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This research applies tensor networks to optimize reservoir computing models for chaotic time series prediction, effectively mitigating the exponential parameter growth that plagues traditional Volterra-based approaches. By decomposing high-dimensional arrays into low-rank structures, the method achieves superior accuracy and computational efficiency compared to conventional echo state networks without sacrificing the memory benefits of dynamical systems. The work represents a significant theoretical advance in machine learning architectures designed for complex nonlinear forecasting tasks.
A tensor network approach for chaotic time series prediction
arXiv:2505.17740v2 Announce Type: replace 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.
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.
15 pages, 4 figures. Comments are welcome!
Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Computational Physics (physics.comp-ph)
arXiv:2505.17740 [cs.LG]
(or arXiv:2505.17740v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2505.17740 Focus to learn more arXiv-issued DOI via DataCite
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