Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A tensor network approach for chaotic time series prediction

Rodrigo Martínez-Peña, Román Orús

TL;DR

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.

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.

A tensor network approach for chaotic time series prediction

TL;DR

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.

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.

Paper Structure

This paper contains 16 sections, 31 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Results
  4. Discussion
  5. Appendix: Minimal-norm and symmetric solution of $\textbf{H}$
  6. Data and code availability
  7. Acknowledgements
  8. Author contributions
  9. Competing interests

Figures (3)

  • Figure 1: Comparison of the VPT and sMAPE and Wasserstein metrics for the TN and ESN models.
  • Figure 2: Histogram of CPU training times in seconds for the optimized hyperparameters.
  • Figure 3: Singular values of ${\bf U}$ for $N=50,100$ for $P=1$, $M=4$ and $D=4$ when given random uncorrelated inputs (blue) and correlated data (red) from the example of Table \ref{['table:svd']}.