  Due to the dynamic characteristics of instantaneity and steepness, employing
domain decomposition techniques for simulating rogue wave solutions is highly
appropriate. Wherein, the backward compatible PINN (bc-PINN) is a temporally
sequential scheme to solve PDEs over successive time segments while satisfying
all previously obtained solutions. In this work, we propose improvements to the
original bc-PINN algorithm in two aspects based on the characteristics of error
propagation. One is to modify the loss term for ensuring backward compatibility
by selecting the earliest learned solution for each sub-domain as pseudo
reference solution. The other is to adopt the concatenation of solutions
obtained from individual subnetworks as the final form of the predicted
solution. The improved backward compatible PINN (Ibc-PINN) is applied to study
data-driven higher-order rogue waves for the nonlinear Schr\"{o}dinger (NLS)
equation and the AB system to demonstrate the effectiveness and advantages.
Transfer learning and initial condition guided learning (ICGL) techniques are
also utilized to accelerate the training. Moreover, the error analysis is
conducted on each sub-domain and it turns out that the slowdown of Ibc-PINN in
error accumulation speed can yield greater advantages in accuracy. In short,
numerical results fully indicate that Ibc-PINN significantly outperforms
bc-PINN in terms of accuracy and stability without sacrificing efficiency.

Computational Physics;Numerical Analysis;Numerical Analysis;Pattern Formation and Solitons