Tavakoli S Kamyar, Longtin André
Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada K1N6N5.
Centre for Neural Dynamics and AI, University of Ottawa, Ottawa, Ontario, Canada K1N6N5.
Phys Rev E. 2024 May;109(5-1):054203. doi: 10.1103/PhysRevE.109.054203.
Time delays play a significant role in dynamical systems, as they affect their transient behavior and the dimensionality of their attractors. The number, values, and spacing of these time delays influences the eigenvalues of a nonlinear delay-differential system at its fixed point. Here we explore a multidelay system as the core computational element of a reservoir computer making predictions on its input in the usual regime close to fixed point instability. Variations in the number and separation of time delays are first examined to determine the effect of such parameters of the delay distribution on the effectiveness of time-delay reservoirs for nonlinear time series prediction. We demonstrate computationally that an optoelectronic device with multiple different delays can improve the mapping of scalar input into higher-dimensional dynamics, and thus its memory and prediction capabilities for input time series generated by low- and high-dimensional dynamical systems. In particular, this enhances the suitability of such reservoir computers for predicting input data with temporal correlations. Additionally, we highlight the pronounced harmful resonance condition for reservoir computing when using an electro-optic oscillator model with multiple delays. We illustrate that the resonance point may shift depending on the task at hand, such as cross prediction or multistep ahead prediction, in both single delay and multiple delay cases.
时间延迟在动力系统中起着重要作用，因为它们会影响系统的瞬态行为及其吸引子的维度。这些时间延迟的数量、值和间隔会影响非线性延迟微分系统在其不动点处的特征值。在此，我们探索一个多延迟系统，将其作为储层计算机的核心计算元件，该储层计算机在接近不动点不稳定性的通常状态下对其输入进行预测。首先研究时间延迟的数量和间隔的变化，以确定延迟分布的此类参数对用于非线性时间序列预测的时间延迟储层有效性的影响。我们通过计算证明，具有多个不同延迟的光电器件可以改善标量输入到高维动力学的映射，从而提高其对低维和高维动力系统生成的输入时间序列的记忆和预测能力。特别是，这增强了此类储层计算机预测具有时间相关性的输入数据的适用性。此外，我们强调了在使用具有多个延迟的电光振荡器模型进行储层计算时明显的有害共振条件。我们表明，共振点可能会根据手头的任务而移动，例如在单延迟和多延迟情况下的交叉预测或多步超前预测。
