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Sparse Reconstructions for Inverse PDE Problems
, 2009 We are concerned with the numerical solution of linear parameter identification problems for parabolic PDE, written as an operator equation $Ku=f$. The target object $u$ is assumed to have a sparse expansion with respect to a wavelet system $Psi={psi_lambda}$ in space-time, being equivalent to a priori information on the regularity of $u=mathbf u ...
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EntropyPhysics-informed neural networks (PINNs) have garnered widespread use for solving a variety of complex partial differential equations (PDEs). Nevertheless, when addressing certain specific problem types, traditional sampling algorithms still reveal ...
Yanbing Liu +3 more
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A General Method for the Solution of Inverse Problems in Transport Phenomena
Chemical Engineering Transactions, 2015 The typical inverse problems in transport phenomena are given by partial differential equations with unknown boundary conditions, which are to be estimated from measurements corresponding to solutions of the PDEs or of their gradients.
M. Vocciante, A. Reverberi, V. Dovi
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Accelerated PDE's for efficient solution of regularized inversion problems
, 2018 We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDE's.
Benyamin, Minas +3 more
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Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems Using Transfer Learning
Applied SciencesPhysics-Informed Neural Network (PINN) is a data-driven solver for partial and ordinary differential equations (ODEs/PDEs). It provides a unified framework to address both forward and inverse problems.
Abdul Hannan Mustajab +3 more
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Graph Neural Regularizers for PDE Inverse Problems
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme that alternates between FEM-based inversion and learned graph neural regularization.
Lauga, William +5 more
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Data-Centric EngineeringWe propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary both in space and time.
Daniel Kelshaw, Luca Magri
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Multigrid Algorithms for Inverse Problems with Linear Parabolic PDE Constraints
SIAM Journal on Scientific Computing, 2008 We present a multigrid algorithm for the solution of source identification inverse problems constrained by variable-coefficient linear parabolic partial differential equations. We consider problems in which the inversion variable is a function of space only. We consider the case of $L^2$ Tikhonov regularization. The convergence rate of our algorithm is
Adavani, Santi S, Biros, George
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Gaussian Process Regression for Inverse Problems in Linear PDEs
IFAC-PapersOnLineThis paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic
Li, Xin +2 more
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Wasit Journal of Computer and Mathematics ScienceThis paper addresses the inverse problem of reconstructing complete steady-state solutions for elliptic partial differential equations when boundary information is incomplete a situation common in electromagnetic, thermal, and geophysical modeling where ...
ABBAS ALDNADOI
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