Goldmann Mirko, Fischer Ingo, Mirasso Claudio R, C Soriano Miguel
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
Chaos. 2023 Sep 1;33(9). doi: 10.1063/5.0156494.
Nonlinear dynamical systems exhibiting inherent memory can process temporal information by exploiting their responses to input drives. Reservoir computing is a prominent approach to leverage this ability for time-series forecasting. The computational capabilities of analog computing systems often depend on both the dynamical regime of the system and the input drive. Most studies have focused on systems exhibiting a stable fixed-point solution in the absence of input. Here, we go beyond that limitation, investigating the computational capabilities of a paradigmatic delay system in three different dynamical regimes. The system we chose has an Ikeda-type nonlinearity and exhibits fixed point, bistable, and limit-cycle dynamics in the absence of input. When driving the system, new input-driven dynamics emerge from the autonomous ones featuring characteristic properties. Here, we show that it is feasible to attain consistent responses across all three regimes, which is an essential prerequisite for the successful execution of the tasks. Furthermore, we demonstrate that we can exploit all three regimes in two time-series forecasting tasks, showcasing the versatility of this paradigmatic delay system in an analog computing context. In all tasks, the lowest prediction errors were obtained in the regime that exhibits limit-cycle dynamics in the undriven reservoir. To gain further insights, we analyzed the diverse time-distributed node responses generated in the three regimes of the undriven system. An increase in the effective dimensionality of the reservoir response is shown to affect the prediction error, as also fine-tuning of the distribution of nonlinear responses. Finally, we demonstrate that a trade-off between prediction accuracy and computational speed is possible in our continuous delay systems. Our results not only provide valuable insights into the computational capabilities of complex dynamical systems but also open a new perspective on enhancing the potential of analog computing systems implemented on various hardware platforms.
具有固有记忆的非线性动力系统可以通过利用其对输入驱动的响应来处理时间信息。储层计算是利用这种能力进行时间序列预测的一种突出方法。模拟计算系统的计算能力通常取决于系统的动力学状态和输入驱动。大多数研究都集中在无输入时表现出稳定不动点解的系统上。在此，我们超越了这一限制，研究了一个典型延迟系统在三种不同动力学状态下的计算能力。我们选择的系统具有池田型非线性，在无输入时表现出不动点、双稳和极限环动力学。当驱动该系统时，新的输入驱动动力学从具有特征性质的自主动力学中出现。在此，我们表明在所有三种状态下获得一致响应是可行的，这是成功执行任务的一个基本前提。此外，我们证明在两个时间序列预测任务中可以利用所有三种状态，展示了这个典型延迟系统在模拟计算环境中的多功能性。在所有任务中，在无驱动储层中表现出极限环动力学的状态下获得了最低的预测误差。为了获得更深入的见解，我们分析了无驱动系统三种状态下产生的不同时间分布的节点响应。结果表明，储层响应有效维数的增加会影响预测误差，非线性响应分布的微调也是如此。最后，我们证明在我们的连续延迟系统中，预测精度和计算速度之间可以进行权衡。我们的结果不仅为复杂动力系统的计算能力提供了有价值的见解，还为增强在各种硬件平台上实现的模拟计算系统的潜力开辟了新的视角。
