A probabilistic finite element method based on random meshes: a posteriori error estimators and Bayesian inverse problems
DOI10.1016/j.cma.2021.113961zbMath1506.65200arXiv2103.06204OpenAlexW3134305408MaRDI QIDQ2237464
Giacomo Garegnani, Assyr Abdulle
Publication date: 27 October 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.06204
a posteriori error estimatorsuncertainty quantificationBayesian inverse problemsprobabilistic methods for PDEsrandom meshes
Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Bayesian inference (62F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)
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Cites Work
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- Robust adaptive Metropolis algorithm with coerced acceptance rate
- Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
- Bayesian solution uncertainty quantification for differential equations
- Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients
- Numerical models for differential problems. Translated by Silvia Quarteroni.
- A posteriori error estimation and adaptive mesh-refinement techniques
- Inferring solutions of differential equations using noisy multi-fidelity data
- Machine learning of linear differential equations using Gaussian processes
- Statistical analysis of differential equations: introducing probability measures on numerical solutions
- Statistical and computational inverse problems.
- Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors
- The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions
- Complexity bounds on supermesh construction for quasi-uniform meshes
- Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration
- Convergence rates of Gaussian ODE filters
- Strong convergence rates of probabilistic integrators for ordinary differential equations
- Adaptive step-size selection for state-space probabilistic differential equation solvers
- Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective
- A modern retrospective on probabilistic numerics
- A probabilistic model for the numerical solution of initial value problems
- Inverse problems: A Bayesian perspective
- Dynamic updating of numerical model discrepancy using sequential sampling
- Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
- A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
- The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
- The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
- Iterative updating of model error for Bayesian inversion
- Random Forward Models and Log-Likelihoods in Bayesian Inverse Problems
- Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes
- A Bayesian Numerical Homogenization Method for Elliptic Multiscale Inverse Problems
- Ensemble Kalman Filter for Multiscale Inverse Problems
- Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
- Bayesian Probabilistic Numerical Methods
- Bayesian Numerical Homogenization
- Probabilistic numerics and uncertainty in computations
- The Mathematical Theory of Finite Element Methods
- MCMC methods for functions: modifying old algorithms to make them faster
