A data-driven model reduction method for parabolic inverse source problems and its convergence analysis
DOI10.1016/j.jcp.2023.112156arXiv2110.07676OpenAlexW4366824811MaRDI QIDQ6158111
Wenlong Zhang, Zhiwen Zhang, Zhongjian Wang
Publication date: 31 May 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.07676
regularization methodproper orthogonal decomposition (POD)optimal regularization parameterdata-driven model reduction methodparabolic inverse source problemsstochastic error estimate
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Miscellaneous topics in partial differential equations (35Rxx)
Related Items (1)
Cites Work
- Unnamed Item
- Source term identification for an axisymmetric inverse heat conduction problem
- An inverse source problem for parabolic equations with local measurements
- Determination of a spacewise dependent heat source
- An iterative algorithm for POD basis adaptation in solving parametric convection-diffusion equations
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- Lipschitz stability estimates for an inverse source problem in an elliptic equation from interior measurements
- A heat source reconstruction formula from single internal measurements using a family of null controls
- A FE-based algorithm for the inverse natural convection problem
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number
- A Balanced Oversampling Finite Element Method for Elliptic Problems with Observational Boundary Data
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- Turbulence, Coherent Structures, Dynamical Systems and Symmetry
- Stochastic Convergence of a Nonconforming Finite Element Method for the Thin Plate Spline Smoother for Observational Data
- HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems
- Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems
- Proper Orthogonal Decomposition Method to Nonlinear Filtering Problems in Medium-High Dimension
- Reconstruction of a spacewise-dependent heat source in a time-dependent heat diffusion process
- Error Estimates for a POD Method for Solving Viscous G-Equations in Incompressible Cellular Flows
- Inverse problems for partial differential equations
- Galerkin proper orthogonal decomposition methods for parabolic problems
This page was built for publication: A data-driven model reduction method for parabolic inverse source problems and its convergence analysis
