A tensor network approach for chaotic time series prediction

TL;DR

This paper introduces a tensor network-based method for chaotic time series prediction, improving accuracy and efficiency over traditional reservoir computing techniques by effectively managing high-dimensional data.

Contribution

It applies tensor networks to chaotic time series prediction, addressing hyperparameter complexity and computational challenges inherent in reservoir computing.

Findings

Tensor network approach outperforms echo state networks in accuracy

Method reduces computational complexity and mitigates curse of dimensionality

Bridges tensor network and reservoir computing communities

Abstract

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.