基于贝叶斯推断的畸形波重构及其不确定性量化研究

Rogue Wave Reconstruction Based on Bayesian Inference and Uncertainty Quantification

摘要: 畸形波(Rogue Wave)作为一种极端海洋现象，因其突发性与巨大破坏力，已成为海洋学与非线性物理领域的关键研究对象。尽管已有大量研究，其生成机制仍存在争议。现有重构方法在参数估计精度与完备性方面均显不足。本文提出一种基于贝叶斯推断的畸形波重构框架：通过解析波场的非线性相互作用，将动力学机制与统计规律耦合，不仅给出参数的点估计，同时量化其不确定性。核心步骤包括：对未知参数赋予无信息均匀先验，构建观测数据的似然函数，并采用马尔可夫链蒙特卡洛(MCMC)算法逼近后验分布。实验结果表明，所提方法可在强噪声背景下准确恢复畸形波特征，为海洋灾害预警、等离子体实验优化及光电器件设计提供可靠工具。

Abstract: Rogue waves, as extreme marine phenomena, represent a critical research focus in oceanography and nonlinear physics due to their sudden occurrence and immense destructive potential. Despite extensive research, the formation mechanisms of rogue waves remain debated. Traditional reconstruction methods exhibit limitations in both the accuracy of parameter estimation and comprehensiveness. This study proposes an innovative rogue wave reconstruction framework based on Bayesian inference. By analyzing the nonlinear interactions of wave fields and integrating dynamical mechanisms with statistical patterns, our approach not only generates point estimates of parameters but also quantifies their associated uncertainties. Key steps include defining parameters with uniform prior distributions, constructing likelihood functions for observed data, and applying Markov Chain Monte Carlo (MCMC) for posterior distribution approximation. Experimental results demonstrate that the proposed method can effectively recover rogue wave characteristics from noisy data, offering a valuable tool for ocean disaster early warning, plasma experiment optimization, and optical device design.