73 citations · 343 across the 31 of their papers we have counts for
12 papers · 1 filter
Optimal Recovery for Solving Variational Problems
Ting Wang, Gideon Simpson, Jaroslaw Knap
In science and engineering, many physical laws and scientific principles naturally arise as variational problems of minimizing an energy functional over an appropriate functional s…
Iterate Averaging, the Kalman Filter, and 3DVAR for Linear Inverse Problem
Felix G. Jones, Gideon Simpson
It has been proposed that classical filtering methods, like the Kalman filter and 3DVAR, can be used to solve linear statistical inverse problems. In the work of Iglesias, Lin, Lu,…
A Numerical Method for a Nonlocal Diffusion Equation with Additive Noise
Georgi Medvedev, Gideon Simpson
We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of…
A splitting method to reduce MCMC variance
Robert J. Webber, David Aristoff, Gideon Simpson
We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions.…
Sampling from Rough Energy Landscapes
Petr Plecháč, Gideon Simpson
We examine challenges to sampling from Boltzmann distributions associated with multiscale energy landscapes. The multiscale features, or "roughness," corresponds to highly oscillat…
Conservative Integrators for a Toy Model of Weak Turbulence
Aquil D. Jones, Gideon Simpson, William Wilson
Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourg…
A Theoretical Examination of Diffusive Molecular Dynamics
Gideon Simpson, Mitchell Luskin, David J. Srolovitz
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to fi…
Relative Entropy Minimization over Hilbert Spaces via Robbins-Monro
Gideon Simpson, Daniel Watkins
One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to…
Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions
Frank J. Pinski, Gideon Simpson, Andrew M. Stuart +1
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density…
A Generalized Parallel Replica Dynamics
Andrew Binder, Tony Lelièvre, Gideon Simpson
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynam…
The parallel replica method for simulating long trajectories of Markov chains
David Aristoff, Tony Lelièvre, Gideon Simpson
The parallel replica dynamics, originally developed by A.F. Voter, efficiently simulates very long trajectories of metastable Langevin dynamics. We present an analogous algorithm f…
Numerical Analysis of Parallel Replica Dynamics
Gideon Simpson, Mitchell Luskin
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by th…