PhD candidate, Center for Computational Science and Engineering, MIT.

## About me

I am a PhD student at MIT in Computational Science and Engineering advised by Prof. Youssef Marzouk of the Uncertainty Quantification Group. My research is broadly in numerical methods for uncertainty quantification and probabilistic machine learning. I am currently interested in techniques that can uncover and exploit structure in statistical inference problems. Before joining MIT, I received an M.S. in Mathematics from Virginia Tech, where I studied nonlinear eigenvalue problems and reduced order modeling.

### Research Projects

**Exploiting structure in statistical inference problems**

High-dimensional inference problems pose challenges for both sampling methods (e.g., MCMC) and posterior approximation methods (e.g., variational inference). We overcome some of the challenges of high-dimensional inference by uncovering and exploiting low-dimensional structure in the problem.

- Greedy inference with structure-exploiting lazy maps,
*M. Brennan, D. Bigoni, O. Zahm, A. Spantini, Y. Marzouk*, Neurips 2020: Paper, Oral presentation, arXiv:1906.00031

**Nonlinear eigenvalue problems**

Nonlinear eigenvalue problems arise throughout many engineering and science applications. In these works, we use contour integration + rational interpolation via the Loewner framework to compute eigenvalues in a given region of the complex plane.

- Contour integral methods for nonlinear eigenvalue problems: a system theoretic approach,
*M. Brennan, M. Embree, S. Gugercin,*2020: arXiv:2012.14979 - Rational Interpolation Methods for Nonlinear Eigenvalue Problems,
*M. Brennan*, (Master’s Thesis), Virginia Tech, 2018: pdf