标题： 基于共振计算的异常波浪无模型预测 显示英文标题

标题： Model-free Forecasting of Rogue Waves using Reservoir Computing

摘要： 最近的研究表明，储备计算能够模拟各种混沌动力系统，但其在哈密顿系统中的应用仍相对未被探索。 本文研究了储备计算在从非线性薛定谔方程中捕捉异常波动力学的有效性，这是一个具有调制不稳定的挑战性哈密顿系统。 无模型的方法从五个不稳定模式的呼吸子模拟中学习。 一个适当调整的并行回声状态网络可以预测来自两个不同测试数据集的动力学。 第一组是训练数据的延续，而第二组涉及高阶呼吸子。 对一步预测能力的调查显示出测试数据与模型之间显著的一致性。 此外，我们展示了训练后的储备可以在面对未见过的动力学时，相对长时间地预测异常波的传播。 最后，我们介绍了一种显著提高储备计算在自主模式下预测性能的方法，增强了其长期预测能力。 这些结果推进了储备计算在时空哈密顿系统中的应用，并强调了在设计训练数据时相空间覆盖的重要性。 显示英文摘要

摘要： Recent research has demonstrated Reservoir Computing's capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir Computing in capturing rogue wave dynamics from the nonlinear Schr\"{o}dinger equation, a challenging Hamiltonian system with modulation instability. The model-free approach learns from breather simulations with five unstable modes. A properly tuned parallel Echo State Network can predict dynamics from two distinct testing datasets. The first set is a continuation of the training data, whereas the second set involves a higher-order breather. An investigation of the one-step prediction capability shows remarkable agreement between the testing data and the models. Furthermore, we show that the trained reservoir can predict the propagation of rogue waves over a relatively long prediction horizon, despite facing unseen dynamics. Finally, we introduce a method to significantly improve the Reservoir Computing prediction in autonomous mode, enhancing its long-term forecasting ability. These results advance the application of Reservoir Computing to spatio-temporal Hamiltonian systems and highlight the critical importance of phase space coverage in the design of training data.