Tensor Network Framework for Forecasting Nonlinear and Chaotic Dynamics

TL;DR

This paper introduces a tensor network model that effectively forecasts nonlinear and chaotic dynamics, capturing complex behaviors with interpretability and robustness, and demonstrating superior short-term prediction capabilities in benchmark chaotic systems.

Contribution

The work develops a novel tensor network framework for modeling chaotic systems, integrating quantum-inspired methods with classical dynamics, and shows its advantages over existing approaches in accuracy and robustness.

Findings

Accurately reconstructs short-term trajectories of chaotic systems.

Captures attractor geometry and enables robust forecasting beyond Lyapunov times.

Inhomogeneous parametrization improves convergence and robustness.

Abstract

We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal correlations and multiscale structures, enabling compact and interpretable representations of chaotic flows. Using the Lorenz and R\"{o}ssler systems as benchmarks, we show that the TNM accurately reconstructs short-term trajectories and faithfully captures the attractor geometry. The model enables robust short-term forecasting beyond several Lyapunov times, offering a meaningful horizon for data-driven prediction under chaos. Inhomogeneous parametrization of weight tensors improves convergence and robustness compared to homogeneous parametrization, while scaling with bond dimension reveals saturation beyond modest values, consistent with the low intrinsic dimensionality of the chaotic attractor. This work establishes tensor networks as a universal paradigm for data-driven modeling of complex dynamical systems, offering physically motivated control of model expressivity and opening pathways toward applications in climate systems and hybrid quantum-classical simulations.