Jonathan Weare

Warren Weaver Hall, Room 1103
251 Mercer Street
New York, NY 10012-1185
[my last name]@nyu.edu






Our group is primarily focused on the design, mathematical analysis, and application of stochastic algorithms and models. Our work draws on tools from probability theory, numerical analysis, and statistical and machine learning. Research in the group is informed by our long term collaborations with applications experts in areas such as astrophysics, biophysics, computational chemistry, and weather and climate science.

I am a 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.



Research areas

Monte Carlo sampling
multiscale analysis and simulation
randomized numerical linear algebra
rare event analysis and simulation
statistical and machine learning for science



People

High school students
Anna Zhang, Stuyvesant High School 2020-2021

Undergraduate students
James Butler, mathematics, University of Chicago (co-mentored with D. Abbot) 2020-2021
Runxin Ni, mathematics, New York University (co-mentored with D. Abbot) Summer 2020

Charlie Marshall, mathematics, University of Chicago (co-mentored with D. Abbot) 2019-2020
Douglas Dow, mathematics, University of Chicago 2019-2020
Bradley Stadie, mathematics, University of Chicago 2013-2014

Masters students
Bixing Qiao, mathematics, New York University 2019-2020
Eileen Li, statistics, University of Chicago (co-mentored with A. Dinner) 2016-2017

Doctoral students
Natalia Hajłasz, New York University 2022-
Xiaoou Cheng, New York University 2020-
Huan Zhang, mathematics, New York University 2019-
Chatipat Lorpaiboon, chemistry, University of Chicago (co-mentored with A. Dinner) 2018-
John Strahan, chemistry, University of Chicago (co-mentored with A. Dinner) 2018-2024
Anya Katsevich, mathematics, New York University 2017-2022
Justin Finkel, applied math, University of Chicago (co-mentored with D. Abbot) 2017-2022
Adam Antoszewski, chemistry, University of Chicago (co-mentored with A. Dinner) 2017-2022
Sam Greene, chemistry, Columbia (co-mentored with T. Berkelbach) 2017-2022
Robert Webber, mathematics, New York University 2015-2021
Bodhi Vani, chemistry, University of Chicago (co-mentored with A. Dinner) 2015-2021
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

Instructors and postdoctoral scholars
Yifan Chen, mathematics, New York University 2023-
Michael Lindsey, mathematics, New York University 2019-2022
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

Current
Communications on Pure and Applied
                      Mathematics     Stochastics and Partial Differential
                      Equations: Analysis and Computations

Past
SIAM/ASA Journal on Uncertainty
                      Quantification



Publications (sorted roughly by area)

Preprints can be found on arXiv

Monte Carlo, Markov chains, and related
Ensemble Markov chain Monte Carlo with teleporting walkers
with M. Lindsey and A. Zhang, SIAM Journal on Uncertainty Quantification, 10(3) [2022], 860-885
A metric on directed graphs and Markov chains based on hitting probabilities
with Z.M. Boyd, N. Fraiman, J.L. Marzuola, P.J. Mucha, and B. Osting, SIAM Journal on Mathematics of Data Science, 3(2) [2021], 467-493
Stratification as a general variance reduction method for Markov chain Monte Carlo
with A.R. Dinner, E.H. Thiede, and B. Van Koten, SIAM/ASA Journal on Uncertainty Quantification (JUQ), 8(3) [2020], 1139-1188
Langevin Markov chain Monte Carlo with stochastic gradients
with C. Matthews [2018]
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) [2018], 4069-4079
Ensemble preconditioning for Markov chain Monte Carlo simulation
with B. Leimkuhler and C. Matthews, Statistics and Computing, 28(2) [2017], 277-290
Eigenvector method for umbrella sampling enables error analysis
with E. Thiede, B. Van Koten, and A. Dinner, Journal of Chemical Physics, 145(8) [2016], 084115
Sharp entrywise perturbation bounds for Markov chains
with E. Thiede and B. Van Koten, SIAM Journal on Matrix Analysis and Applications, 36(3) [2015], 917-941
On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method
with B. Roux, Journal of Chemical Physics, 138(8) [2013], 084107
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 [2012], 198
Ensemble samplers with affine invariance
with J. Goodman, Communications in Applied Mathematics and Computational Science, 5 [2010], 65-80
Efficient Monte Carlo sampling by parallel marginalization
Proceedings of the National Academy of Science, 104(31) [2007], 12657-12662

Multiscale analysis and simulation
Mercury's chaotic secular evolution as a subdiffusive process  
with D.S. Abbot, R.J. Webber, D.M. Hernandez, and S. Hadden
, The Astrophysical Journal, 967(2) [2024], 121
A Kinetic Monte Carlo approach for simulating cascading transmission line failure
with J. Roth, D.A. Barajas-Solano, P. Stinis, and M. Anitescu, SIAM Multiscale Modeling and Simulation, 19(1) [2021], 208-241
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) [2016], 1449-1458
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) [2014], 5467-5475
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) [2014], 184114
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) [2014], 1710-1720
The relaxation of a family of broken bond crystal surface models
with J. Marzuola, Physical Review E, 88 [2013], 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) [2013], 2466-2480
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) [2013], 094111
Extending molecular simulation time scales: Parallel-in-time integration for high-level quantum chemistry and complex force representations
with E. Bylaska and J.H. Weare, Journal of Chemical Physics, 139 [2013], 074114
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 [2011], 1771-1784
Variance reduction for particle filters of systems with time-scale separation
with D. Givon and P. Stinis, IEEE Transactions on Signal Processing, 57(2) [2009], 424-435

Randomized numerical linear algebra
Full configuration interaction excited-state energies in large active spaces from subspace iteration with repeated random sparsification
with S.M. Greene, R.J. Webber, J.E.T. Smith, and T.C. Berkelbach, Journal of Chemical Theory and Computation, 18(12) [2022], 7218-7232
Approximating matrix eigenvalues by subspace iteration with repeated random sparsification
with S.M. Greene, R.J. Webber, and T.C. Berkelbach, SIAM Journal on Scientific Computing, 44(5) [2022], A3067-A3097
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) [2020], 5572–5585
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) [2019], 4834-4850
Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra
with L.H. Lim, SIAM Reviews: Research Spotlight, 59(3) [2017], 547-587

Rare event analysis and simulation
BAD-NEUS: Rapidly converging trajectory stratification
with J. Strahan, C. Lorpaiboon, and A.R. Dinner, Journal of Chemical Physics, 161 [2024], 084109
Revealing the statistics of extreme events hidden in short weather forecast data
with
J. Finkel, E.P. Gerber, and D.S. Abbot, AGU Advances, 4 [2023], e2023AV000881
(Featured as an Editor's Highlight)
Simple physics and integrators accurately reproduce Mercury instability statistics
with D.S. Abbot, D.M. Hernandez, S. Hadden, R.J. Webber, and G.P. Afentakis, The Astrophysical Journal
, 944(2) [2023], 190
Data-driven transition path analysis yields a statistical understanding of sudden stratospheric warming events in an idealized model
with J. Finkel, R.J. Webber, E.P. Gerber, and D.S. Abbot, Journal of the Atmospheric Sciences, 80 [2023], 519-534

Augmented transition path theory for sequences of events
with C. Lorpaiboon and A.R. Dinner, Journal of Chemical Physics, 157(9) [2022], 094115
Computing transition path theory quantities with trajectory stratification
with B.P. Vani and A.R. Dinner, Journal of Chemical Physics, 157(3) [2022], 034106
Rare event sampling improves Mercury instability statistics
with D.S. Abott, R.J. Webber, and S. Hadden, Astrophysical Journal, 923(2) [2021], 236
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) [2020], 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) [2020], 2327-2347
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 [2019], 053109
(Featured in SIAM News)
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) [2019], 863-891
Trajectory stratification of stochastic dynamics
with A.R. Dinner, J.C. Mattingly, J. Tempkin, and B. Van Koten, SIAM Reviews: Research Spotlight, 60(4) [2018], 909–938
Simulating the stochastic dynamics and cascade failure of power networks
with C. Matthews, B. Stadie, M. Anitescu, and C. Demarco, [2017]
The Brownian fan
with M. Hairer, Communications in Pure and Applied Mathematics, 68(1) [2015], 1-60
Improved diffusion Monte Carlo
with M. Hairer, Communications in Pure and Applied Mathematics, 67(12) [2014], 1995-2021
Data assimilation in the low noise regime with applications to the Kuroshio
with E. Vanden-Eijnden, Monthly Weather Review, 141 [2013], 1822-1841
Steered transition path sampling
with N. Guttenberg and A. Dinner, Journal of Chemical Physics, 136 [2012], 234103
Rare event simulation for small noise diffusions
with E. Vanden-Eijnden, Communications in Pure and Applied Mathematics, 65(12) [2012], 1770-1803
Particle filtering with path sampling and an application to a bimodal ocean current model
Journal of Computational Physics, 228 [2009], 4312-4331
Efficient Conditional Path Sampling of Stochastic Differential Equations
Thesis (Ph.D.) - University of California, Berkeley, ProQuest, [2007], ISBN: 978-0549-73732-2

Statistical and machine learning for science
The surprising efficiency of temporal difference learning for rare event prediction
with
X. Cheng, NeurIPS 2024
Using explainable AI and transfer learning to understand and predict the maintenance of Atlantic blocking with limited observational data
with H. Zhang, J. Finkel, D.S. Abbot, and E.P. Gerber,
JGR - Machine Learning and Computation , accepted
Improved active learning via dependent leverage score sampling
with
A. Shimizu, X. Cheng, and C. Musco, ICLR 2024
(Oral presentation, top 1.2% of submissions)

Accurate estimates of dynamical statistics using memory
with
C. Lorpaiboon, S.C. Guo, J. Strahan, and A.R. Dinner, Journal of Chemical Physics, accepted
(Featured as an Editor's Pick)
AI can identify Solar System instability billions of years in advance
with
D.S. Abbot, J.D. Laurence-Chasen, R.J. Webber, and D.M. Hernandez, Research Notes of the AAS, 8(1) [2024]
Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction
with J. Strahan,
S.C. Guo, C. Lorpaiboon, and A.R. Dinner, Journal of Chemical Physics, 159 [2023], 014110

Predicting rare events using neural networks and short-trajectory data
with J. Strahan, J. Finkel, and A.R. Dinner, Journal of Computational Physics, 488 [2023],
112152
Understanding and eliminating spurious modes in variational Monte Carlo using collective variables
with H. Zhang, R.J. Webber, M. Lindsey, and T.C. Berkelbach, Physical Review Research, 5 [2023], 023101

Learning forecasts of rare stratospheric transitions from short simulations

with J. Finkel, R.J. Webber, D.S. Abbot, and E.P. Gerber, Monthly Weather Review, 149(11) [2021], 3649-3669
Long-timescale predictions from short-trajectory data: A benchmark analysis of the trp-cage miniprotein
with J. Strahan, A. Antoszewski, C. Lorpaiboon, B. Vani, and A.R. Dinner, Journal of Chemical Theory and Computation, 17(5) [2021], 2948-2963
Error bounds for dynamical spectral estimation
with R.J. Webber, E.H. Thiede, D. Dow, and A.R. Dinner, SIAM Journal on Mathematics of Data Science, 3(1) [2021], 225-252
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, 124(42) [2020], 9354-9364
Galerkin approximation of dynamical quantities using trajectory data
with E.H. Thiede, D. Giannakis, and A.R. Dinner, Journal of Chemical Physics, 150 [2019], 24111
Distinguishing meanders of the Kuroshio using machine learning
with D. Plotkin and D. Abbot, Journal of Geophysical Research - Oceans, 119(10) [2014], 6593-6604



Software

Fast Randomized Iteration for Electronic Structure (FRIES)
S.M. Greene
(I am not an author)
C++ implementations of various methods within the Fast Randomized Iteration (FRI) framework for performing Full Configuration Interaction calculations on molecular systems and the Hubbard model.

pyEDGAR
E.H. 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)
E.H. Thiede (I am not an author)
Python implementation of a stratification approach to MCMC

Umbrella Sampling for Data Science Applications
C. Matthews (I am not an author)
Lightweight Python implementation of EMUS for data science applications

A very nice EMUS tutorial in Python
G.J. Gilbert (I am not an author)

Ensemble QuasiNewton MCMC (EQN)
C. Matthews (I am not an author)
Python implementation of an emsemble preconditioning approach to MCMC
 
Fast Randomized Iteration (FRI)
with J. Dama
Demonstration C++ implementation of randomized power iteration.
 
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)
J. Dama (I am not an author)
Demonstration C++ implementation of an improved diffusion Monte Carlo method.
 
emcee: The MCMC Hammer
D. Foreman-Mackey, D. Hogg, D. Lang, and J. Goodman (I am not an author)
Python implementation of an affine invariant ensemble MCMC scheme.