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.

翻译：鉴于怪波解具有瞬时性和陡峭性等动态特征，采用区域分解技术对其进行数值模拟十分恰当。其中，向后兼容物理信息神经网络（bc-PINN）是一种时间序列化方案，可在连续时间区间内求解偏微分方程，同时满足所有先前获得的解。本文基于误差传播特性，从两方面对原始bc-PINN算法进行改进：其一，通过选取各子域最早学习的解作为伪参考解，修改用于确保向后兼容性的损失项；其二，采用各子网络所得解的拼接形式作为预测解的最终形式。将改进的向后兼容物理信息神经网络（Ibc-PINN）应用于非线性薛定谔方程和AB系统的数据驱动高阶怪波研究，以验证其有效性与优势。同时采用迁移学习和初始条件引导学习技术加速训练。此外，对各子域进行误差分析，结果表明Ibc-PINN在减缓误差累积速度方面具有更大优势，从而提升精度。简言之，数值结果充分表明：在不牺牲效率的前提下，Ibc-PINN在精度和稳定性方面均显著优于bc-PINN。