Related papers: Krylov Subspace Method for Nonlinear Dynamical Sys…
This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of…
Predicting the behavior of AI-driven agents is particularly challenging without a preexisting model. In our paper, we address this by treating AI agents as nonlinear dynamical systems and adopting a probabilistic perspective to predict…
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the…
In this paper, we provide a new algorithm for the finite dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time series data. We argue that existing approach for the finite dimensional approximation…
The SOAR method for computing an orthonormal basis of a second-order Krylov subspace can be numerically unstable (see Lu et al. (2016)). In the Two-level orthogonal Arnoldi(TOAR) procedure, an alternative to SOAR, the problem of instability…
In this work we consider a class of delay eigenvalue problems that admit a spectrum similar to that of a Hamiltonian matrix, in the sense that the spectrum is symmetric with respect to both the real and imaginary axis. More precisely, we…
Dynamical system-based linear transfer Perron- Frobenius (P-F) operator framework is developed to address analysis and design problems in the building system. In particular, the problems of fast contaminant propagation and optimal placement…
A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…
This paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from…
Krylov subspace methods for approximating a matrix function $f(A)$ times a vector $v$ are analyzed in this paper. For the Arnoldi approximation to $e^{-\tau A}v$, two reliable a posteriori error estimates are derived from the new bounds and…
The estimation of weather forecast uncertainty with ensemble systems requires a careful selection of perturbations to establish a reliable sampling of the error growth potential in the phase space of the model. Usually, the singular vectors…
The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the choice of lifting…
This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
Second-order optimization methods, such as cubic regularized Newton methods, are known for their rapid convergence rates; nevertheless, they become impractical in high-dimensional problems due to their substantial memory requirements and…
In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank…