differential
equations(PDEs). In this paper, we first investigate the extrapolation
capability of the PINN method for time-dependent PDEs. Taking advantage of this
extrapolation property, we can generalize the training result obtained in the
time subinterval to the large interval by adding a correction term to the
network parameters of the subinterval. The correction term is determined by
further training with the sample points in the added subinterval. Secondly, by
designing an extrapolation control function with special characteristics and
combining it with the correction term, we construct a new neural network
architecture whose network parameters are coupled with the time variable, which
we call the extrapolation-driven network architecture. Based on this
architecture, using a single neural network, we can obtain the overall PINN
solution of the whole domain with the following two characteristics: (1) it
completely inherits the local solution of the interval obtained from the
previous training, (2) at the interval node, it strictly maintains the
continuity and smoothness that the true solution has. The extrapolation-driven
network architecture allows us to divide a large time domain into multiple
subintervals and solve the time-dependent PDEs one by one in chronological
order. This training scheme respects the causality principle and effectively
overcomes the difficulties of the conventional PINN method in solving the
evolution equation on a large time domain. Numerical experiments verify the
performance of our proposed method.
