Because the Navier–Stokes equations are dissipative, the long-time dynamics of a flow in
state space are expected to collapse onto a manifold whose dimension may be much lower …

The least squares linear filter, also called the Wiener filter, is a popular tool to predict the
next element (s) of time series by linear combination of time-delayed observations. We …

Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data
with methods from dynamical systems theory, but their application to prediction models, such …

Sensing is a universal task in science and engineering. Downstream tasks from sensing
include inferring full-state estimates of a system (system identification), control decisions and …

We propose a method based on autoencoders to reconstruct attractors from recorded
footage, preserving the topology of the underlying phase space. We provide theoretical …

In many practical scenarios, the dynamical system is not available and standard data
assimilation methods are not applicable. Our objective is to construct a data-driven model for …

As digital distribution networks grow in complexity, ensuring efficient fault localization has
become critical for reliable power delivery. This paper introduces a novel fault localization …

The celebrated Takens' embedding theorem provides a theoretical foundation for
reconstructing the full state of a dynamical system from partial observations. However, the …

Using data alone, without knowledge of underlying physical models, nonlinear discrete time
regional forecasting dynamical rules are constructed employing well tested methods from …

Invariant measures are widely used to compare chaotic dynamical systems, as they offer
robustness to noisy data, uncertain initial conditions, and irregular sampling. However, large …