4 papers
Second Order Ensemble Langevin Method for Sampling and Inverse Problems
Ziming Liu, Andrew M. Stuart, Yixuan Wang
We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum…
The Parametric Complexity of Operator Learning
Samuel Lanthaler, Andrew M. Stuart
Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used to accelerate model evaluations via emula…
Ensemble Kalman Methods: A Mean Field Perspective
Edoardo Calvello, Sebastian Reich, Andrew M. Stuart
Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical…
Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions
Andrew M. Stuart, Aretha L. Teckentrup
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on…