Research profile

My research addresses fundamental mathematical and computational challenges in infinite-dimensional inverse problems governed by partial differential equations (PDEs) and uncertainty quantification (UQ). By integrating tools from mathematical and numerical analysis, operator theory, probability, and statistics, I develop methods for predictive modeling and decision-making in complex physical systems.

Specifically, my current work focuses on advancing the theory and numerical methods for (i) optimal experimental design in infinite-dimensional Bayesian inverse problems, informing how to collect data to optimize the quality of the estimates parameters; (ii) sensitivity analysis of deterministic and Bayesian inverse problems, revealing modeling parameters most influential to inverse problem solution; and (iii) and optimal control of systems governed by PDEs under uncertainty, enabling decision-making under uncertainty. Another major track in my research involves tractable methods for global sensitivity analysis to identify the uncertain parameters most influential to the output of complex mathematical models. My research in this direction builds on tools from variance-based sensitivity analysis, derivative-based methods, and the theory of reproducing kernel Hilbert spaces (RKHS).

Overall, my research is driven by the need to solve challenging application problems in the engineering and sciences. My current work is motivated largely by applications in subsurface flow, heat/mass transport, chemical kinetics, epidemiology, and cardiovascular modeling.

Here you can find a list of my publications, including my peer-reviewed research articles, technical reports, conference proceedings, and abstracts. You can also find my papers in my page Google Scholar page. 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

    Books

    Alen Alexanderian. Computational Inverse Problems Governed by PDEs. In preproduction, SIAM, 2026. Book Website

    Peer-reviewed journal articles

  1. Alen Alexanderian. A primer on the Karhunen-Loève expansion. Submitted. 2026.
  2. Madhusudan Madhavan, Alen Alexanderian, and Arvind Saibaba. FlexTrace: Exchangeable Randomized Trace Estimation for Matrix Functions In review. 2026. [ preprint ]
  3. Troy Larsen and Alen Alexanderian, A new kernel-based index for the global sensitivity analysis of models with correlated inputs. In review. 2026. [ preprint ]
  4. Alen Alexanderian and Steven Maio. Submodularity of the expected information gain in infinite-dimensional linear inverse problems. In review. 2026. [ preprint ]
  5. J. Nicholas Neuberger, Alen Alexanderian, Bart van Bloemen Waanders, and Ahmed Attia. Path-OED for infinite-dimensional Bayesian linear inverse problems governed by PDEs. In review. 2026. [ preprint ]
  6. Madhusudan Madhavan, Alen Alexanderian, Arvind K. Saibaba, Bart van Bloemen Waanders, and Rebekah White. A control-oriented approach to optimal sensor placement. SIAM/ASA Journal on Uncertainty Quantification. Accepted, 2026. [ preprint ]
  7. Joseph Hart, Alen Alexanderian, and Bart van Bloemen Waanders. Preconditioned pseudo-time continuation for parameterized inverse problems. SIAM Journal on Scientific Computing, Accepted. 2026. [ preprint ]
  8. Abhijit Chowdhary, Ahmed Attia, and Alen Alexanderian. Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems. SIAM Journal on Scientific Computing. 2026. [ preprint ]
  9. Lev Kakasenko, Alen Alexanderian, Mohammad Farazmand, and Arvind K. Saibaba. Bridging the Gap Between Deterministic and Probabilistic Approaches to State Estimation. Physica D, 2026. [ preprint ]
  10. Alen Alexanderian, Hugo Diaz, Vishwas Rao and Arvind K. Saibaba. Optimal sensor placement under model uncertainty in the weak-constraint 4D-Var framework. Foundations of Data Science. 2025. [ preprint ]
  11. J. Nicholas Neuberger, Alen Alexanderian, and Bart van Bloemen Waanders. Goal oriented optimal design of infinite-dimensional Bayesian inverse problems using quadratic approximations. Journal of Scientific Computing2025. [ preprint ]
  12. John Darges, Alen Alexanderian, and Pierre Gremaud. Variance-based sensitivity of Bayesian inverse problems to the prior distribution. International Journal for Uncertainty Quantification 2024. [ preprint | journal ]
  13. Abhi Chowdhary, Shanyin Tong, Georg Stadler, and Alen Alexanderian. Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems. International Journal for Uncertainty Quantification, 2023. [ preprint | journal ]
  14. Alen Alexanderian, Ruanui Nicholson, and Noemi Petra. Optimal design of large-scale nonlinear Bayesian inverse problems under model uncertainty. Inverse Problems. 2024. [ preprint | journal ]
  15. John Darges, Alen Alexanderian, Pierre Gremaud. Extreme learning machines for variance-based global sensitivity analysis. International Journal for Uncertainty Quantification. 2024. [ preprint | journal ]
  16. Isaac Sunseri, Alen Alexanderian, Joseph Hart, Bart van Bloemen Waanders. Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems. International Journal for Uncertainty Quantification. 2023. [ preprint | journal ]
  17. Alen Alexanderian, Joseph Hart, and Mason Stevens. A new perspective on parameter study of optimization problems. Applied Mathematics Letters. 2023. [ preprint | journal ]
  18. Mason Stevens, Isaac Sunseri, Alen Alexanderian. Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID–19 modeling. Mathematical Biosciences. 2022. [ journal ]
  19. R.D. White, A. Alexanderian, O. Yousefian, Y. Karbalaeisadegh, A. Kasali, H.T. Banks, M. Talmant, Q. Grimal, Marie Muller, and K. Bekele-Maxwell. Using Ultrasonic Attenuation in Cortical Bone to Infer Distributions on Pore Size. Applied Mathematical Modelling 2022. [ journal ]
  20. Ethan Dudley, Arvind Saibaba, and Alen Alexanderian. Monte carlo estimators for the Schatten p-norm of symmetric positive semidefinite matrices. Electronic Transactions on Numerical Analysis, 55:213-241. 2022. [ preprint | journal ]
  21. Michael Merritt, Alen Alexanderian, and Pierre Gremaud. Global sensitivity analysis of rare event probabilities using subset simulation and polynomial chaos expansions. International Journal for Uncertainty Quantification, Accepted. 2022. [ preprint | journal ]
  22. Helen Cleaves, Alen Alexanderian, and Bilal Saad. Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media. Computational Geosciences, 25(6):2167--2189. 2021. [ preprint | journal ]
  23. Alen Alexanderian, Noemi Petra, Georg Stadler, and Isaac Sunseri. Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know. SIAM/ASA Journal on Uncertainty Quantification, 9(1), 163-184, 2021. [ preprint | journal ]
  24. Alen Alexanderian. Optimal Experimental Design for infinite-dimensional Bayesian Inverse Problems Governed by PDEs: A Review. Inverse Problems. 2021. [ preprint | journal ]
  25. E. Benjamin Randall, Nicholas Z. Randolph, Alen Alexanderian, and Mette S. Olufsen. Global sensitivity analysis informed model reduction and selection applied to a Valsalva maneuver model. Journal of Theoretical Biology 2021. [ preprint | journal ]
  26. Rebekah White, Omid Yousefian, H.T. Banks, Alen Alexanderian, and Marie Muller. Inferring pore radius and density from ultrasonic attenuation using physics-based modeling. The Journal of the Acoustical Society of America, 2021. [ journal ]
  27. Michael Merritt, Alen Alexanderian, and Pierre Gremaud. Multiscale global sensitivity analysis for stochastic chemical systems, SIAM Journal on Multiscale Modeling and Simulation, 2021. [ preprint | journal ]
  28. Isaac Sunseri, Joseph Hart, Bart van Bloemen Waanders, and Alen Alexanderian. Hyper-Differential Sensitivity Analysis for Inverse Problems Constrained by Partial Differential Equations. Inverse Problems, 36(12), 2020. [ preprint | journal ]
  29. Karina Koval, Alen Alexanderian, and Georg Stadler. Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs. Inverse Problems, 36(7), 2020. [ preprint | journal ]
  30. Hayley Guy, Alen Alexanderian, and Meilin Yu. A distributed active subspace method for scalable surrogate modeling of function valued outputs. Journal of Scientific Computing, 85(36), 2020. [ preprint | journal ]
  31. Elizabeth Herman, Alen Alexanderian, and Arvind K. Saibaba. Randomization and reweighted $\ell_1$-minimization for A-optimal design of linear inverse problems. SIAM Journal on Scientific Computing, 42(3), A1714-A1740, 2020. [ preprint | journal ]
  32. Alen Alexanderian, Pierre Gremaud, and Ralph C. Smith. Variance-based sensitivity analysis for time-dependent processes. Reliability Engineering & System Safety, 2020. [ preprint | journal ]
  33. Helen L. Cleaves, Alen Alexanderian, Hayley Guy, Ralph C. Smith, and Meilin Yu. Derivative based global sensitivity analysis for models with high-dimensional inputs and functional outputs. SIAM Journal on Scientific Computing, 41(6), A3524–A3551. 2019. [ preprint | journal ]
  34. Alen Alexanderian, William Reese, Ralph C. Smith, and Meilin Yu. Model input and output dimension reduction using Karhunen-Loève expansions with application to biotransport. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part B: Mechanical Engineering, (5)4:041014, 2019. [ preprint | journal ]
  35. Manav Vohra, Alen Alexanderian, Hayley Guy, Sankaran Mahadevan. Active subspace-based dimension reduction for chemical kinetics applications with epistemic uncertainty. Combustion and Flame. 204:152–161, 2019. [ preprint | journal ]
  36. Arvind Saibaba, Jonathan Bardsley, Andrew Brown, Alen Alexanderian. Efficient marginalization-based MCMC Methods for hierarchical Bayesian inverse problems. SIAM Journal on Uncertainty Quantification, 7(3), 1105--1131, 2019. [ preprint | journal ]
  37. Manav Vohra, Alen Alexanderian, Cosmin Safta, and Sankaran Mahadevan. Sensitivity-driven adaptive construction of reduced-space surrogates. Journal of Scientific Computing, 79(2):1335–1359, 2019. [ preprint | journal ]
  38. Alen Alexanderian and Arvind K. Saibaba. Efficient D-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems. SIAM Journal on Scientific Computing, 40(5):A2956--A2985, 2018. [ preprint | journal ]
  39. Ahmed Attia, Alen Alexanderian, and Arvind K. Saibaba. Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems. Inverse Problems, 34(9). 2018. [ preprint | journal ]
  40. Bilal Saad, Alen Alexanderian, Serge Prudhomme, and Omar Knio. Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach. Applied Mathematical Modelling, 53:584--601. 2018. [ preprint | journal ]
  41. Alen Alexanderian, Noemi Petra, Georg Stadler, and Omar Ghattas. Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations. SIAM Journal on Uncertainty Quantification, 5(1):1166–1192. 2017. [ preprint | journal ]
  42. Joseph Hart, Alen Alexanderian, and Pierre Gremaud. Efficient computation of Sobol indices for stochastic models. SIAM Jounral on Scientific Computing. 39(4). 2017. [ preprint |  journal ]
  43. Alen Alexanderian, Liang Zhu, Maher Salloum, Ronghui Ma, and Meilin Yu. Investigation of biotransport in a tumor with uncertain material properties using a non-intrusive spectral uncertainty quantification method. ASME Journal of Biomechanical Engineering, In press. 2017. [ preprint |  journal ]
  44. Arvind K. Saibaba, Alen Alexanderian, and Ilse Ipsen. Randomized matrix-free trace and log-Determinant estimators. Numerische Mathematik, Numerische Mathematik. 137(2). 2017. [ preprint | journal ]
  45. Ben Crestel, Alen Alexanderian, Georg Stadler, and Omar Ghattas. A-optimal source encoding for inverse problems, with applications to seismic inversion. Inverse Problems, In press. 2017. [ preprint | journal ]
  46. Craig Michoski, Alen Alexanderian, Charles Paillet, Clint Dawson, and Ethan Kubatko. Stability of Nonlinear Convection–Diffusion–Reaction Systems in Discontinuous Galerkin Methods. Journal of Scientific Computing. 70(2):516-550. 2017. [ journal ]
  47. 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. SIAM Journal on Scientific Computing, 38(1):A243-A272. 2016. [ preprint | journal ]
  48. Alen Alexanderian, Philip Gloor, Omar Ghattas. On Bayesian A- and D-optimal experimental designs in infinite dimensions. Bayesian Analysis. 2016.. [ preprint | journal ]
  49. Alen Alexanderian. A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions. Rocky Mountain Journal of Mathematics. 2015. [  preprint | journal  ]
  50. 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. [ preprint | journal ]
  51. 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. [ preprint | journal ]
  52. Alen Alexanderian. On spectral methods for variance based sensitivity analysis. Probability Surveys, Volume 10 (2013). [ preprint | journal ]
  53. 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. [ journal ]
  54. 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. [ reprint | journal ]
  55. 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. [  reprint | journal ]
  56. 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. [ preprint | journal ]
  57. 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. [ preprint | journal ]
  58. Alen Alexanderian, Muruhan Rathinam, and Rouben Rostamian. Homogenization, symmetry, and periodization in diffusive random media. Acta Mathematica Scientia, 32(1):129-154, 2012. [ preprint | journal ]
  59. Alen Alexanderian, Muruhan Rathinam, and Rouben Rostamian. Irreducibility of symmetry groups implies isotropy. Journal of Elasticity, 102(2), 2011. [ preprint | journal ]
  60. 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. [ reprint ]

    Peer-reviewed proceedings

  61. Nick Neuberger, Bart Van Bloemen Waanders, and Alen Alexanderian. Computational aspects of optimal experimental design for large-scale Bayesian linear inverse problems. Computer Science Research Institute Summer Proceedings 2023, Sandia National Laboratories, 2023. [ preprint ]
  62. White, R.D., Yousefian, O., Alexanderian, A., and Muller, M. Modeling Frequency Dependent Ultrasound Attenuation in Cortical Bone: Solving Direct and Inverse Problems. In 2020 IEEE International Ultrasonics Symposium (IUS) (pp. 1-3). IEEE.
  63. Alen Alexanderian, William Reese, Ralph C. Smith, and Meilin Yu. Efficient uncertainty quantification for biotransport in tumors with uncertain material properties. (SB3C2017). 2018.
  64. Miao Lu, A. Alexanderian, Maher Salloum, Liang Zhu, Ronghui Ma, and M. L. Yu. Stochastic modeling of biotransport in a tumor with uncertain material properties. Summer Biomechanics, Bioengineering and Biotransport Conference. (SB3C2017). 2017.

    PhD Thesis

  65. 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 non-peer-reviewed proceedings

  66. Stevan Maio and Alen Alexanderian On submodularity of the expected information gain. [arXiv].
  67. Isaac Sunseri, and Alen Alexanderian On marginals of Gaussian random vectors. 2018. [ download pdf ]
  68. Alen Alexanderian. A brief note on the Karhunen-Loève expansion. 2016. [ arXiv ]
  69. 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.
  70. 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.
  71. 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.
  72. 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.
  73. 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.

Technical Notes

Since my graduate students days, when doing research or studying a specific topic, I sometimes create detailed notes that I can refer to later. These notes mostly aim to provide a clear discussion of a single topic or a collection of results in a self-contained manner; though they occasionally contain new observations, proofs, or minor extensions of known results which I either needed in my work, or just happened to notice. Since coming to NC State, I have also augmented this section with notes coming from my teaching and short notes I sometimes write to clarify issues that came up in conversations with graduate students or colleagues.

From time to time, I revisit individual notes and 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.

    Numerical Analysis:

  • Dependence of simple eigenpairs to differentiable perturbations [download pdf].
  • A basic note on iterative matrix inversion [download pdf].
  • A basic note on convergence of quadrature formulas [download pdf].
  • Notes on Gaussian quadrature [download pdf].
  • A brief note on sparse grids [download pdf].
  • Notes on linear multistep methods [download pdf].
  • A basic note on QR factorization [download pdf].
  • A brief note on Gershgorin's Theorem [download pdf].
  • Error in numerical differentiation [download pdf].

    Inverse Problems, Optimization, and Uncertainty Quantification

  • Optimization in infinite-dimensional Hilbert spaces [download pdf].
  • Gaussian Hilbert Spaces and Homogeneous Chaos: From theory to applications. [download pdf].
  • A brief note on the Karhunen-Loève expansion [ arXiv ].
  • Computing gradients and Hessians using the adjoint method [download pdf].
  • Sensitivity of estimating parameters in an SIR epidemic model to observed data at different times [download pdf].
  • Mean and variance of quadratic functionals of Gaussian random vectors [ download pdf ].
  • A brief note on Bayesian D-optimality criterion [ arXiv ].
  • On Bayes risk of the posterior mean in linear inverse problems [arXiv].
  • Why can't we define PDFs in infinite dimensions? [download pdf].
  • Eigenvalue sensitivity analysis for a class of implicitly defined matrices. [download pdf].
  • A brief note on approximate optimization of submodular functions. [download pdf].

    Analysis:

  • Rellich's Theorem and some of its applications [download pdf].
  • Groups of linear operators on Banach spaces [download pdf].
  • Some notes on Riemann-Lebesgue lemma [download pdf].
  • On continuous dependence of roots of polynomials on coefficients [download pdf].
  • A brief note on tensor products of Hilbert spaces [download pdf].
  • On compact operators [download pdf].
  • Approximate inversion of compact perturbations of identity. [download pdf].
  • A brief note on reproducing kernel Hilbert spaces. [download pdf].

    Probability, stochastic processes, and applications :

  • Some notes on asymptotic theory in probability [download pdf].
  • A brief note on stochastic homogenization in 1D [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].

    Misc:

  • On Stability of linear complementarity systems [download pdf].
  • A basic note on single phase flow in porous media [download pdf].
  • Disease modeling with social distancing: application to COVID-19 [ download pdf ].