Nawaf Bou-Rabee
Assistant Professor of Mathematics

I completed my PhD in 2007 from the California Institute of Technology under the supervision of the late Jerrold E. Marsden. From 2008-2011, I was an NSF Mathematical Sciences Postdoctoral Fellow at New York University. Since 2011, I have been an Assistant Professor at the Mathematical Sciences Department of Rutgers University in Camden, New Jersey. I am interested in the numerical solution of stochastic partial differential equations and Markov Chain Monte Carlo methods.

Papers and Preprints

SPECTRWM: Spectral Random Walk Method for the Numerical Solution of Stochastic Partial Differential Equations,
arXiv:1608.00885 [math.PR].
Randomized Hamiltonian Monte Carlo,
with Jesús María Sanz-Serna,
arXiv:1511.09382 [math.PR], To be published in Annals of Applied Probability.
Continuous Time Random Walks for the Numerical Solution of Stochastic Differential Equations,
with Eric Vanden-Eijnden,
arXiv:1502.05034 [math.PR], To be published in Memoirs of the American Mathematical Society.
Metropolis Integration Schemes for Self-Adjoint Diffusions,
with Aleksandar Donev and Eric Vanden-Eijnden,
Multiscale Modeling & Simulation, Vol. 12, No. 2, pp. 781-831, 2014.
Time Integrators for Molecular Dynamics,
Entropy, 16, 138-162, 2014.
Non-asymptotic mixing of the MALA algorithm,
with Martin Hairer,
IMA J Numer Anal, 33, 80-110, 2013.
A patch that imparts unconditional stability to explicit integrators for Langevin-like equations,
with Eric Vanden-Eijnden,
J Comput Phys, 231, 2565-2580, 2012.
Pathwise accuracy and ergodicity of Metropolized integrators for SDEs,
with Eric Vanden-Eijnden,
Commun Pure Appl Math, 63, 655-696, 2010.
Long-run accuracy of variational integrators in the stochastic context,
with Houman Owhadi,
SIAM J of Numer Anal, 48, 278-297, 2010.
A Comparison of GHMC with and without Momentum Flips,
with Elena Akhmatskaya and Sebastian Reich,
J Comput Phys, 228, 2256 - 2265, 2009.
Stochastic variational integrators,
with Houman Owhadi,
IMA J of Numer Anal, 2, 421-443, 2009.
Hamilton-Pontryagin integrators on Lie groups,
with Jerrold Marsden,
Found Comput Math, 9, 197-219, 2009.

Slides from Talks and Mini-Courses

Good/Bad News on Hamiltonian Monte-Carlo
Oberseminar on Stochastic Analysis, Institute for Applied Mathematics, Bonn University, Bonn, Germany, January, 2017
Mini-Course at Gene Golub SIAM Summer School 2016 entitled: SPECTRWM: Spectral Random Walk Method for the Numerical Solution of Stochastic Partial Differential Equations.
Drexel University, Philadelphia, PA, July 25-August 5, 2016
q.v. SPECTRWM paper
Generalized Markov Chain Approximation Methods
Mathematics Colloquium, UC3M, Madrid, Spain, May, 2016
Markov Chain Approximation Methods for Sampling Quasistationary Distributions
Oberseminar on Stochastic Analysis, Institute for Applied Mathematics, Bonn University, Bonn, Germany, September, 2015
Mini-Course at New Perspectives in Markov Chain Monte Carlo entitled: MCMC-based integrators for Stochastic Differential Equations
Mathematics Research Institute at University of Valladolid, Valladolid, Spain, June 8-12, 2015
  1. Discrete-Time MCMC
  2. Steady-State Simulation of Self-Adjoint Diffusions
  3. Continuous-Time MCMC
  4. Markov Chain Approximation Methods
How to simulate stochastic differential equations without discretizing time?
Stochastic Computation Workshop, Montevideo, Uruguay, December 2014
Structure-preserving algorithms for self-adjoint diffusions
Scientific and Statistical Computing Seminar, U. of Chicago, IL, 2014

Numerical Solution of Stochastic Partial Differential Equations

This video animates a random walk approximation of Brownian motion on the interval shown with periodic boundary conditions. The state space of the walker is an evenly spaced grid. The walker jumps left or right with equal probability. Note that the jump size of the walker is fixed. The amount of time the walker spends in any given state is an exponentially distributed random variable with mean given by the jump size squared - as required by local accuracy. The spectral random walk method (SPECTRWM) generalizes this simple concept to stochastic partial differential equations (SPDE). SPECTRWM makes jumps of fixed size forward or backward along the leading eigenfunctions of the linear part of the drift of the SPDE with probabilities that depend only on its current state. Moreover, like the 1D random walk, the holding time of SPECTRWM is an exponentially distributed random variable whose mean is determined by local accuracy.

Aside from its mathematical interest, this generalization allows the following benefits:

To read more about SPECTRWM, click here.

Markov Chain Monte Carlo

Research Support

I would like to gratefully acknowledge the extensive support I have received from Rutgers University and the National Science Foundation.