Related papers: Additive Nonparametric Reconstruction of Dynamical…
The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
This paper addresses the problem of row-by-row (or diagonal) decoupling of discrete-time linear multi-input multi-output systems with periodic time-varying coefficients using periodic state feedback. Previous solutions have tackled…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods (MCMC). The underlying unknown noise process (possibly) exhibits…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic…
We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…
We present a semiclassical approach for time delay statistics in quantum chaotic systems, in the presence of absorption, for broken time-reversal symmetry. We derive three kinds of expressions for Schur-moments of the time delay operator:…
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…