Results 211 to 220 of about 35,012 (233)

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.
George Biros, Günay Dogan
openaire   +1 more source

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
openaire   +1 more source

Anisotropic variational models and PDEs for inverse imaging problems

2019
In this thesis we study new anisotropic variational regularisers and partial differential equations (PDEs) for solving inverse imaging problems that arise in a variety of real-world applications. Firstly, we introduce a new anisotropic higher-order total directional variation regulariser.
openaire   +1 more source

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

IMA Journal of Numerical Analysis, 2022
Siddhartha Mishra, Roberto Molinaro
exaly  

hIPPYlib

ACM Transactions on Mathematical Software, 2021
Umberto Villa, Noemi Petra, Omar Ghattas
exaly  

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

Journal of Computational Physics, 2021
Liu Yang
exaly  

Generalized conditional symmetry enhanced physics-informed neural network and application to the forward and inverse problems of nonlinear diffusion equations

Chaos, Solitons and Fractals, 2023
Zhi-yong Zhang
exaly  

A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations

Journal of Computational Physics, 2022
Yi-Qing Ni
exaly  

Solving and learning nonlinear PDEs with Gaussian processes

Journal of Computational Physics, 2021
Yifan Chen, Bamdad Hosseini, Houman Owhadi   +2 more
exaly  

Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs

SIAM Journal of Scientific Computing, 2020
Ilona Ambartsumyan, Wajih Boukaram, Tan Bui-Thanh   +2 more
exaly