  A physics informed neural network (PINN) incorporates the physics of a system
by satisfying its boundary value problem through a neural network's loss
function. The PINN approach has shown great success in approximating the map
between the solution of a partial differential equation (PDE) and its
spatio-temporal input. However, for strongly non-linear and higher order
partial differential equations PINN's accuracy reduces significantly. To
resolve this problem, we propose a novel PINN scheme that solves the PDE
sequentially over successive time segments using a single neural network. The
key idea is to re-train the same neural network for solving the PDE over
successive time segments while satisfying the already obtained solution for all
previous time segments. Thus it is named as backward compatible PINN (bc-PINN).
To illustrate the advantages of bc-PINN, we have used the Cahn Hilliard and
Allen Cahn equations, which are widely used to describe phase separation and
reaction diffusion systems. Our results show significant improvement in
accuracy over the PINN method while using a smaller number of collocation
points. Additionally, we have shown that using the phase space technique for a
higher order PDE could further improve the accuracy and efficiency of the
bc-PINN scheme.
