Reservoir computers (RCs) are powerful machine learning architectures for
time series prediction. Recently, next generation reservoir computers (NGRCs)
have been introduced, offering distinct advantages over RCs, such as reduced
computational expense and lower data requirements. However, NGRCs have their
own practical difficulties distinct from those of RCs, including sensitivity to
sampling time and type of nonlinearities in the data. Here, we introduce a
hybrid RC-NGRC approach for time series forecasting of complex and chaotic
dynamical systems. We show that our hybrid approach can produce accurate short
term predictions and capture the long term statistics of dynamical systems in
situations where the RC and NGRC components alone are insufficient. The
advantage of the hybrid RC-NGRC approach is most pronounced when both
components are limited in their prediction capabilities, e.g. for a small RC
and a large sampling time in the training data. Under these conditions, we show
for several chaotic systems that the hybrid RC-NGRC method with a small
reservoir ($N \approx 100$) can achieve prediction performance rivaling that of
a pure RC with a much larger reservoir ($N \approx 1000$), illustrating that
the hybrid approach offers significant gains in computational efficiency over
traditional RCs while simultaneously addressing some of the limitations of
NGRCs.

基于混合模型的混沌动力系统时间序列预测方法能够提高计算效率和解决传统模型的局限性。

传统与新一代蓄水库计算的混合应用在动力系统精确高效预测中

Hybridizing Traditional and Next-Generation Reservoir Computing to  Accurately and Efficiently Forecast Dynamical Systems

In this work, we bound a machine's ability to learn based on computational
limitations implied by physicality. We start by considering the information
processing capacity (IPC), a normalized measure of the expected squared error
of a collection of signals to a complete basis of functions. We use the IPC to
measure the degradation under noise of the performance of reservoir computers,
a particular kind of recurrent network, when constrained by physical
considerations. First, we show that the IPC is at most a polynomial in the
system size $n$, even when considering the collection of $2^n$ possible
pointwise products of the $n$ output signals. Next, we argue that this
degradation implies that the family of functions represented by the reservoir
requires an exponential number of samples to learn in the presence of the
reservoir's noise. Finally, we conclude with a discussion of the performance of
the same collection of $2^n$ functions without noise when being used for binary
classification.

该研究探讨了机器学习的计算限制、信息处理能力、水库计算机和二进制分类这些主要主题。