Related papers: Large-time uniqueness in a data assimilation probl…
In this paper, a generic extension of variational mode decomposition (VMD) algorithm for multivariate or multichannel data sets is presented. We first define a model for multivariate modulated oscillations that is based on the presence of a…
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…
This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…
This paper considers a class of real-time decision making problems to minimize the expected value of a function that depends on a random variable $\xi$ under an unknown distribution $\mathbb{P}$. In this process, samples of $\xi$ are…
In this paper, the new (2+1)-dimensional Burgers equation has been derived using the Burgers equation' recursion operator as follows \begin{equation*} u_{xt}+\left(u_{t}+uu_{x}-\nu…
In some applications, acquiring covariates comes at a cost which is not negligible. For example in the medical domain, in order to classify whether a patient has diabetes or not, measuring glucose tolerance can be expensive. Assuming that…
Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…
Some variational problems for a Foppl-von Karman plate subject to general equilibrated loads are studied. The existence of global minimizers is proved under the assumption that the out-of-plane displacement fulfils homogeneous Dirichlet…
The paper introduces a general strategy for identifying strong local minimizers of variational functionals. It is based on the idea that any variation of the integral functional can be evaluated directly in terms of the appropriate…
We consider the large time behavior of the solutions to the Cauchy problem for the BBM-Burgers equation. We prove that the solution to this problem goes to the self-similar solution to the Burgers equation called the nonlinear diffusion…
The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and…
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…
Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers'…
In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on…
Many modern statistical estimation problems are defined by three major components: a statistical model that postulates the dependence of an output variable on the input features; a loss function measuring the error between the observed…
In this paper, we apply sensitivity methods to nonlinear PDEs like Burgers and KPZ equations. These equations are known to have analytical solutions which make easier the analysis of the sensitivity of their solutions to initial conditions.…
This article focuses on a nonlinear Neumann boundary feedback control formulation for the viscous Burgers' equation and develops a class of finite difference schemes to achieve global stabilization. The proposed procedure, known as the…
We study large-scale classification problems in changing environments where a small part of the dataset is modified, and the effect of the data modification must be quickly incorporated into the classifier. When the entire dataset is large,…