Results 21 to 30 of about 2,057 (240)

Lift and Relax for PDE-Constrained Inverse Problems in Seismic Imaging [PDF]

IEEE Transactions on Geoscience and Remote Sensing, 2021
We present Lift and Relax for Waveform Inversion (LRWI), an approach that mitigates the local minima issue in seismic full waveform inversion (FWI) via a combination of two convexification techniques. The first technique (Lift) extends the set of variables in the optimization problem to products of those variables, arranged as a moment matrix.
Zhilong Fang, Laurent Demanet
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Fully probabilistic deep models for forward and inverse problems in parametric PDEs [PDF]

, 2023
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional
Arnaud Vadeboncoeur, Fehmi Cirak, Vadeboncoeur, Arnaud, Ieva Kazlauskaite, Kazlauskaite, Ieva, Cirak, Fehmi, Ömer Deniz Akyildiz, Mark Girolami, Akyildiz, Ömer Deniz, Girolami, Mark   +9 more
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On inverse problems modeled by PDE’s [PDF]

Matemática Contemporânea, 2000
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each iteration of the analyzed methods consists on the solution of a well posed boundary (or initial) value problem. The
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On some nonlinear fractional PDEs in physics

Bibechana, 2014
In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find
Jamshad Ahmad, Syed Tauseef Mohyud-Din
doaj   +3 more sources

Sparse deterministic approximation of Bayesian inverse problems [PDF]

, 2011
We present a parametric deterministic formulation of Bayesian inverse problems with an input parameter from infinite-dimensional, separable Banach spaces.
A M Stuart, C Schwab, Stuart, Andrew M., Schwab, Christoph, Schwab, Ch. (Christoph), Stuart, A. M.   +5 more
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Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data Inverse and ill-posed problems series ;, v. 63./ Michael V. Klibanov, Jingzhi Li. [PDF]

, 2021
In English.This book summarizes the main analytical and numerical results of Carleman estimates. In the analytical part, Carleman estimates for three main types of Partial Differential Equations (PDEs) are derived.
Klibanov M. V. ((Michael V.),), Li Jingzhi   +1 more
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Polynomial differentiation decreases the training time complexity of physics-informed neural networks and strengthens their approximation power

Machine Learning: Science and Technology, 2023
We present novel approximates of variational losses, being applicable for the training of physics-informed neural networks (PINNs). The formulations reflect classic Sobolev space theory for partial differential equations (PDEs) and their weak ...
Juan-Esteban Suarez Cardona, Michael Hecht   +1 more
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Uncertainty quantification and weak approximation of an elliptic inverse problem [PDF]

, 2011
We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation ...
Worthington, Claire, Robinson, Stewart, Davis, Neil D., Radnor, Zoe, Cooke, Matthew W, Burgess, Nicola, Cooke, Matthew, M. Dashti, Davies, Neil, Dashti, M., A. M. Stuart, Masoumeh Dashti (4463344), Worthington, Claire H, A M Stuart (13396491), Stuart, A. M.   +14 more
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The General Fractional Derivative and Related Fractional Differential Equations

Mathematics, 2020
In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
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Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

International Journal of Mathematics and Mathematical Sciences, 2014
Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction
Nemat Dalir
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