Results 211 to 220 of about 37,100 (232)

A probabilistic white‐box model for PDE constrained inverse problems

PAMM, 2018
AbstractInstead of employing deterministic solvers in a black‐box fashion, we seek to address the inherent challenges of uncertainty quantification by restating the solution of a PDE as a problem of probabilistic inference. In doing so, state variables are treated as random fields, constrained or mutually entangled by underlying physical laws.
Maximilian Koschade, Phaedon‐Stelios Koutsourelakis   +1 more
openaire   +1 more source

Adaptive reduced basis trust region methods for parabolic inverse problems

Inverse Problems
We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized Gauss–Newton method ...
Michael Kartmann, Benedikt Klein, Mario Ohlberger, Thomas Schuster, Stefan Volkwein   +4 more
semanticscholar   +1 more source

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

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
openaire   +2 more sources

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

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

VC-PINN: Variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient

Physica A: Statistical Mechanics and its Applications, 2023
Zhengwu Miao, Yong Chen
semanticscholar   +1 more source

E-PINN: extended physics informed neural network for the forward and inverse problems of high-order nonlinear integro-differential equations

International Journal of Computational Mathematics
Physics informed neural network (PINN) is a new deep learning paradigm, which embeds the physical information delineated by PDEs in the loss function and optimizes the weights in the neural network.
HongMing Zhang, Xinping Shao, Zhengfang Zhang, Mingyan He   +3 more
semanticscholar   +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

Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations

arXiv.org
Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions.
Wei Zhou, Y. F. Xu
semanticscholar   +1 more source