Mustafa A. Mohamad
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.
Feel free to reach out to me via email: mus-m at outlook.com
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.
- M. A. Mohamad, A. J. Majda, Eulerian energy spectra estimation from Lagrangian drifters through joint data assimilation and MCMC parameter estimation, in preperation.
- 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, 2019 (accepted). [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, 115, p. 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), 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]
- 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.