Related papers: Data-driven Discovery of Invariant Measures
We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods adopt a Lagrangian perspective by directly treating…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…
The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of…
We consider the problem of computing the maximal invariant set of discrete-time black-box nonlinear systems without analytic dynamical models. Under the assumption that the system is asymptotically stable, the maximal invariant set…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
This paper develops a method to learn optimal controls from data for bilinear systems without a priori knowledge of the system dynamics. Given an unknown bilinear system, we first characterize when the available data is suitable to solve…
We propose a data-driven online convex optimization algorithm for controlling dynamical systems. In particular, the control scheme makes use of an initially measured input-output trajectory and behavioral systems theory which enable it to…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
This paper studies the rich dynamics of one-dimensional granular media equations with attractive quadratic interactions. Building on the monotone dynamical systems framework developed in an earlier work, we allow for multiplicative noise,…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…