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Inverse problems are ubiquitous because they formalize the integration of data with mathematical models.
A method for the solution of certain non-linear problems in least squares
K. Levenberg · 1944
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A stochastic approximation method
H. Robbins and S. Monro · 1951
Earlier work this paper cites.
Methods of conjugate gradients for solving linear systems
M. R. Hestenes and E. Stiefel · 1952
Earlier work this paper cites.
Equation of state calculations by fast computing machines
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller · 1953
Earlier work this paper cites.
An algorithm for least-squares estimation of nonlinear parameters
D. W. Marquardt · 1963
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Monte Carlo sampling methods using Markov chains and their applications
W. K. Hastings · 1970
Earlier work this paper cites.
Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation
K. M. Brown and J. E. Dennis, Jr · 1971
Earlier work this paper cites.
Computing forward-difference intervals for numerical optimization
P. E. Gill, W. Murray, M. A. Saunders, and Margaret H. Wright · 1983
Earlier work this paper cites.
Optimization by simulated annealing
S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi · 1983
Earlier work this paper cites.
Two-point step size gradient methods
J. Barzilai and J. M. Borwein · 1988
Earlier work this paper cites.
Numerical solution of stochastic differential equations
P. E. Kloeden and E. Platen · 1992
Earlier work this paper cites.
Particle swarm optimization
J. Kennedy and R. Eberhart · 1995
Earlier work this paper cites.
The law of the Euler scheme for stochastic differential equations. I. Convergence rate of the distribution function
V. Bally and D. Talay · 1996
Earlier work this paper cites.
The law of the Euler scheme for stochastic differential equations. II. Convergence rate of the density
V. Bally and D. Talay · 1996
Earlier work this paper cites.
Exponential convergence of Langevin distributions and their discrete approximations
G. O. Roberts and R. L. Tweedie · 1996
Earlier work this paper cites.
The effective energy transformation scheme as a special continuation approach to global optimization with application to molecular conformation
Z. Wu · 1996
Earlier work this paper cites.
A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems
M. Hanke · 1997
Earlier work this paper cites.
Weak convergence and optimal scaling of random walk Metropolis algorithms
G. O. Roberts, A. Gelman, and W. R. Gilks · 1997
Earlier work this paper cites.
On the Poisson equation and diffusion approximation. I
E. Pardoux and A. Yu. Veretennikov · 2001
Earlier work this paper cites.
Optimal scaling for various Metropolis-Hastings algorithms
G. O. Roberts and J. S. Rosenthal · 2001
Earlier work this paper cites.
Parallel multiscale Gauss–Newton–Krylov methods for inverse wave propagation
V. Akcelik, G. Biros, and O. Ghattas · 2002
Earlier work this paper cites.
Stochastic approximation and recursive algorithms and applications
H. J. Kushner and G. G. Yin · 2003
Earlier work this paper cites.
White noise limits for inertial particles in a random field
G. A. Pavliotis and A. M. Stuart · 2003
Earlier work this paper cites.
Analysis of multiscale methods for stochastic differential equations
W. E, D. Liu, and E. Vanden-Eijnden · 2005
Earlier work this paper cites.
Statistical and computational inverse problems
J. Kaipio and E. Somersalo · 2005
Earlier work this paper cites.
Sequential Monte Carlo samplers
P. Del Moral, A. Doucet, and A. Jasra · 2006
Earlier work this paper cites.
Approximate Gauss-Newton methods for nonlinear least squares problems
S. Gratton, A. S. Lawless, and N. K. Nichols · 2007
Earlier work this paper cites.
Stochastic differential equations and applications
X. Mao · 2008
Earlier work this paper cites.
Multiscale methods
G. A. Pavliotis and A. M. Stuart · 2008
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Introduction to derivative-free optimization
A. R. Conn, K. Scheinberg, and L. N. Vicente · 2009
Earlier work this paper cites.
Data assimilation
G. Evensen · 2009
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Sufficient conditions for torpid mixing of parallel and simulated tempering
D. B. Woodard, S. C. Schmidler, and M. Huber · 2009
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Pathwise accuracy and ergodicity of metropolized integrators for SDEs
N. Bou-Rabee and E. Vanden-Eijnden · 2010
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Ensemble samplers with affine invariance
J. Goodman and J. Weare · 2010
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Convergence of numerical time-averaging and stationary measures via Poisson equations
J. C. Mattingly, A. M. Stuart, and M. V. Tretyakov · 2010
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Inverse problems: a Bayesian perspective
A. M. Stuart · 2010
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Spectral methods for multiscale stochastic differential equations
A. Abdulle, G. A. Pavliotis, and U. Vaes · 2017
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The Bayesian approach to inverse problems
M. Dashti and A. M. Stuart · 2017
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A consensus-based model for global optimization and its mean-field limit
R. Pinnau, C. Totzeck, O. Tse, and S. Martin · 2017
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Analysis of the ensemble Kalman filter for inverse problems
C. Schillings and A. M. Stuart · 2017
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Sparsity-promoting and edge-preserving maximum a posteriori
S. Agapiou, M. Burger, M. Dashti, and T. Helin · 2018
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An analytical framework for consensus-based global optimization method
J. A. Carrillo, Y.-P. Choi, C. Totzeck, and O. Tse · 2018
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Hierarchical models in statistical inverse problems and the Mumford-Shah functional
T. Helin and M. Lassas · 2011
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Asymptotic analysis for the generalized Langevin equation
M. Ottobre and G. A. Pavliotis · 2011
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A dynamical systems framework for intermittent data assimilation
S. Reich · 2011
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Ensemble randomized maximum likelihood method as an iterative ensemble smoother
Y. Chen and D. S. Oliver · 2012
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An iterative EnKF for strongly nonlinear systems
P. Sakov, D. S. Oliver, and L. Bertino · 2012
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MCMC methods for functions: modifying old algorithms to make them faster
S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White · 2013
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Deep relaxation: partial differential equations for optimizing deep neural networks
P. Chaudhari, A. Oberman, S. Osher, S. Soatto, and G. Carlier · 2018
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Never look back - A modified EnKF method and its application to the training of neural networks without back propagation
E. Haber, F. Lucka, and L. Ruthotto · 2018
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Ensemble preconditioning for Markov chain Monte Carlo simulation
B. Leimkuhler, C. Matthews, and J. Weare · 2018
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Scaling limit of the Stein variational gradient descent part i: the mean field regime
J. Lu, Y. Lu, and J. Nolen · 2018
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Importance sampling for metastable dynamical systems in molecular dynamics
J. Quer · 2018
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Convergence analysis of ensemble Kalman inversion: the linear, noisy case
C. Schillings and A. M. Stuart · 2018
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Generalized modes in Bayesian inverse problems
C. Clason, T. Helin, R. Kretschmann, and P. Piiroinen · 2019
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Kinetic Methods for Inverse Problems
M. Herty and G. Visconti · 2019
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The sharp, the flat and the shallow: Can weakly interacting agents learn to escape bad minima?
N. Kantas, P. Parpas, and G. A. Pavliotis · 2019
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Ensemble Kalman inversion: a derivative-free technique for machine learning tasks
N. B. Kovachki and A. M. Stuart · 2019
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Derivative-free optimization methods
J. Larson, M. Menickelly, and S. M. Wild · 2019
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Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force
B. Leimkuhler and M. Sachs · 2019
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Note on Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler by Garbuno-Inigo, Hoffmann, Li and Stuart
N. Nüsken and S. Reich · 2019
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Gridap: An extensible Finite Element toolbox in Julia
S. Badia and F. Verdugo · 2020
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To interact or not? The convergence properties of interacting stochastic mirror descent
A. Borovykh, N. Kantas, P. Parpas, and G. A. Pavliotis · 2020
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Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM
O. R. A. Dunbar, A. Garbuno-Inigo, T. Schneider, and A. M. Stuart · 2020
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Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler
A. Garbuno-Inigo, F. Hoffmann, W. Li, and A. M. Stuart · 2020
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Affine invariant interacting Langevin dynamics for Bayesian inference
A. Garbuno-Inigo, N. Nüsken, and S. Reich · 2020
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On stochastic mirror descent with interacting particles: Convergence properties and variance reduction
A. Borovykh, N. Kantas, P. Parpas, and G.A. Pavliotis · 2021
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Consensus Based Sampling
J. A. Carrillo, F. Hoffmann, A. M. Stuart, and U. Vaes · 2021
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Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations
J. A. Carrillo and U. Vaes · 2021
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Unscented Kalman Inversion
D. Z. Huang, T. Schneider, and A. M. Stuart · 2021
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Scaling Limits for the Generalized Langevin Equation
G. A. Pavliotis, G. Stoltz, and U. Vaes · 2021
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Fokker-Planck particle systems for Bayesian inference: computational approaches
S. Reich and S. Weissmann · 2021
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