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首页> 外文期刊>Applied Intelligence: The International Journal of Artificial Intelligence, Neural Networks, and Complex Problem-Solving Technologies >Dynamic ridge polynomial neural network with Lyapunov function for time series forecasting
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Dynamic ridge polynomial neural network with Lyapunov function for time series forecasting

机译：带Lyapunov函数的动态岭多项式神经网络用于时间序列预测

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摘要

The ability to model the behaviour of arbitrary dynamic system is one of the most useful properties of recurrent networks. Dynamic ridge polynomial neural network (DRPNN) is a recurrent neural network used for time series forecasting. Despite the potential and capability of the DRPNN, stability problems could occur in the DRPNN due to the existence of the recurrent feedback. Therefore, in this study, a sufficient condition based on an approach that uses adaptive learning rate is developed by introducing a Lyapunov function. To compare the performance of the proposed solution with the existing solution, which is derived based on the stability theorem for a feedback network, we used six time series, namely Darwin sea level pressure, monthly smoothed sunspot numbers, Lorenz, Santa Fe laser, daily Euro/Dollar exchange rate and Mackey-Glass time-delay differential equation. Simulation results proved the stability of the proposed solution and showed an average 21.45% improvement in Root Mean Square Error (RMSE) with respect to the existing solution. Furthermore, the proposed solution is faster than the existing solution. This is due to the fact that the proposed solution solves network size restriction found in the existing solution and takes advantage of the calculated dynamic system variable to check the stability, unlike the existing solution that needs more calculation steps.
机译：模拟任意动态系统行为的能力是经常性网络最有用的属性之一。动态脊多项式神经网络（DRPNN）是一种用于时间序列预测的经常性神经网络。尽管DRPNN的潜力和能力，但由于经常反馈的存在，DRPNN可能发生稳定性问题。因此，在本研究中，通过引入Lyapunov函数开发了一种基于使用自适应学习率的方法的足够的条件。为了将提出的解决方案与现有解决方案的性能进行比较，该解决方案是基于反馈网络的稳定性定理导出的，我们使用了六次时间序列，即达尔文海平面压力，每月平滑的Sunspot号码，日常平滑的Sunspot号码，Lorenz，Santa Fe激光器，每日欧元/美元汇率和Mackey-玻璃时滞微分方程。仿真结果证明了所提出的解决方案的稳定性，并且表现出对现有解决方案的均均线误差（RMSE）的平均改善。此外，所提出的解决方案比现有解决方案快。这是由于所提出的解决方案解决了现有解决方案中的网络尺寸限制并利用计算的动态系统变量来检查稳定性，与需要更多计算步骤的现有解决方案不同。

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