Reservoir computing (RC) systems can efficiently forecast chaotic time series
using nonlinear dynamical properties of an artificial neural network of random
connections. The versatility of RC systems has motivated further research on
both hardware counterparts of traditional RC algorithms and more efficient
RC-like schemes. Inspired by the nonlinear processes in a living biological
brain and using solitary waves excited on the surface of a flowing liquid film,
in this paper we experimentally validate a physical RC system that substitutes
the effect of randomness for a nonlinear transformation of input data. Carrying
out all operations using a microcontroller with a minimal computational power,
we demonstrate that the so-designed RC system serves as a technically simple
hardware counterpart to the `next-generation' improvement of the traditional RC
algorithm.

利用表面流动液膜上激发的孤立波，实验证明一种物理上的储备计算系统，该系统通过对输入数据进行非线性转换来替代随机性的影响，从而作为传统储备计算算法的技术简单的硬件改进。

基于孤立波和生物灵感非线性变换的物理储层计算

Physical Reservoir Computing Enabled by Solitary Waves and  Biologically-Inspired Nonlinear Transformation of Input Data

Photonic reservoir computing has been recently utilized in time series
forecasting as the need for hardware implementations to accelerate these
predictions has increased. Forecasting chaotic time series remains a
significant challenge, an area where the conventional reservoir computing
framework encounters limitations of prediction accuracy. We introduce an
attention mechanism to the reservoir computing model in the output stage. This
attention layer is designed to prioritize distinct features and temporal
sequences, thereby substantially enhancing the forecasting accuracy. Our
results show that a photonic reservoir computer enhanced with the attention
mechanism exhibits improved forecasting capabilities for smaller reservoirs.
These advancements highlight the transformative possibilities of reservoir
computing for practical applications where accurate forecasting of chaotic time
series is crucial.

光子储水池计算作为加速时间序列预测的硬件实现需求的最新技术，已被广泛运用，然而在预测混沌时间序列方面，传统的储水池计算模型在准确性方面存在一定局限性，因此我们引入了一种注意力机制，用于增强储水池计算模型输出阶段的预测准确性，实验结果表明，采用注意力机制的光子储水池计算能够提高较小储水池的预测能力，这些进展凸显了储水池计算在准确预测混沌时间序列的实际应用中的变革性可能性。

注意力增强的储备计算

Attention-Enhanced Reservoir Computing

To understand the ability and limitations of convolutional neural networks to
generate time series that mimic complex temporal signals, we trained a
generative adversarial network consisting of deep convolutional networks to
generate chaotic time series and used nonlinear time series analysis to
evaluate the generated time series. A numerical measure of determinism and the
Lyapunov exponent, a measure of trajectory instability, showed that the
generated time series well reproduce the chaotic properties of the original
time series. However, error distribution analyses showed that large errors
appeared at a low but non-negligible rate. Such errors would not be expected if
the distribution were assumed to be exponential.

使用卷积神经网络和生成式对抗网络，我们生成了混沌时间序列，并使用非线性时间序列分析方法计算得出，该生成模型可以较好地重现原始时间序列的混沌特性，但存在学习误差。

卷积生成对抗网络生成混沌时间序列的评估

Evaluating generation of chaotic time series by convolutional generative  adversarial networks

Identifying causal relations among simultaneously acquired signals is an
important problem in multivariate time series analysis. For linear stochastic
systems Granger proposed a simple procedure called the Granger causality to
detect such relations. In this work we consider nonlinear extensions of
Granger's idea and refer to the result as Extended Granger Causality. A simple
approach implementing the Extended Granger Causality is presented and applied
to multiple chaotic time series and other types of nonlinear signals. In
addition, for situations with three or more time series we propose a
conditional Extended Granger Causality measure that enables us to determine
whether the causal relation between two signals is direct or mediated by
another process.

本文提出了扩展格兰杰因果关系方法，应用于多个混沌时间序列和其他非线性信号，同时在三个或更多时间序列的情况下提出了条件扩展格兰杰因果关系度量。