Cluster-based network modeling -- automated robust modeling of complex dynamical systems

TL;DR

This paper introduces a universal, automated, cluster-based network modeling method that captures complex nonlinear dynamics from data without prior assumptions, applicable across various scientific fields.

Contribution

The paper presents a novel cluster-based network modeling approach that does not assume low-dimensionality, enabling robust, automated modeling of complex nonlinear systems from data.

Findings

Successfully modeled Lorenz attractor dynamics.

Accurately captured ECG heartbeat signals.

Effectively modeled rare events in turbulent flow.

Abstract

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM only assumes smoothness of the dynamics in the state space, robustly describes short- and long-term behavior and is fully automatable as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict and control complex systems in all scientific fields.