Found 1494 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Data-Driven Approach for Uncertainty Propagation and Reachability
Analysis in **Dynamical** **Systems**

In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a

**dynamical****system**. Expand abstract. In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a

**dynamical****system**. The proposed approach relies on the linear lifting of a nonlinear**system**using linear Perron-Frobenius (P-F) and Koopman operators. The uncertainty can be characterized in terms of the moments of a probability density function. We demonstrate how the P-F and Koopman operators are used for propagating the moments. Time-series data is used for the finite-dimensional approximation of the linear operators, thereby enabling data-driven approach for moment propagation. Simulation results are presented to demonstrate the effectiveness of the proposed method.3 days ago

8/10 relevant

arXiv

8/10 relevant

arXiv

Almost periodicity and periodicity for nonautonomous random **dynamical**
**systems**

We present a notion of almost periodicity wich can be applied to random

**dynamical****systems**as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). Expand abstract. We present a notion of almost periodicity wich can be applied to random

**dynamical****systems**as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept allows for improvements of known results of almost periodicity in distribution, for general random processes and for solutions to stochastic differential equations.3 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

TPFA Finite Volume Approximation of Wasserstein Gradient Flows

Numerous infinite dimensional

**dynamical****systems**arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. Expand abstract. Numerous infinite dimensional

**dynamical****systems**arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes to discretize these problems preserving their variational structure and obtaining second order accuracy in space. The choice of the discrete solver plays an important role in designing these schemes for robustness purposes. We present two applications to test the scheme and show its order of convergence.4 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Approximation of linear controlled **dynamical** **systems** with small random
noise and fast periodic sampling

In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise perturbations of size $\varepsilon$ ($0 Expand abstract.

In this paper, we study the dynamics of a linear control

**system**with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise perturbations of size $\varepsilon$ ($04 days ago

9/10 relevant

arXiv

9/10 relevant

arXiv

**Dynamical** spectrum via determinant-free linear algebra

We consider a sequence of matrices that are associated to Markov

**dynamical****systems**and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix simultaneously without doing any calculations on the matrices themselves. Expand abstract. We consider a sequence of matrices that are associated to Markov

**dynamical****systems**and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix simultaneously without doing any calculations on the matrices themselves. As a corollary, we obtain mixing rates for every**system**at once, as well as symmetry properties of densities associated to the system; we also find the spectral properties of a sequence of related factor**systems**.5 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Causal models for **dynamical** **systems**

In this chapter, we provide a natural and straight-forward extension of this concept to

**dynamical****systems**, focusing on continuous time models. Expand abstract. A probabilistic model describes a

**system**in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to model the behaviour under interventions. It can been taken as a starting point to answer a plethora of causal questions, including the identification of causal effects or causal structure learning. In this chapter, we provide a natural and straight-forward extension of this concept to**dynamical**systems, focusing on continuous time models. In particular, we introduce two types of causal kinetic models that differ in how the randomness enters into the model: it may either be considered as observational noise or as systematic driving noise. In both cases, we define interventions and therefore provide a possible starting point for causal inference. In this sense, the book chapter provides more questions than answers. The focus of the proposed causal kinetic models lies on the dynamics themselves rather than corresponding stationary distributions, for example. We believe that this is beneficial when the aim is to model the full time evolution of the**system**and data are measured at different time points. Under this focus, it is natural to consider interventions in the differential equations themselves.7 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

$C^0$-Stability of Topological Entropy for Contactomorphisms

In this note we show that for some special classes of

**dynamical****systems**(geodesic flows, Reeb flows, positive contactomorphisms) topological entropy at least is stable in the sense that there exists a nontrivial continuous lower bound, given that a certain homological invariant grows exponentially. Expand abstract. Topological entropy is not lower semi-continous: small perturbation of the

**dynamical****system**can lead to a collapse of entropy. In this note we show that for some special classes of**dynamical****systems**(geodesic flows, Reeb flows, positive contactomorphisms) topological entropy at least is stable in the sense that there exists a nontrivial continuous lower bound, given that a certain homological invariant grows exponentially.8 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

A Tree Adjoining Grammar Representation for Models Of Stochastic
**Dynamical** **Systems**

In this paper, we propose a TAG that can

**system**atically generate models ranging from FIRs to polynomial NARMAX models. Expand abstract. Model structure and complexity selection remains a challenging problem in

**system**identification, especially for parametric non-linear models. Many Evolutionary Algorithm (EA) based methods have been proposed in the literature for estimating model structure and complexity. In most cases, the proposed methods are devised for estimating structure and complexity within a specified model class and hence these methods do not extend to other model structures without significant changes. In this paper, we propose a Tree Adjoining Grammar (TAG) for stochastic parametric models. TAGs can be used to generate models in an EA framework while imposing desirable structural constraints and incorporating prior knowledge. In this paper, we propose a TAG that can systematically generate models ranging from FIRs to polynomial NARMAX models. Furthermore, we demonstrate that TAGs can be easily extended to more general model classes, such as the non-linear Box-Jenkins model class, enabling the realization of flexible and automatic model structure and complexity selection via EA.9 days ago

8/10 relevant

arXiv

8/10 relevant

arXiv

The Impact of Equilibria on the Shape of Hysteresis Loops

Hysteresis is a common phenomenon found in many

**dynamical****systems**. It is typically described as a looping behaviour in the system's input-output graph. For a**dynamical****system**to exhibit hysteresis, it must have multiple stable equilibria. This work examines the impact that different types of equilibria can have on the shape of hysteresis loops exhibited in input-output graphs of ordinary differential equations.11 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations

We develop a thorough analysis of the Mori-Zwanzig (MZ) formulation for stochastic

**dynamical****systems**driven by multiplicative white noise. Expand abstract. We develop a thorough analysis of the Mori-Zwanzig (MZ) formulation for stochastic

**dynamical****systems**driven by multiplicative white noise. To this end, we first derive a new type of MZ equation, which we call effective Mori-Zwanzig (EMZ) equation, that governs the temporal dynamics of noise-averaged observables. Such dynamics is generated by a Kolmogorov operator obtained by averaging It\^{o}'s representation of the stochastic Liouvillian of the**system**. Building upon recent work on hypoelliptic operators, we prove that the generator of the EMZ orthogonal dynamics has a spectrum that lies within cusp-shaped region of the complex plane. This allows to rigorously prove that the EMZ memory kernel and fluctuation terms converge exponentially fast in time to an unique equilibrium state. We apply the new theoretical results to the stochastic dynamics of an interacting particle**system**widely studied in molecular dynamics, and show that such equilibrium state admits an explicit representation.11 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv