Results 31 to 40 of about 37,100 (232)
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
openaire +3 more sources
Advanced numerical methods for inverse problems in evolutionary PDEs
, 2017 Michal Galba
openalex +3 more sources
Probabilistic numerical methods for PDE-constrained Bayesian inverse problems [PDF]
AIP Conference Proceedings, 2017 This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem.
Cockayne, J +3 more
openaire +3 more sources
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
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 +1 more
doaj +1 more source
Mathematics, 2023 Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws.
Zhixiang Liu +4 more
doaj +1 more source
The Cauchy problem for the Pavlov equation [PDF]
, 2014 Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature.
Grinevich, P. G., Santini, P. M., Wu, D.
core +1 more source
Continuous analogue to iterative optimization for PDE-constrained inverse problems [PDF]
Inverse Problems in Science and Engineering, 2018 The parameters of many physical processes are unknown and have to be inferred from experimental data. The corresponding parameter estimation problem is often solved using iterative methods such as steepest descent methods combined with trust regions. For a few problem classes also continuous analogues of iterative methods are available.
Boiger, R. +3 more
openaire +3 more sources
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
doaj +1 more source
Model Reduction and Neural Networks for Parametric PDEs [PDF]
, 2020 We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model ...
Bhattacharya, Kaushik +3 more
core +4 more sources