Related papers: Dimensional reduction in nonlinear filtering: A ho…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…
We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
For sound waves impinging on a one-dimensional medium, we show that nonlinearity can lead to nonreciprocal transmission, without dissipation or broken time reversal invariance. Placing quasi-monochromatic filters at the ends of the…
The paper presents a reflectionless stripline filter with reduced dimensions having a single bandwidth over a wide frequency range. The filter consists of coupled strip lines and RLC circuits included in the diagonal ports of the coupled…
In this paper we prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of epsilon. The main…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the…
Numerical homogenization, i.e. the finite-dimensional approximation of solution spaces of PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements. These basis elements are oftentimes found after a…
This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…
In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.
In this work, we systematically benchmark two recently developed deep density methods for nonlinear filtering. We model the filtering density of a discretely observed stochastic differential equation through the associated Fokker--Planck…
We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on $\mathbb{R}^d$ with stationary law (i.e. spatially…