# Mustafa A. Mohamad

# About

I'm a postdoctoral research fellow at the Courant Institute of Mathematical Sciences. Formerly, I was a research assistant at the Massachusetts Institute of Technology, where I completed my S.M. and Ph.D. degrees in Mechanical Engineering and Computation. Before then, I was an undergraduate student at the University of Illinois at Urbana-Champaign where I received my B.Sc. in Engineering Mechanics and a minor in Mathematics.

# Contact

Feel free to reach out to me via email: *mus-m* at *outlook.com*

# Research Interests

Generally, my work focuses on the broad topic
*uncertainty
quantification*, from a broad perspective and has focused on the study of extreme events. My expertise lies at the intersection of computational mathematics, stochastic dynamical
systems, machine learning, data assimilation, and extreme events. I consider myself a researcher that takes a holistic approach, by taking the perspective that newly developed methods need practical demonstration on hard problems in real-world applications and in engineering tasks.

Most of my work has been on developing efficient methods to quantify *extreme events* (bursting phenomena) in
physical systems. My research here has involved developing new quantification strategies by blending ideas from
probability theory and dynamical systems theory. Most recently, I worked on a new technique utilizing Gaussian process regression, a popular method machine
learning, to develop efficient sampling algorithms that targets heavy-tailed output statistics.

Recently, another topic of interest is centered around data assimilation and Bayesian parameter estimation methods from noisy measurement instruments. In particular, I have been working on this topic in the context of prediction of flow fields from measurements obtained from instruments (i.e. tracer particles) that are being advected by a flow field. In particular, this is a practically important problem in the assimilation of tracer particle observations used to track oceanic and atmospheric flows to understand various mechanisms in the climate and also for state prediction.

I am a big advocate and contributor to open source software, in particular the Julia language and packages in the Julia ecosystem. My projects and contributions are available on Github.

# Publications

Most of my journal publications should be available on Google Scholar and arXiv. You may also contact me via email for preprints.

## Journal Publications

- M. A. Mohamad, A. J. Majda, Eulerian energy spectra estimation from Lagrangian drifters through joint data assimilation and MCMC parameter estimation, in preparation.
- M. A. Mohamad, A. J. Majda, Eulerian and Lagrangian statistics in an exactly solvable turbulent shear
model
with a random background mean,
*Physics of Fluids*, Volume 31 (10), p. 105115, Oct 2019. [pdf] - M. A. Mohamad, A. J. Majda, Recovering the Eulerian energy spectrum from noisy Lagrangian tracers, (Physica D, 2019, submitted). [pdf]
- M. A. Mohamad, T. P. Sapsis, A sequential sampling
strategy for extreme event statistics in nonlinear dynamical systems,
*Proceedings of the National Academy of Sciences*, Volume 115 (44), pp. 11138-11143, Oct 2018. [pdf] [supporting information] - H. K. Joo, M. A. Mohamad, T. P. Sapsis, Heavy-tailed
response of structural systems subjected to extreme
forcing events,
*ASME Journal of Computational and Nonlinear Dynamics*, Volume 13 (9), p. 090914, Jul 2018. [pdf] - H. K. Joo, M. A. Mohamad, T. P. Sapsis, Extreme events and their
optimal mitigation in nonlinear structural systems excited by stochastic loads: Application to ocean
engineering systems,
*Ocean Engineering*, Volume 142, pp. 145-160, Sept 2017. [pdf] - M. A. Mohamad, W. Cousins, T. P. Sapsis, A probabilistic
decomposition-synthesis method for the
quantification of rare events due to internal instabilities,
*Journal of Computational Physics*, Volume 322, pp. 288-308, Oct 2016. [pdf] - M. A. Mohamad, T. P. Sapsis, Probabilistic response and
rare events in Mathieu's equation under correlated
parametric excitation,
*Journal of Ocean Engineering*, Volume 120, pp. 289-297, Jul. 2016. [pdf] - M. A. Mohamad, T. P. Sapsis, Probabilistic
description of extreme events in intermittently unstable systems
excited by correlated stochastic processes,
*SIAM/ASA Journal on Uncertainty Quantification*, Volume 3 (1), pp. 709-736, Aug 2015. [pdf]

## Conference Publications

- M. A. Mohamad, T. P. Sapsis, Efficient sampling for extreme event statistics of the wave loads on an
offshore platform,
*The 30th American Towing Tank Conference*, West Bethesda, Maryland, Oct 2017. - T. P. Sapsis, M. A. Mohamad, Probabilistic quantification of extreme events in complex systems,
*9th European Nonlinear Dynamics Conference*, Budapest, Hungary, Jun 2017. - T. P. Sapsis, M. A. Mohamad, H. K. Joo, Extreme response mitigation of stochastically forced nonlinear
structures,
*9th European Nonlinear Dynamics Conference*, Budapest, Hungary, Jun 2017. - M. A. Mohamad, T. P. Sapsis, Probabilistic response of Mathieu equation excited by correlated parametric
excitation,
*Proceedings of STAB 2015*, Glasgow, UK, Jun 2015. - M. A. Mohamad, T. P. Sapsis, Analytical approximation of the heavy-tail structure for intermittently
unstable complex modes,
*Proceedings of the Dynamic Data Driven Environmental Systems Science Conference*, Cambridge, Massachusetts, Nov 2014.