About

My name is Sean Reiter. I am a Courant Instructor with the Courant Institute of Mathematical Sciences, New York University. There, I am working in the research group of Dr. Benjamin Peherstorfer.

Prior to moving to New York University, I obtained my doctoral degree in mathematics from Virginia Tech in Blacksburg, Virginia, under the supervision of Dr. Mark Embree and Dr. Serkan Gugercin.

I am an applied mathematician. My research focuses on theoretical and computational aspects of numerical method development for large-scale and structured dynamical systems. Dynamical systems are mathematical models of real-world phenomena that change their behavior over time. They are widely used as computational tools for understanding and making reliable predictions about physical systems.

To capture the underlying behavior accurately, such models are often large, requiring many degrees of freedom and becoming expensive to evaluate. Much of my work concerns system approximation, or model reduction: replacing a large-scale, expensive-to-evaluate system with a smaller, cheaper-to-evaluate surrogate that faithfully reproduces the behavior of the original. This is possible because such systems, despite their size, frequently evolve along low-dimensional structures that can be identified and exploited. Related threads of my work address data-driven modeling — the construction of surrogate models directly from measured data — and state estimation, the problem of reconstructing a system's internal state from limited observations. I am interested in classical approaches to these problems, grounded in systems and control theory, as well as those based on modern machine learning tools. The input-to-output frequency response of numerous types of dynamical systems can be understood through rational functions. To this end, I am interested in computational methods for rational function approximation, with a specific focus on algorithms for best $\mathcal{L}_{2}$ approximation.

The central themes of my research are systems and control theory, numerical linear algebra, approximation theory, and scientific machine learning.

I am also committed to reproducibility in the computational sciences. Each of my written works below is accompanied by a link to a supplementary software package containing the code and data that can be used to reproduce the results in the accompanying manuscript.

Experience & Education

Professional Experience

Courant Instructor Courant Institute of Mathematical Sciences, New York University New York, NY August 2025 – Present
Graduate Research and Teaching Assistant Department of Mathematics, Virginia Tech Blacksburg, VA January 2019 – May 2025
Givens Associate MCS Division, Argonne National Laboratory Lemont, IL June – August 2022, 2023

Education

Ph.D. in Mathematics Virginia Tech Advised by Dr. Mark Embree and Dr. Serkan Gugercin
Dissertation: Dimension Reduction in Structured Dynamical Systems: Optimal-$\mathcal{H}_{2}$ Approximation, Data-Driven Balancing, and Real-Time Monitoring.
Blacksburg, VA May 2025
M.S. in Mathematics Virginia Tech Advised by Dr. Mark Embree and Dr. Serkan Gugercin
Thesis: On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems
Blacksburg, VA December 2021
B.S. in Mathematics Virginia Tech In Honors, Minor in Chemistry, Summa Cum Laude Blacksburg, VA May 2018

Publications

Journal Articles

  • [J4] Reiter, S., and Werner, S. W. R. (2026). Data-driven balanced truncation for second-order systems with generalized proportional damping. SIAM Journal on Scientific Computing, 48(3):C526–C552. 10.1137/25M1768217
  • [J3] Reiter, S., Pontes Duff, I., Gosea, I. V., and Gugercin, S. (2026). $H_{2}$ Optimal Model Reduction of Linear Systems with Multiple Quadratic Outputs. IEEE Transactions on Automatic Control, 71(5):3168–3183. 10.1109/TAC.2025.3636441
  • [J2] Reiter, S., Gosea, I. V., and Gugercin, S. (2025). Generalizations of data-driven balancing: What to sample for different balancing-based reduced models. Automatica, 182:112518. 10.1016/j.automatica.2025.112518
  • [J1] Reiter, S., Damm, T., Embree, M., and Gugercin, S. (2024). On the balanced truncation error bound and sign parameters from arrowhead realizations. Advances in Computational Mathematics, 50:10. 10.1007/s10444-024-10105-y
    Preprint

Conference Proceedings

  • [C1] Reiter, S., and Werner, S. W. R. (2025). Interpolatory model reduction of dynamical systems with root mean squared error. IFAC-PapersOnLine, 59(1):385–390. 10.1016/j.ifacol.2025.03.066

Accepted

  • [A3] Ackermann, M. S., Reiter, S., and Trefethen, L. N. (2026). $L^{2}$ and $L^{\infty}$ rational approximation on the unit disk. Research in the Mathematical Sciences (accepted). arXiv:2512.23357
  • [A2] Reiter, S., Embree, M., Gugercin, S., and Kekatos, V. (2026). Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection. IEEE Transactions on Power Systems (accepted). 10.1109/TPWRS.2026.3707037
  • [A1] Reiter, S., Gosea, I. V., Pontes Duff, I., and Gugercin, S. (2026). $\mathcal{H}_{2}$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation. SIAM Journal on Matrix Analysis and Applications (accepted). arXiv:2505.03057

Submitted (arXiv Preprints)

  • [P1] Reiter, S., and Werner, S. W. R. (2026). Symmetric Hermite quadrature-based balanced truncation for learning linear dynamical systems from derivative data. arXiv preprint arXiv:2606.00298. 10.48550/arXiv.2606.00298

Theses

  • [D] Reiter, S. J. (2025). Dimension Reduction in Structured Dynamical Systems: Optimal-$\mathcal{H}_{2}$ Approximation, Data-Driven Balancing, and Real-Time Monitoring. Ph.D. dissertation, Virginia Polytechnic Institute and State University. hdl:10919/134223
  • [M] Reiter, S. J. (2022). On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems. M.S. thesis, Virginia Polytechnic Institute and State University. hdl:10919/107999

Teaching

I have a strong commitment to mathematics education at both the undergraduate and graduate levels. My teaching statement (as of August 2025) describes my philosophy and approach in detail.

Instructor of Record MATH-UA 4424: Numerical Analysis New York University, New York NY Spring 2026
Instructor of Record MATH-UA 352: Numerical Analysis New York University, New York NY Fall 2025
Graduate Teaching Assistant MATH 4864: Computational Modeling and Data Analytics Capstone Virginia Tech, Blacksburg VA Fall 2024
Graduate Instructor of Record MATH 2534: Intro to Discrete Math Virginia Tech, Blacksburg VA Fall 2023
Graduate Instructor of Record CMDA 1634: Discovering Computational Modeling and Data Analytics Virginia Tech, Blacksburg VA Fall 2022
Graduate Instructor of Record MATH 1225: Calculus of a Single Variable Virginia Tech, Blacksburg VA Fall 2021
Graduate Teaching Assistant CMDA 1984: First-year Experience Virginia Tech, Blacksburg VA Fall 2019, 2020
Urban Teachers Resident Teacher College and Career Readiness Math New Era Academy, Baltimore MD Fall 2018

Talks & Presentations

Conference & Oral Presentations

The Loewner Framework Beyond Linear Outputs 27th Conference of the International Linear Algebra Society, YMMOR 2026 Blacksburg, VA May 26 – 29, 2026
The Loewner Framework Beyond Linear Outputs Young Mathematicians in Model Order Reduction (YMMOR) Conference 2026 Blacksburg, VA May 18 – 22, 2026
Optimal-$\mathcal{H}_{2}$ approximation of linear quadratic output systems by multivariate rational interpolation Joint Mathematics Meeting 2026 Washington, D.C. Jan 4 – 7, 2026
$\mathcal{H}_{2}$-optimal model reduction by multivariate rational interpolation Challenges, Opportunities, and New Horizons in Rational Approximation Banff, Canada Apr 6 – 11, 2025
Interpolatory model reduction of dynamical systems with root mean squared error MATHMOD 2025, 11th Vienna International Conference on Mathematical Modeling Vienna, Austria Feb 19 – 21, 2025
Interpolatory $\mathcal{H}_{2}$ optimal model reduction of linear systems with quadratic outputs Model Reduction and Surrogate Modeling (MORe24) La Jolla, CA Sep 9 – 13, 2024
Generalizations of data-driven balancing: what to sample for different Riccati equation-based variants SIAM Conference on Applied Linear Algebra Paris, France May 13 – 17, 2024
$\mathcal{H}_{2}$-optimal model reduction of linear systems with quadratic outputs Young Mathematicians in Model Order Reduction (YMMOR) Conference 2024 Stuttgart, Germany March 4 – 8, 2024
Generalizations of data-driven balancing: What do you need to sample for different balancing-based reduced models? Mid-Atlantic Numerical Analysis Day Philadelphia, PA November 10, 2023
Interpolatory Matrix Approximations for Pilot Bus Selection and Disturbance Detection 2023 Algorithms for Threat Detection PI Workshop Fairfax, VA October 10 – 12, 2023
Interpolation-based $\mathcal{H}_{2}$-optimal model reduction of systems with quadratic outputs Nonlinear Model Reduction for Control Blacksburg, VA May 22 – 26, 2023
Structure-preserving Extensions of the QuadBT Framework SIAM Southeastern Atlantic Section Annual Meeting Blacksburg, VA March 25 – 26, 2023
Power System Event Localization via DEIM SIAM Conference on Computational Science and Engineering Amsterdam, The Netherlands February 26 – March 3, 2023

Poster Presentations

Interpolatory Approximations for PMU Data: Dimension Reduction, Pilot Bus Selection, and Event Detection 2024 AMPS/ATD PI Workshop Alexandria, VA October 7 – 9, 2024
On Balanced Truncation Error Bound and Sign Parameters Model Reduction and Surrogate Modeling (MORe22) 2022 Berlin, Germany September 19 – 23, 2022
On the Tightness of the Balanced Truncation Error Bound, with an Application to Arrowhead Systems Southeast Control Conference Blacksburg, VA November 29 – 30, 2021
A Tight Balanced Truncation Error Bound for a Certain Class of SISO Systems SIAM Conference on Computational Science and Engineering Virtual March 1 – 5, 2021

Conference Organization

Minisymposium Organizer “Numerical Linear Algebra Tools for Model Order Reduction”, 27th Conference of the International Linear Algebra Society, ILAS 2026 Co-organizer: Mattia Mannuci (Karlsruhe Institute of Technology) Blacksburg, VA May 2026
Local Organizing Committee Member Young Mathematicians in Model Order Reduction (YMMOR) 2026 Blacksburg, VA May 2026
Minisymposium Organizer “Recent Advances in Model Order Reduction and Data-driven Modeling”, MATHMOD 2025, 11th Vienna International Conference on Mathematical Modeling Co-organizers: Hendrik Kleikamp (University of Münster), Steffen W. R. Werner (Virginia Tech), Jens Saak (MPI Magdeburg) Vienna, Austria February 2025
Organizing Committee Member Young Mathematicians in Model Order Reduction (YMMOR)