Related papers: Gradient-Based Estimation of Uncertain Parameters …
Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…
The problem of estimating the eddy diffusivity from Lagrangian observations in the presence of measurement error is studied in this paper. We consider a class of incompressible velocity fields for which is can be rigorously proved that the…
In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the…
For the stochastic heat equation with multiplicative noise we consider the problem of estimating the diffusivity parameter in front of the Laplace operator. Based on local observations in space, we first study an estimator that was derived…
This paper studies global a priori gradient estimates for divergence-type equations patterned over the $p$-Laplacian with first-order terms having polynomial growth with respect to the gradient, under suitable integrability assumptions on…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…
Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a…
In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an $H^1(\Omega)$…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…
A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…
This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
Stochastic partial differential equations of second order with two unknown parameters are studied. Based on ergodicity, two suitable families of minimum constrast estimators are introduced. Strong consistency and asymptotic normality of…