Related papers: On the choice of coarse variables for dynamics

Given an autonomous system of ordinary differential equations (ODE), we consider developing practical models for the deterministic, slow/coarse behavior of the ODE system. Two types of coarse variables are considered. The first type…

Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an…

Given a fine-scale physical theory characterized by an evolutionary system of equations and a set of quantities, defined from the variables of the fine theory, that serve as a coarse representation of the fine scale phenomena, a systematic…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

This work explores the trade-off between the number of samples required to accurately build models of dynamical systems and the degradation of performance in various control objectives due to a coarse approximation. In particular, we show…

In this paper, we introduce a new class of dynamical systems on a coarse space with coarse time called, coarse dynamical system. The notion of coarse conjugacy is studied from coarse geometry point of view. Coarse orbits as invariant sets…

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…

Consider the macroscale modelling of microscale spatiotemporal dynamics. Here we develop a new approach to ensure coarse scale discrete models preserve important self-adjoint properties of the fine scale dynamics. The first part explores…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that…

This article proposes a new way to construct computationally efficient `wrappers' around fine scale, microscopic, detailed descriptions of dynamical systems, such as molecular dynamics, to make predictions at the macroscale `continuum'…

We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…

In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solutions. Dynamic renormalization and fixed point algorithms for…

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…

Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for…