基于混合回波状态网络/适当正交分解模型的混沌系统学习

IF 2.4 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Mathias Lesjak, N. Doan
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引用次数: 1

摘要

摘要我们探索了将基于知识的降阶模型(ROM)与储层计算方法相结合来学习和预测混沌系统动力学的可能性。ROM基于具有Galerkin投影的适当正交分解(POD)来捕捉混沌系统的基本动力学,而所使用的储层计算方法基于回波状态网络(ESN)。探索了两种不同的混合方法:一种是ESN校正ROM的模态系数(hybrid-ESN-A),另一种是在全状态空间中使用并校正ROM预测(hybrid-ESN-B)。这些方法应用于两个混沌系统:Charney–DeVore系统和Kuramoto–Sivashinsky方程,并与使用POD/Galerkin投影获得的ROM和唯一基于ESN的纯数据方法进行了比较。混合-ESN-B方法被认为提供了最佳的预测精度,优于其他混合方法、POD/Galerkin投影ROM和仅数据ESN,尤其是当使用具有少量神经元的ESN时。此外,通过考虑由不同数量的POD模式组成的ROM,严格评估ROM的准确性对杂交-ESN-B的总体预测准确性的影响。还提供了关于hybrid-ESN-B如何混合来自ROM和ESN的预测以预测系统的进化的进一步分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model
Abstract We explore the possibility of combining a knowledge-based reduced order model (ROM) with a reservoir computing approach to learn and predict the dynamics of chaotic systems. The ROM is based on proper orthogonal decomposition (POD) with Galerkin projection to capture the essential dynamics of the chaotic system while the reservoir computing approach used is based on echo state networks (ESNs). Two different hybrid approaches are explored: one where the ESN corrects the modal coefficients of the ROM (hybrid-ESN-A) and one where the ESN uses and corrects the ROM prediction in full state space (hybrid-ESN-B). These approaches are applied on two chaotic systems: the Charney–DeVore system and the Kuramoto–Sivashinsky equation and are compared to the ROM obtained using POD/Galerkin projection and to the data-only approach based uniquely on the ESN. The hybrid-ESN-B approach is seen to provide the best prediction accuracy, outperforming the other hybrid approach, the POD/Galerkin projection ROM, and the data-only ESN, especially when using ESNs with a small number of neurons. In addition, the influence of the accuracy of the ROM on the overall prediction accuracy of the hybrid-ESN-B is assessed rigorously by considering ROMs composed of different numbers of POD modes. Further analysis on how hybrid-ESN-B blends the prediction from the ROM and the ESN to predict the evolution of the system is also provided.
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来源期刊
DataCentric Engineering
DataCentric Engineering Engineering-General Engineering
CiteScore
5.60
自引率
0.00%
发文量
26
审稿时长
12 weeks
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