Results 201 to 210 of about 2,048 (231)

Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data. [PDF]

Adv Sci (Weinh)
Srikitrungruang T, Aghaee Dabaghan Fard S, Lemon M, Lee J, Zhou Y.   +4 more
europepmc   +1 more source

Correction to: Remarks on control and inverse problems for PDEs

SeMA Journal
openaire   +1 more source

Stochastic Algorithms for Inverse Problems Involving PDEs and many Measurements

SIAM Journal of Scientific Computing, 2014
Inverse problems involving systems of partial differential equations (PDEs) can be very expensive to solve numerically. This is so especially when many experiments, involving different combinations of sources and receivers, are employed in order to obtain reconstructions of acceptable quality.
Farbod Roosta-Khorasani, Kees Van Den Doel, Uri M Ascher   +2 more
exaly   +6 more sources

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Inverse Problems Involving PDEs with Applications to Imaging

Industrial and Applied Mathematics, 2020
In this chapter, we introduce the general idea of inverse problems particularly with applications to imaging. We use two well-known imaging modalities namely electrical impedance and diffuse optical tomography to introduce and describe inverse problems involving PDEs. We also discuss the mathematical difficulties and challenges for image reconstruction
Taufiquar Khan
exaly   +2 more sources

Inverse problems for DEs and PDEs using the collage theorem: a survey

International Journal of Applied Nonlinear Science, 2013
In this paper, we present several methods based on the collage theorem and its extensions for solving inverse problems for initial value and boundary value problems. Several numerical examples show the quality of this approach and its stability. At the end we present an application to the Euler-Bernoulli beam equation with boundary measurements.
Herb Kunze, Davide la Torre, Franklin Mendivil   +2 more
exaly   +2 more sources

Neural networks as smooth priors for inverse problems for PDEs

Journal of Computational Mathematics and Data Science, 2021
In this paper we discuss the potential of using artificial neural networks as smooth priors in classical methods for inverse problems for PDEs. Exploring that neural networks are global and smooth function approximators, the idea is that neural networks ...
Jens Berg, KAJ Nyström
exaly   +2 more sources

A collage-based approach to solving inverse problems for second-order nonlinear parabolic PDEs

Journal of Mathematical Analysis and Applications, 2013
The essence of collage-based methods for solving inverse problems is to bound the approximation error above by a more readily minimizable distance. The original collage method applies to ordinary differential equations (ODEs) and makes use of Banach's ...
H Kunze, Davide la Torre
exaly   +2 more sources

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

SIAM Journal on Scientific Computing, 2022
This paper deals with solving an inverse problem of electrocardiography involving deep learning (DL). In more detail: ``The goal of this work is to show how the integration between DL techniques and physically based regularization allows one to accurately solve the inverse problem of electrocardiography, even in a small data regime.'' (page B608).
Riccardo Tenderini, Stefano Pagani, Alfio Quarteroni, Simone Deparis   +3 more
openaire   +2 more sources

A collage-based approach to solving inverse problems for second-order nonlinear hyperbolic PDEs [PDF]

Communications in Nonlinear Science and Numerical Simulation, 2015
A goal of many inverse problems is to find unknown parameter values, λ ∈ Λ, so that the given observed data utrue agrees well with the solution data produced using these parameters uλ.
H Kunze, Davide la Torre
exaly   +2 more sources