Research profile

In my current work, I utilize theories and methods from numerical analysis, PDE theory, probability and statistics, inverse problems, and optimization to develop scalable numerical methods for optimal experimental design for large-scale statistical inverse problems governed by PDEs, and optimal control of systems governed by PDEs with random coefficients. My recent work also involves spectral methods for uncertainty quantification with applications in reduction of stochastic dynamics, stochastic chemical kinetics, and ocean circulation modeling under uncertainty. I am also interested in problems of mathematical epidemiology with emphasis on spread of infectious diseases; my work in this area has thus far focused on age/time dynamics of epidemic cholera. My PhD research was in the area of averaging of differential operators with random coefficients. My work in that area focused on modeling of ergodic random media, their symmetries, and numerical computation of their effective properties. The study of symmetries of elastic bodies with random structure led to interesting problems of abstract algebra and applications of group representation theory.

Here you can find a list of my publications, including my peer-reviewed research articles, technical reports, conference proceedings, and abstracts. Below you can also find my technical notes, which I have written over the years as I entered new areas of research or just followed my own curiosity in various areas.

Publications

Research articles in peer-reviewed journals

[1] Alen Alexanderian, Noemi Petra, Georg Stadler, and Omar Ghattas. A fast and scalable method for A-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems. In revision. 2015. [ arXiv ]
[2] Alen Alexanderian, Philip Gloor, Omar Ghattas. On Bayesian A- and D-optimal experimental designs in infinite dimensions. Accepted for publication in Bayesian Analysis. 2015. [ arXiv ]
[3] Alen Alexanderian, Noemi Petra, Georg Stadler, and Omar Ghattas. A-Optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized $\ell_0$-sparsification. SIAM Journal on Scientific Computing. 36(5). 2014. [ published version  | preprint ]
[4] Alen Alexanderian, Francesco Rizzi, Muruhan Rathinam, Olivier Le Maître, and Omar M. Knio. Preconditioned bayesian regression for stochastic chemical kinetics. Journal of Scientific Computing, 58(3):592-626, 2014. [ bib  |  published version  |  preprint ]
[5] Alen Alexanderian. On spectral methods for variance based sensitivity analysis. Probability Surveys, Volume 10 (2013). [ preprint  |  published version ]
[6] Ihab Sraj, Mohamed Iskandarani, Ashwanth Srinivasan, Carlisle Thacker, Justin Winokur, Alen Alexanderian, Chiaying Lee, Shuyi Chen, and Omar M Knio. Bayesian Inference of Dependence of Drag Coefficient on Wind Speed using AXBT data from Typhoon Fanapi. Monthly Weather Review, 141(7):2347-2367, 2013. [ bib  |  published version ]
[7] Alen Alexanderian, Justin Winokur, Ihab Sraj, Ashwanth Srinivasan, Mohamed Iskandarani, William C. Thacker, and Omar M. Knio. Global sensitivity analysis in an ocean general circulation model: A sparse spectral projection approach. Computational Geosciences, 16(3):757-778, 2012. [ bib  |  published version  |  reprint ]
[8] Maher Salloum, Alen Alexanderian, Olivier Le Maître, Habib N. Najm, and Omar M. Knio. Simplified CSP analysis of a stiff stochastic ODE system. Computer Methods in Applied Mechanics and Engineering. 217-220:121–138, 2012. [ bib  |  published version  |  reprint ]
[9] Alen Alexanderian, Olivier Le Maître, Habib Najm, Mohamed Iskandarani, and Omar Knio. Multiscale stochastic preconditioners in non-intrusive spectral projection. Journal of Scientific Computing, 50:306-340, 2012. [ bib  |  published version  |  preprint ]
[10] Alen Alexanderian, Matthias K. Gobbert, K. Renee Fister, Holly Gaff, Suzanne Lenhart, and Elsa Schaefer. An age-structured model for the spread of epidemic cholera: Analysis and simulation. Nonlinear Analysis: Real World Applications, 12(6):3483-3498, 2011. [ bib  |  published version  |  preprint ]
[11] Alen Alexanderian, Muruhan Rathinam, and Rouben Rostamian. Homogenization, symmetry, and periodization in diffusive random media. Acta Mathematica Scientia, 32(1):129-154, 2012. [ bib  |  preprint ]
[12] Alen Alexanderian, Muruhan Rathinam, and Rouben Rostamian. Irreducibility of symmetry groups implies isotropy. Journal of Elasticity, 102(2), 2011. [ bib  |  published version  |  preprint ]
[13] Daniel Mueller, George Dimitoglou, Benjamin Caplins, Juan Pablo Garcia Ortiz, Benjamin Wamsler, Keith Hughitt, Alen Alexanderian, Jack Ireland, Desmond Amadigwe, and Bernhard Fleck. Jhelioviewer - visualizing large sets of solar images using jpeg 2000. Computing in Science & Engineering, 11(5):38-47, 2009. [ bib  |  reprint ]

Educational/expository articles in peer-reviewed journals

[14] Alen Alexanderian. A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions. Rocky Mountain Journal of Mathematics. Accepted. 2014. [ arXiv ]

PhD Thesis

[15] Alen Alexanderian. Random composite media: Homogenization, modeling, simulation, and material symmetry. PhD Thesis. University of Maryland, Baltimore County. Available from: http://www.proquest.com/, Publication Number: AAT 3422788., 2010.

Technical reports and conference proceedings

[16] Habib Najm, Bert Debusschere, Michael Eldred, Cosmin Safta, John Jakeman, David Higdon, James Gattiker, Roger Ghanem, Omar Knio, Alen Alexanderian, Youssef M. Marzouk, Tarek A. El Moselhy, Jinglai Li, Patrick R. Conrad, Tan Bui-Thanh, Omar Ghattas, James Martin, Robert Moser, Ernesto Prudencio, and Georg Stadler. Quantification of uncertainty in extreme scale computations (QUEST). In DOE Exascale Research Conference, 2012. [ bib ]
[17] Daniel Mueller, George Dimitoglou, Alen Alexanderian Juan Pablo Garcia Ortiz,Ludwig Schmidt,Vincent K. Hughitt,Jack Ireland, and Bernhard Fleck. A Novel Approach to Discovery and Image Access in the Petabyte Age. American Geophysical Union, Fall Meeting 2009.
[18] Vincent K. Hughitt, Jack Ireland, Daniel Mueller, George Dimitoglou, Juan Pablo Garcia Ortiz, Ludwig Schmidt, Benjamin Wamsler, Jaclyn Beck, Alen Alexanderian, and Bernhard Fleck. Helioviewer.org: Browsing Very Large Image Archives Online Using JPEG 2000. American Geophysical Union, Fall Meeting 2009.
[19] Alen Agheksanterian and Matthias K. Gobbert. Modeling the spread of epidemic cholera: an age-structured model. Technical Report number TR2007­9, Department of Mathematics and Statistics, University of Maryland, Baltimore County, 2007.
[20] Alen Agheksanderian and George Dimitoglou. Algorithms paradigms and case studies as a problem-solving methodology. In ASEE Mid-Atlantic Section Spring 2005 Conference, Fairleigh Dickinson University Teaneck, NJ, April 2005.

This file was generated by bibtex2html 1.96.

Technical notes

Since my graduate students days, when doing research or studying a specific topic, I sometimes create detailed notes which may become useful later. These notes mostly aim to provide a clear discussion of a single topic or a collection of results in a self-contained fashion; though they occasionally contain new observations or small extensions of known results which I either needed in my work, or just happened to notice. Whenever I have the time, or happen to revisit a note for one reason or another, I may update them as needed. I place some of these notes here in case others may find them helpful also. Please email me should there be any questions or comments regarding these, and I would appreciate any suggestions to make these notes better.

    Functional analysis:

  • Rellich's Theorem and some of its applications [download pdf].
  • Groups of linear operators on Banach spaces [download pdf].
  • A brief note on tensor products of Hilbert spaces [download pdf].
  • Optimization in infinite-dimensional Hilbert spaces [download pdf].
  • On compact operators [download pdf].

    Probability, stochastic processes, and applications :

  • Gaussian Hilbert Spaces and Homogeneous Chaos: From theory to applications. [download pdf].
  • A brief note on the Karhunen-Loève expansion [download pdf].
  • Spectral representation of a stochastic matrix [download pdf].
  • Some notes on asymptotic theory in probability [download pdf].
  • A brief note on stochastic homogenization in 1D [download pdf].

    Analysis:

  • Some notes on Riemann-Lebesgue lemma [download pdf].
  • On continuous dependence of roots of polynomials on coefficients [download pdf].
  • On non-existence of a Lebesgue-like measure in infinite-dimension [download pdf].

    Algebra:

  • A basic note on group representations and Schur’s lemma [download pdf].
  • Some commutation theorems in finite-dimensional vector spaces [download pdf].
  • Matrix Lie groups and their Lie algebras [download pdf].

    Matrix Analysis:

  • Dependence of simple eigenpairs to differentiable perturbations [download pdf].
  • A basic note on iterative matrix inversion [download pdf].

    Linear complementarity systems:

  • On Stability of linear complementarity systems [download pdf].