An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations

DOI10.1088/1361-6420/ac0e80zbMath1478.65109arXiv2103.11176OpenAlexW3136669531MaRDI QIDQ5002581

WenYi Tian, Hangrui Yue, Xiao-Ming Yuan

Publication date: 28 July 2021

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.11176

zbMATH Keywords

total variationalternating direction method of multipliersconvolutional neural networkSchur complement reductionactive-set Newton methoddiffusion coefficient identification

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Smoothness and regularity of solutions to PDEs (35B65) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Nonlinear elliptic equations (35J60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Higher-order elliptic equations (35J30) Preconditioners for iterative methods (65F08) PDE constrained optimization (numerical aspects) (49M41)

Related Items (2)

Convergence rate analysis of the coefficient identification problems in a Kuramoto–Sivashinsky equation ⋮ Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation

Uses Software

• iFEM
• ImageNet
• AlexNet
• DnCNN

Cites Work

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• Nonlinear total variation based noise removal algorithms
• Stability and experimental comparison of prototypical iterative schemes for total variation regularized problems
• Remarks on parameter identification. I
• A new inexact alternating directions method for monotone variational inequalities
• A saddle point variational formulation for projection-regularized parameter identification
• Variational method for multiple parameter identification in elliptic PDEs
• Estimation techniques for distributed parameter systems
• Multiplier and gradient methods
• An Efficient Linear Solver for Nonlinear Parameter Identification Problems
• Matrix coefficient identification in an elliptic equation with the convex energy functional method
• Finite element methods for coefficient identification in an elliptic equation
• On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
• Total Variation Minimization with Finite Elements: Convergence and Iterative Solution
• The Finite Element Method: Theory, Implementation, and Applications
• Convergence rates for total variation regularization of coefficient identification problems in elliptic equations I
• Convergence rates for Tikhonov regularization of coefficient identification problems in Laplace-type equations
• A Numerical Study of an Augmented Lagrangian Method for the Estimation of Parameters in Elliptic Systems
• Variational Analysis in Sobolev andBVSpaces
• Numerical solution of saddle point problems
• The Augmented Lagrangian Method for Parameter Estimation in Elliptic Systems
• Optimization with PDE Constraints
• Optimization and nonsmooth analysis
• Determining conductivity by boundary measurements
• A variational method for parameter identification
• Relaxation of a variational method for impedance computed tomography
• Weakly Differentiable Functions
• Numerical methods for elliptic inverse problems
• An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
• Analysis of bounded variation penalty methods for ill-posed problems
• Numerical identifications of parameters in parabolic systems
• Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization
• A Multigrid Tutorial, Second Edition
• Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
• Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
• Augmented Lagrangian-SQP-Methods in Hilbert Spaces and Application to Control in the Coefficients Problems
• Parameter identification for elliptic problems

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