Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems without requiring extensive parameter tuning. However, selecting and optimizing reservoir architectures remains an open problem. Next-generation reservoir computing simplifies this problem by employing nonlinear vector autoregression based on truncated Volterra series, thereby reducing hyperparameter complexity. Nevertheless, the latter suffers from exponential parameter growth in terms of the maximum monomial degree. Tensor networks offer a promising solution to this issue by decomposing multidimensional arrays into low-dimensional structures, thus mitigating the curse of dimensionality. This paper explores the application of a previously proposed tensor network model for predicting chaotic time series, demonstrating its advantages in terms of accuracy and computational efficiency compared to conventional echo state networks. Using a state-of-the-art tensor network approach enables us to bridge the gap between the tensor network and reservoir computing communities, fostering advances in both fields.

翻译：对混沌时间序列进行精确预测是一项复杂的挑战。储层计算作为一种受神经形态启发的计算方法，已成为解决该问题的有力工具。它利用动力系统的记忆性和非线性特性，无需复杂的参数调节。然而，如何选择并优化储层架构仍是一个未解决的问题。下一代储层计算通过基于截断Volterra级数的非线性向量自回归简化了该问题，从而降低了超参数复杂度。但该方法存在最大单项式阶数增加时参数指数增长的问题。张量网络通过将多维数组分解为低维结构来缓解维度灾难，为此提供了可行的解决方案。本文探索了先前提出的张量网络模型在混沌时间序列预测中的应用，证明了其相比传统回声状态网络在精度和计算效率上的优势。采用先进张量网络方法能够架起张量网络与储层计算领域间的桥梁，促进两个领域的共同发展。