On Bayesian data assimilation for PDEs with ill-posed forward problems
From MaRDI portal
Publication:5089412
DOI10.1088/1361-6420/ac7acdzbMath1495.35206arXiv2107.07593OpenAlexW4283275932WikidataQ114096858 ScholiaQ114096858MaRDI QIDQ5089412
Franziska Weber, Siddhartha Mishra, Samuel Lanthaler
Publication date: 19 July 2022
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.07593
Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Navier-Stokes equations (35Q30) Initial-boundary value problems for nonlinear higher-order PDEs (35G31)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Burgers' equation with vanishing hyper-viscosity
- The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
- A spectral vanishing viscosity method for large eddy simulations
- An analysis of numerical errors in large-eddy simulations of turbulence
- Stability and spectral convergence of Fourier method for nonlinear problems: on the shortcomings of the \(2/3\) de-aliasing method
- On the convergence of the spectral viscosity method for the two-dimensional incompressible Euler equations with rough initial data
- Construction of approximate entropy measure-valued solutions for hyperbolic systems of conservation laws
- Inverse problems: A Bayesian perspective
- Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws
- Convergence of Spectral Methods for Nonlinear Conservation Laws
- Nonstationary inverse problems and state estimation
- Inverse Problem Theory and Methods for Model Parameter Estimation
- Statistical solutions of hyperbolic systems of conservation laws: Numerical approximation
- On the Well-posedness of Bayesian Inverse Problems
- On the conservation of energy in two-dimensional incompressible flows
- On the local Lipschitz stability of Bayesian inverse problems
- Deep neural network expression of posterior expectations in Bayesian PDE inversion
- Statistical solutions of the incompressible Euler equations
- Data Assimilation
- The ensemble Kalman filter for combined state and parameter estimation
- Data assimilation: Mathematical and statistical perspectives
- Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
- Numerical Solution of the Navier-Stokes Equations
- A critical analysis of Rayleigh-Taylor growth rates