Related papers: Automated Global Analysis of Experimental Dynamics…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
The exploding research interest for neural networks in modeling nonlinear dynamical systems is largely explained by the networks' capacity to model complex input-output relations directly from data. However, they typically need vast…
Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…