  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.
