Results 221 to 230 of about 35,710 (245)

Numerical Solution Of Inverse Problem For Elliptic Pdes

International Journal of Computer Mathematics, 2003
This work is concerned with computing the solution of the following inverse problem: Finding u and „on D such that: $$\nabla \cdot (\rho \nabla u) = 0,\quad \hbox{on}\ D;$$ $$u = g,\quad \hbox{on}\ \partial D;\qquad \rho u_n = f,\quad \hbox{on}\ \partial D;$$ $$\rho (x_0, y_0) = \rho_0,\quad \hbox{for a given point}\ (x_0, y_0) \in D$$ where f and g ...
Sadia M. Makky, Ali Sayfy
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Completeness of the products of solutions of PDE and inverse problems [PDF]

Inverse Problems, 1990
The author discusses the characterisation problem in 3D inverse scattering theory, an inverse spectral problem, and an inverse problem for the wave equation.
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On global normal linear approximations for nonlinear Bayesian inverse problems

Inverse Problems, 2023
The replacement of a nonlinear parameter-to-observable mapping with a linear (affine) approximation is often carried out to reduce the computational costs associated with solving large-scale inverse problems governed by partial differential equations ...
R. Nicholson, N. Petra, Umberto Villa, J. Kaipio   +3 more
semanticscholar   +1 more source

Inverse Problems Involving PDEs with Applications to Imaging

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
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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.
H. Kunze, D.La Torre, F. Mendivil, E. Vrscay   +3 more
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A multilevel algorithm for inverse problems with elliptic PDE constraints

Inverse Problems, 2008
We present a multilevel algorithm for the solution of a source identification problem in which the forward problem is an elliptic partial differential equation on the 2D unit box. The Hessian corresponds to a Tikhonov-regularized first-kind Fredholm equation.
Giinay Dogan, George Biros
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Unifying and extending Diffusion Models through PDEs for solving Inverse Problems

Computer Methods in Applied Mechanics and Engineering
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems.
Agnimitra Dasgupta, Alexsander Marciano da Cunha, Ali Fardisi, M. Aminy, Brianna Binder, B. Shaddy, Assad A. Oberai   +6 more
semanticscholar   +1 more source

Geometric Methods in Inverse Problems and PDE Control

2004
Foreword * Preface * On the construction of isospectral manifolds, Werner Ballman * Statistical stability and time-reversal imaging in random media, James G. Berryman, Liliana Borcea, George C. Papanicolaou, and Chrysoul Tsogka * A review of selected works on crack identification, Kurt Bryan and Michael S.
Croke, Christopher B., Lasiecka, Irena, Uhlmann, Gunther, Vogelius, Michael S.   +3 more
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Physics-informed quantum neural network for solving forward and inverse problems of partial differential equations

The Physics of Fluids
Recently, physics-informed neural networks (PINNs) have aroused an upsurge in the field of scientific computing including solving partial differential equations (PDEs), which convert the task of solving PDEs into an optimization challenge by adopting ...
Y. Xiao, L. M. Yang, C. Shu, S. C. Chew, B. Khoo, Y. D. Cui, Y. Liu   +6 more
semanticscholar   +1 more source

Stochastic Algorithms for Inverse Problems Involving PDEs and many Measurements

SIAM Journal on 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.
Roosta-Khorasani, Farbod, Van Den Doel, Kees, Ascher, Uri   +2 more
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