Widening the Time Horizon: Predicting the Long-Term Behavior of Chaotic Systems
Widening the Time Horizon: Predicting the Long-Term Behavior of Chaotic Systems
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DOI：
10.1109/icdm54844.2022.00094
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Yong Zhuang;Matthew Almeida;Wei Ding;Patrick D Flynn;S. Islam;Ping Chen
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文献类型：
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作者：
Yong Zhuang;Matthew Almeida;Wei Ding;Patrick D Flynn;S. Islam;Ping Chen
对混沌系统的理解不仅对于理论研究而且对于许多重要的应用来说都具有挑战性。混沌行为存在于许多非线性动力系统中，例如气候动力学、天气、股票市场和病毒传播的时空动力学中的系统。这些系统的可靠解决方案必须处理其复杂的时空动力学和对初始条件的敏感依赖性。我们开发了一个深度学习框架，通过在非线性系统建模时更好地评估局部误差的后果，来推动未来做出可靠预测的时间范围。我们的方法观察某个时间范围内初始误差的未来轨迹，以通过两个主要组件对损失到该点的演变进行建模：1）循环架构，误差轨迹跟踪，旨在通过相空间跟踪预测误差的轨迹；2）训练制度，地平线强制，将模型的焦点推向预定的时间范围。我们在经典混沌系统和具有混沌特征的现实时间序列预测任务上验证了我们的方法，并表明我们的方法优于当前最先进的方法。
The understanding of chaotic systems is challenging not only for theoretical research but also for many important applications. Chaotic behavior is found in many nonlinear dynamical systems, such as those found in climate dynamics, weather, the stock market, and the space-time dynamics of virus spread. A reliable solution for these systems must handle their complex space-time dynamics and sensitive dependence on initial conditions. We develop a deep learning framework to push the time horizon at which reliable predictions can be made further into the future by better evaluating the consequences of local errors when modeling nonlinear systems. Our approach observes the future trajectories of initial errors at a time horizon to model the evolution of the loss to that point with two major components: 1) a recurrent architecture, Error Trajectory Tracing, that is designed to trace the trajectories of predictive errors through phase space, and 2) a training regime, Horizon Forcing, that pushes the model’s focus out to a predetermined time horizon. We validate our method on classic chaotic systems and real-world time series prediction tasks with chaotic characteristics, and show that our approach outperforms the current state-of-the-art methods.