Strong and weak prediction of stochastic dynamics using reservoir computing.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-03-01 DOI:10.1063/5.0252908
Alexander E Hramov, Nikita Kulagin, Alexander N Pisarchik, Andrey V Andreev
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Abstract

We propose an approach to replicate a stochastic system and forecast its dynamics using a reservoir computing (RC). We show that such machine learning models enable the prediction of the behavior of stochastic systems in a wide range of control parameters. However, the quality of forecasting depends significantly on the training approach used for the RC. Specifically, we distinguish two types of prediction-weak and strong predictions. We get what is called a strong prediction when the testing parameters are close to the training parameters, and almost a true replica of the system trajectory is obtained, which is determined by noise and initial conditions. On the contrary, we call the prediction weak if we can only predict probabilistic characteristics of a stochastic process, which happens if there exists a mismatch between training and testing parameters. The efficiency of our approach is demonstrated with the models of single and coupled stochastic FitzHugh-Nagumo oscillators and the model of an erbium-doped fiber laser with noisy diode pumping. With the help of a RC, we predict the system dynamics for a wide range of noise parameters. In addition, we find a particular regime when the model exhibits switches between strong and weak prediction types, resembling probabilistic properties of on-off intermittency.

利用储层计算进行随机动力学的强弱预测。
我们提出了一种利用储层计算(RC)来复制随机系统并预测其动力学的方法。我们表明,这样的机器学习模型能够在广泛的控制参数范围内预测随机系统的行为。然而,预测的质量在很大程度上取决于RC所使用的训练方法。具体来说,我们区分了两种类型的预测——弱预测和强预测。当测试参数接近训练参数时,我们得到了所谓的强预测,并且几乎得到了系统轨迹的真实复制品,这是由噪声和初始条件决定的。相反,如果我们只能预测一个随机过程的概率特征,我们称之为弱预测,这种情况发生在训练参数和测试参数不匹配的情况下。用单个和耦合的随机FitzHugh-Nagumo振子模型和带噪声二极管泵浦的掺铒光纤激光器模型证明了该方法的有效性。在RC的帮助下,我们预测了大范围噪声参数下的系统动力学。此外,我们发现当模型在强预测类型和弱预测类型之间切换时,有一个特殊的状态,类似于开关间歇的概率特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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