Statistical Finite Elements via Langevin Dynamics
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Publication:5880613
DOI10.1137/21M1463094zbMath1506.65006arXiv2110.11131OpenAlexW4312190934MaRDI QIDQ5880613
Connor Duffin, Sotirios Sabanis, Ömer Deniz Akyildiz, Mark A. Girolami
Publication date: 3 March 2023
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.11131
Monte Carlo methods (65C05) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)
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Uses Software
Cites Work
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- An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach
- GitHub
- Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
- Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
- Automated solution of differential equations by the finite element method. The FEniCS book
- Optimal scaling for various Metropolis-Hastings algorithms.
- Geometric MCMC for infinite-dimensional inverse problems
- Logarithmic Sobolev inequalities and stochastic Ising models
- The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions
- A Feynman-Kac approach for logarithmic Sobolev inequalities
- Finite element methods for fractional-order diffusion problems with optimal convergence order
- What is the fractional Laplacian? A comparative review with new results
- Proposals which speed up function-space MCMC
- User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
- High-dimensional Bayesian inference via the unadjusted Langevin algorithm
- Numerical methods for stochastic partial differential equations with white noise
- Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
- Low-rank statistical finite elements for scalable model-data synthesis
- Nonasymptotic estimates for stochastic gradient Langevin dynamics under local conditions in nonconvex optimization
- Bayesian Calibration of Computer Models
- Inverse problems: A Bayesian perspective
- A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
- Multilevel Monte Carlo Methods
- Strong and Weak Convexity of Sets and Functions
- Hessian Matrix vs. Gauss–Newton Hessian Matrix
- A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow
- Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix
- Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
- Gaussian Markov Random Fields
- Some Remarks on Preconditioning Molecular Dynamics
- Statistical finite elements for misspecified models
- Numerical approximation of fractional powers of elliptic operators
- The Mathematical Theory of Finite Element Methods
- Optimal Transport
- MCMC methods for functions: modifying old algorithms to make them faster
- Taming Neural Networks with TUSLA: Nonconvex Learning via Adaptive Stochastic Gradient Langevin Algorithms
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