Results 11 to 20 of about 723 (140)
Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs [PDF]
, 2016 In a series of publications of the second author, including some with coauthors, globally strictly convex Tikhonov-like functionals were constructed for some nonlinear ill-posed problems.
A. Bakushinskii +2 more
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Discretization of parameter identification in PDEs using neural networks [PDF]
Inverse Problems, 2021 We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent partial differential equation model. The nonlinearity is approximated by a neural network (NN), and needs to be determined alongside other unknown physical ...
B. Kaltenbacher, T. Nguyen
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Structure informed neural networks for boundary observation problems [PDF]
Computer Methods in Applied Mechanics and Engineering, 2023 We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on the interior of ...
J. Horsky, Andrew Wynn
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Variational Bayesian approximation of inverse problems using sparse precision matrices [PDF]
Computer Methods in Applied Mechanics and Engineering, 2021 Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem. Among them is
Jan Povala +4 more
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Approximation of Bayesian Inverse Problems for PDEs [PDF]
SIAM Journal on Numerical Analysis, 2009 Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability.
S. Cotter, Masoumeh Dashti, A. Stuart
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A General Method for the Solution of Inverse Problems in Transport Phenomena
Chemical Engineering Transactions, 2015 The typical inverse problems in transport phenomena are given by partial differential equations with unknown boundary conditions, which are to be estimated from measurements corresponding to solutions of the PDEs or of their gradients.
M. Vocciante, A. Reverberi, V. Dovi
doaj +1 more source
Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation
Numerical Functional Analysis and Optimization, 2013 The focus of this article is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in related literature by a couple different methods. In this article, we propose a method called interpolation method, which is based on interpolation in variable Hilbert ...
Tautenhahn, Ulrich +3 more
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Carleman estimates for the regularization of ill-posed Cauchy problems [PDF]
, 2014 This work is a survey of results for ill-posed Cauchy problems for PDEs of the author with co-authors starting from 1991. A universal method of the regularization of these problems is presented here.
M. Klibanov
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Operational calculus approach to PDE arising in QR-regularisation of ill-posed problems
Mathematical and Computer Modelling, 2002 The authors treat two kinds of problems using operational calculus intended for boundary value problems: the first for the backward heat equation, and the second for a nonparabolic evolution equation. They discuss the algebraization of the boundary value problem using the Duhamel principle and obtain their solution in closed form.
Dimovski, I. H., Kalla, S. L., Ali, I.
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Direct and inverse source problems for degenerate parabolic equations
Journal of Inverse and Ill-Posed Problems, 2020 Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied ...
M.S Hussein +3 more
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