Related papers: The Morozov's principle applied to data assimilati…

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…

Variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow…

Optimization problems arising in data science have given rise to a number of new derivative-based optimization methods. Such methods often use standard smoothness assumptions -- namely, global Lipschitz continuity of the gradient function…

This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…

In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences. We present a general framework yielding higher Sobolev…

Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…

We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We…

Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy…

In recent years, machine learning (ML) has been proposed to devise data-driven parametrisations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense,…

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…

In this work we consider, in a Banach space framework, the regularization of linear ill-posed problems. Our focus is on the recovery of solutions that have a logarithmic source representation. Such cases typically occur in exponentially…

Imitation learning methods are used to infer a policy in a Markov decision process from a dataset of expert demonstrations by minimizing a divergence measure between the empirical state occupancy measures of the expert and the policy. The…

In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

An obstacle encountered in applying orthogonal-polynomials fitting is how to select out the proper fitting expression. By adding a Laplace term to the error expression and introducing the concept of overfitting degree, a regularization and…

In this paper the approximate solution of the heat exchange problem by A.N. Tikhonov regularization method is presented. The errror estimation of this approximate is obtained.

We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…

We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and…