Related papers: Wiener system identification with generalized orth…
The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input…
After sixty years of quantitative biophysical modeling of neurons, the identification of neuronal dynamics from input-output data remains a challenging problem, primarily due to the inherently nonlinear nature of excitable behaviors. By…
We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…
This paper presents a Carleman-Fourier linearization method for nonlinear dynamical systems with periodic vector fields involving multiple fundamental frequencies. By employing Fourier basis functions, the nonlinear dynamical system is…
We develop a new effective approximation of the Mori-Zwanzig equation based on operator series expansions of the orthogonal dynamics propagator. In particular, we study the Faber series, which yields asymptotically optimal approximations…
Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by…
In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…
With the ansatz that a data set's correlation matrix has a certain parametrized form (one general enough, however, to allow the arbitrary specification of a slowly-varying decorrelation distance and population variance) the general…
In many applications that involve the inference of an unknown smooth function, the inference of its derivatives will often be just as important as that of the function itself. To make joint inferences of the function and its derivatives, a…
Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in…
We demonstrate a novel algorithm for generating stationary stochastic signals with a specified power spectral density (or equivalently, via the Wiener-Khinchin relation, a specified autocorrelation function) while satisfying constraints on…
We establish a number of new sufficient conditions for the existence of global (defined on the entire time axis) solutions of nonlinear nonautonomous systems by means of the Wazewski topological principle. The systems under consideration…
We consider measurable and topological dynamical systems over locally compact abelian groups. Our main observation relates convergence of Wiener-Wintner type averages to eigenvalues of the dynamical system in question. As a consequence we…
In this article, we have analyzed semi-discrete finite element approximations of the Stochastic linear Schr\"{o}dinger equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for…
This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we…
We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising…
The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
The macroscopic fundamental diagram (MFD) is a powerful and popular tool that describes a network scale traffic operational state and serve as the plant model of perimeter control. As both the supply and the demand suffer from random…