Jonathan Weare

Warren Weaver Hall, Room 1103
251 Mercer Street
New York, NY 10012-1185
weare [AT] cims [DOT] nyu [DOT] edu





Our group is primarily focused on the design, analysis, and application of stochastic algorithms and models. Our work draws on tools from probability theory, the theory of partial differential equations, and numerical analysis. A significant portion of research in the group is organized around long term collaborations with applications experts in areas such as biophysics, computational chemistry, and weather and climate science.

I am currently an associate professor of mathematics in the Courant Institute of Mathematical Sciences at New York University. Previously I was an associate professor in the statistics department and in the James Franck Institute at the University of Chicago and, before that, an assistant professor in the mathematics department there. Before moving to Chicago I was a Courant Instructor of mathematics at NYU and a PhD student in mathematics at the University of California at Berkeley.



Current research areas

Monte Carlo methods
multiscale modeling and simulation
randomized numerical linear algebra
rare event analysis and simulation
statistical and machine learning for dynamical systems



People

High school students
Anna Zhang, Stuyvesant High School 2020-

Undergraduate students
Charlie Marshall, mathematics, University of Chicago 2019-2020
Douglas Dow, mathematics, University of Chicago 2019-2020
Bradley Stadie, mathematics, University of Chicago 2013-2014

Masters students
Bixing Qiao, mathematics, Courant Institute 2019-2020
Eileen Li, statistics, University of Chicago 2016-2017

Doctoral students
Anya Katsevich, mathematics, Courant Institute 2019-
Chatipat Lorpaiboon, chemistry, University of Chicago (co-mentored with A. Dinner) 2018-

John Strahan, chemistry, University of Chicago (co-mentored with A. Dinner) 2018-
Adam Antoszewski, chemistry, University of Chicago (co-mentored with A. Dinner) 2017-
Justin Finkel, applied math, University of Chicago (co-mentored with D. Abbot) 2017-
Sam Greene, chemistry, Columbia (co-mentored with T. Berkelbach) 2017-
Robert Webber, mathematics, Courant Institute 2015-
Bodhi Vani, chemistry, University of Chicago (co-mentored with A. Dinner) 2015-
Erik Thiede, chemistry, University of Chicago (co-mentored with A. Dinner) 2013-2019
David Plotkin, geoscience, University of Chicago (co-mentored with D. Abbot) 2012-2018
Jeremy Tempkin, chemistry, University of Chicago (co-mentored with A. Dinner) 2012-2017

Postdoctoral scholars
Brian Van Koten, applied math, University of Chicago 2014-2018
Charles Matthews, applied math, University of Chicago 2014-2018
Seyit Kale, chemistry, University of Chicago 2012-2015



Editorial work

Stochastics and Partial Differential Equations: Analysis and Computations

SIAM/ASA Journal on Uncertainty Quantification




Publications

A (nearly) complete list of publications and preprints can be found on arXiv

2020
Integrated VAC: A robust strategy for identifying eigenfunctions of dynamical operators
with C. Lorpaiboon, E.H. Thiede, R.J. Webber, and A.R. Dinner, Journal of Physical Chemistry B, accepted
Improved Fast Randomized Iteration approach to Full Configuration Interaction
with S.M. Greene, R.J. Webber, and T.C. Berkelbach, Journal of Chemical Theory and Computation, 16(9), 5572–5585
Insulin dissociates by diverse mechanisms of coupled unfolding and unbinding
with A. Antoszewski, C.-J. Feng, B.P. Vani, E.H. Thiede, L. Hong, A. Tokmakoff, and A.R. Dinner, Journal of Physical Chemistry B, 124(27), 5571–5587
Path properties of atmospheric transitions: illustration with a low-order sudden stratospheric warming model
with J. Finkel, and D.S. Abbot, Journal of Atmospheric Science, 77(7), 2327–2347  
Stratification as a general variance reduction method for Monte Carlo
with A.R. Dinner, E.H. Thiede, and B. Van Koten, SIAM/ASA Journal on Uncertainty Quantification (JUQ), 8(3), 1139-1188

2019
Beyond walkers in stochastic quantum chemistry: reducing error using Fast Randomized Iteration
with S.M. Greene, R.J. Webber, and T.C. Berkelbach, Journal of Chemical Theory and Computation, 15(9), 4834-4850
Galerkin approximation of dynamical quantities using trajectory data
with E.H. Thiede, D. Giannakis, and A.R. Dinner, Journal of Chemical Physics, 150, 24111
Practical rare event simulation for extreme mesoscale weather
with R.J. Webber, D.A. Plotkin, M.E O'Neill, and D.S. Abbot, Chaos, 29, 053109  
Maximizing simulated tropical cyclone intensity with action minimization
with D.A. Plotkin, R.J. Webber, M.E O'Neill, and D.S. Abbot, Journal of Advances in Modeling Earth Systems (JAMES), 11(4), 863-891

2018
Trajectory stratification of stochastic dynamics
with A.R. Dinner, J.C. Mattingly, J. Tempkin, and B. Van Koten, SIAM Reviews: Research Spotlight, 60(4), 909–938  
Umbrella sampling: a powerful method to sample tails of distributions
with C. Matthews, A. Kravstov, and E. Jennings, Monthly Notices of the Royal Astronomical Society, 480(3), 4069-4079


2017
Simulating the stochastic dynamics and cascade failure of power networks
with C. Matthews, B. Stadie, M. Anitescu, and C. Demarco  
Ensemble preconditioning for Markov chain Monte Carlo simulation
with B. Leimkuhler and C. Matthews, Statistics and Computing, 28(2) 277-290
Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra

with L.H. Lim, SIAM Reviews: Research Spotlight, 59(3) 547-587

2016
Eigenvector method for umbrella sampling enables error analysis
with E. Thiede, B. Van Koten, and A. Dinner, Journal of Chemical Physics, 145(8) 084115
Multiple time-step dual-Hamiltonian hybrid molecular dynamics Monte Carlo canonical propagation algorithm
with Y. Chen, S. Kale, A. Dinner, and B. Roux, Journal of Chemical Theory and Computation, 12(4) 1449-1458

2015
Sharp entrywise perturbation bounds for Markov chains
with E. Thiede and B. Van Koten, SIAM Journal on Matrix Analysis and Applications, 36(3), 917-941
The Brownian fan
with M. Hairer, Communications in Pure and Applied Mathematics, 68(1) 1-60

2014
Finding chemical reaction paths with a multilevel preconditioning protocol
with S. Kale, S. Olaseni, and A. Dinner, Journal of Chemical Theory and Simulation, 10(12), 5467-5475
Distinguishing meanders of the Kuroshio using machine learning
with D. Plotkin and D. Abbot, Journal of Geophysical Research - Oceans, 119(10) 6593-6604
Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations
with J. Tempkin, B. Qui, M. Saunders, B. Roux, and A. Dinner, Journal of Chemical Physics, 140(18) 184114
Improved diffusion Monte Carlo
with M. Hairer, Communications in Pure and Applied Mathematics, 67(12) 1995-2021
Nucleotide regulation of the structure and dynamics of G-actin
with M. Saunders, J. Tempkin, A. Dinner, B. Roux, and G. Voth, Biophysical Journal, 106(8) 1710-1720

2013
The relaxation of a family of broken bond crystal surface models
with J. Marzuola, Physical Review E, 88 032403
The theory of ultra coarse graining I, general principles
with J. Dama, A. Sinitskiy, M. McCullagh, B. Roux, A. Dinner, and G. Voth, Journal of Chemical Theory and Computation, 9(5) 2466-2480
On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method
with B. Roux, Journal of Chemical Physics, 138(8) 084107
Minimizing memory as an objective for coarse-graining
with N. Guttenberg, J. Dama, M. Saunders, A. Dinner, and G. Voth, Journal of Chemical Physics, 138(9) 094111
Extending molecular simulation time scales: Parallel-in-time integrations for high-lelel quantum chemistry and complex force representations
with E. Bylaska and J.H. Weare, Journal of Chemical Physics, 139 074114
Data assimilation in the low noise regime with applications to the Kuroshio with E. Vanden-Eijnden, Monthly Weather Review, 141 1822-1841

2012
Steered transition path sampling
with N. Guttenberg and A. Dinner, Journal of Chemical Physics, 136 234103
Rare event simulation for small noise diffusions
with E. Vanden-Eijnden, Communications in Pure and Applied Mathematics, 65(12) 1770-1803
An affine-invariant sampler for exoplanet fitting and discovery in radial velocity data
with F. Hou, J. Goodman, D. Hogg, and C. Schwab, The Astrophysical Journal, 75 198

2011
The evolution of a crystal surface: analysis of a 1D step train connecting two facets in the ADL regime
with H. Al Hajj Shehadeh and R.V. Kohn, Physica D, 240 1771-1784

2010
Ensemble samplers with affine invariance
with J. Goodman, Communications in Applied Mathematics and Computational Science, 5 65-80

2009
Particle filtering with path sampling and an application to a bimodal ocean current model
Journal of Computational Physics, 228 4312-4331
Variance reduction for particle filters of systems with time-scale separation
with D. Givon and P. Stinis, IEEE Transactions on Signal Processing, 57(2) 424-435

2007
Efficient Monte Carlo sampling by parallel marginalization
Proceedings of the National Academy of Science, 104(31) 12657-12662



Software

pyEDGAR
https://github.com/ehthiede/pyEDGAR
E. Thiede
(I am not an author)
Python implementation of Dynamic Galerkin Approximation (DGA) which builds predictions of long-timescale phenomena from short trajectory data.

Eigenvector Method for Umbrella Sampling (EMUS)
https://github.com/ehthiede/EMUS
E. Thiede
(I am not an author)
Python implementation of a stratification approach to MCMC

Ensemble QuasiNewton MCMC (EQN)
https://bitbucket.org/c_matthews/ensembleqn
C. Matthews (I am not an author)
Python implementation of an emsemble preconditioning approach to MCMC
 
Fast Randomized Iteration (FRI)
https://github.com/jonathanweare/Fast-Randomized-Iteration-FRI-
with J. Dama
Demonstration C++ implementation of randomized power iteration.
 
Enhanced Sampling Toolkit
https://github.com/jtempkin/enhanced_sampling_toolkit
J. Tempkin (I am not an author)
The Enhanced Sampling Toolkit provides a flexible and extensible toolkit for rapidly prototyping rare event simulation algorithms. The code is written entirely in Python and acts as a wrapper to various well-established molecular dynamics codes.
 
Ticketed Diffusion Monte Carlo (TDMC)
http://dx.doi.org/10.5281/zenodo.17001
J. Dama (I am not an author)
Demonstration C++ implementation of an improved diffusion Monte Carlo method.
 
emcee: The MCMC Hammer
http://dan.iel.fm/emcee/current/
D. Foreman-Mackey, D. Hogg, D. Lang, and J. Goodman (I am not an author)
Python implementation of an affine invariant ensemble MCMC scheme.