Approximation of Bayesian inverse problems for PDEs [PDF]
SIAM Journal on Numerical Analysis, 2009 Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability.
A. M. Stuart +3 more
core +13 more sources
Bi-level iterative regularization for inverse problems in nonlinear PDEs [PDF]
Inverse Problems, 2023 We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution partial differential equations (PDEs).
Tram Thi Ngoc Nguyen
semanticscholar +7 more sources
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).
Xin Li +2 more
semanticscholar +4 more sources
A deep neural network approach for parameterized PDEs and Bayesian inverse problems
Machine Learning: Science and Technology, 2023 We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems.
Harbir Antil +3 more
doaj +2 more sources
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs [PDF]
Inverse Problems, 2020 We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the model that exist
Karina Koval +2 more
openalex +3 more sources
Inverse problems for PDEs: Models, computations and applications [PDF]
SCIENTIA SINICA Mathematica, 2018 Inverse problems for partial differential equations (PDEs) are of great importance in the areas of applied mathematics, whichcover different mathematical branches including PDEs, functional analysis, nonlinear analysis,optimizations, regularization and ...
Cheng Jin, L. Jijun, Zhang Bo
semanticscholar +2 more sources
Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes [PDF]
arXiv.orgMethods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice of ...
Nicholas H. Nelsen +4 more
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Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs [PDF]
SDM, 2021 We propose quadratic residual networks (QRes) as a new type of parameter-efficient neural network architecture, by adding a quadratic residual term to the weighted sum of inputs before applying activation functions.
Jie Bu, Anuj Karpatne
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Remarks on control and inverse problems for PDEs
SeMA JournalThis paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem.
E. Fernández-Cara
semanticscholar +3 more sources
A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs [PDF]
Inverse Problems, 2018 Joint inversion refers to the simultaneous inference of multiple parameter fields from observations of systems governed by single or multiple forward models.
Benjamin Crestel +2 more
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