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Due to the dynamic characteristics of instantaneity and steepness, employingdomain decomposition techniques for simulating rogue wave solutions is highlyappropriate. Wherein, the backward compatible PINN (bc-PINN) is a temporallysequential scheme to solve PDEs over successive time segments while satisfyingall previously obtained solutions. In this work, we propose improvements to theoriginal bc-PINN algorithm in two aspects based on the characteristics of errorpropagation. One is to modify the loss term for ensuring backward compatibilityby selecting the earliest learned solution for each sub-domain as pseudoreference solution. The other is to adopt the concatenation of solutionsobtained from individual subnetworks as the final form of the predictedsolution. The improved backward compatible PINN (Ibc-PINN) is applied to studydata-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 arealso utilized to accelerate the training. Moreover, the error analysis isconducted on each sub-domain and it turns out that the slowdown of Ibc-PINN inerror accumulation speed can yield greater advantages in accuracy. In short,numerical results fully indicate that Ibc-PINN significantly outperformsbc-PINN in terms of accuracy and stability without sacrificing efficiency.

The improved backward compatible physics-informed neural networks for  reducing error accumulation and applications in data-driven higher-order  rogue waves