Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs
Inverse Problems, 2015 Summary: This is the first publication in which a numerical method with rigorously guaranteed convergence is presented for some ill-posed Cauchy problems for semilinear PDEs of the second order. The key tool is the use of the Carleman weight functions in a Tikhonov-like functionals.
Michael Klibanov
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On Bayesian data assimilation for PDEs with ill-posed forward problems [PDF]
Inverse Problems, 2022 Abstract We study Bayesian data assimilation (filtering) for time-evolution Partial differential equations (PDEs), for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier–Stokes equations of fluid dynamics, are characterized by a high sensitivity of solutions to perturbations of the
S Lanthaler, S Mishra, F Weber
semanticscholar +7 more sources
Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs [PDF]
Nonlinear Analysis: Real World Applications, 2017 29 Pages, 4 ...
Michael Klibanov, Nikolay Koshev
exaly +3 more sources
Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems [PDF]
SIAM Journal on Scientific Computing, 2021 Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high dimensionality
Joseph L. Hart, B. V. B. Waanders
semanticscholar +1 more source
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 +1 more source
Mathematical and Computational Applications, 2023 Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data.
Jacques Francois Du Toit, Ryno Laubscher
doaj +1 more source
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems [PDF]
Inverse Problems, 2020 We introduce subgradient-based Lavrentiev regularisation of the form A(u)+α∂R(u)∋fδ for linear and nonlinear ill-posed problems with monotone operators A and general regularisation functionals R.
M. Grasmair, Fredrik Hildrum
semanticscholar +1 more source
Well-Posed and Ill-Posed Boundary Value Problems for PDE 2013 [PDF]
Abstract and Applied Analysis, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Allaberen Ashyralyev +5 more
openaire +5 more sources
Effective Solution of Ill-Posed Inverse Problems with Stabilized Forward Solver
International Conference on Conceptual Structures, 2021 We consider inverse parametric problems for elliptic variational PDEs. They are solved through the minimization of misfit functionals. Main difficulties encountered consist in the misfit multimodality and insensitivity as well as in the weak conditioning
M. Los, R. Schaefer, M. Smółka
semanticscholar +1 more source
On iterative methods for solving ill-posed problems modeled by PDE's
CoRR, 2020 14 pages, 3 ...
Johann Baumeister, Antonio Leitão
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