Alejandro N. Diaz

I am a Ph.D. candidate in the Department of Computational Applied Mathematics and Operations Research (CMOR) (formerly Computational and Applied Mathematics (CAAM)) at Rice University in Houston, TX. My advisor is Prof. Matthias Heinkenschloss and my research focuses on integrating neural network-based reduced-order models with domain decomposition. I am a National Defense Science and Engineering Graduate (NDSEG) Fellow sponsored by the Air Force Office of Scientific Research. I also maintain a collaboration with Lawrence Livermore National Laboratory (LLNL). Here is my CV.

Contact Info

• Office: Duncan Hall 2108, Rice University
• Email: and5@rice.edu
• LinkedIn: www.linkedin.com/in/alejandro-diaz-855152226

Education

• Ph.D., Computational and Applied Mathematics, Rice University, May 2024 (expected)
• M.A., Computational and Applied Mathematics, Rice University, May 2022
• B.S., Mathematics with Departmental Honors, Minor in Physics, University of Maryland, College Park, May 2019

Research Interests

• Reduced-order modeling
• Surrogate modeling
• Dimension reduction
• Scientific machine learning
• Scientific computing

Research and Work Experience

• Graduate Researcher - Department of Computational Applied Mathematics and Operations Research at Rice University, 2020-present
  • Interpolatory and nonlinear manifold reduced order models with domain decomposition (advisor: Prof. Matthias Heinkenschloss)
• Data Science Intern - Microsoft, Summer 2023
  • Implemented differential privacy auditing algorithm with 170x speedup
• Defense Science and Technology Internship (DSTI) - Graduate Summer Student at Lawrence Livermore National Laboratory (LLNL), Summer 2022
  • Domain-decomposition nonlinear manifold reduced order model using sparse autoencoders (advisor: Youngsoo Choi)
• UCLA Applied Mathematics REU, University of California, Los Angeles, Summer 2018
  • Data-driven approaches for microfluidic device design (advisors: Marcus Roper, Hangjie Ji)
• SMALL NSF REU, Williams College, Summer 2017
  • Tetrahedral tilings, isoperimetric surfaces (advisor: Frank Morgan)
• Summer Student Theoretical Physics Research Session, University of Maryland, College Park, Summer 2016
  • Tensor computations in supersymmetry (advisor: S. James Gates Jr.)

Publications and Preprints

• A. N. Diaz, Y. Choi, M. Heinkenschloss, A fast and accurate domain-decomposition nonlinear manifold reduced order model. Computer Methods in Applied Mechanics and Engineering, Vol. 425, pages 116943 (2024). https://doi.org/10.1016/j.cma.2024.116943.

• A. N. Diaz, I. V. Gosea, M. Heinkenschloss, A. C. Antoulas., Interpolation-based model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs. Adv Comput Math 49, 95 (2023). https://doi.org/10.1007/s10444-023-10096-2

• A. N. Diaz, Y. Choi, M. Heinkenschloss. Nonlinear-manifold reduced order models with domain decomposition. Machine Learning and the Physical Sciences Workshop, NeurIPS (2023). https://ml4physicalsciences.github.io/2023/files/NeurIPS_ML4PS_2023_30.pdf

• A. N. Diaz, M. Heinkenschloss Towards Data-Driven Model Reduction of the Navier-Stokes Equations using the Loewner Framework. Active Flow and Combustion Control 2021, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 152. Springer, Cham. https://doi.org/10.1007/978-3-030-90727-3_14

• E. Bongiovanni, A. N. Diaz, A. Kakkar, et al. The Least-Area Tetrahedral Tile of Space. Geom Dedicata 205, 51–93 (2020). https://doi.org/10.1007/s10711-019-00465-x

• E. Bongiovanni, A. N. Diaz, A. Kakkar, N. Sothanaphan Isoperimetry in Surfaces of Revolution with Density. Missouri J. Math. Sci. 30 (2018), no. 2, 150–165. https://doi.org/10.35834/mjms/1544151692

• E. Bongiovanni, L. Di Giosia, A. N. Diaz, et al. (2018). Double Bubbles on the Real Line with Log-Convex Density. Analysis and Geometry in Metric Spaces, 6(1), pp. 64-88. https://doi.org/10.1515/agms-2018-0004

• W. Caldwell, A. N. Diaz, I. Friend, et al., On the Four Dimensional Holoraumy of the 4D, N=1 Complex Linear Supermultiplet, International Journal of Modern Physics A 33 (2018), 1850072. https://doi.org/10.1142/S0217751X18500720

Honors and Awards

• Honorable Mention for Poster Presentation in Mathematics, NDSEG Fellowship Program 4th Annual Conference, Aug. 2023.
• Global Young Scientists Summit 2022 Attendee, Oct. 2021
• National Defense Science and Engineering Graduate Fellowship, Mar. 2021,
  • Sponsoring Agency: Air Force Research Laboratory.
• National Science Foundation Graduate Research Fellowship Program Honorable Mention , Mar. 2021.
• Ken Kennedy Institute 2020/21 BP Graduate Fellowship, Rice University, Dec. 2020.
• Ken Kennedy Institute Computational Science and Engineering Fellowship, Rice University, May 2019.
• Departmental Honors, Department of Mathematics, University of Maryland, College Park, May 2019.
• Strauss Teaching Assistantship, Department of Mathematics, University of Maryland, College Park, Fall 2018 – Spring 2019.
• University Honors Citation, University of Maryland, College Park, Apr. 2018.
• Outstanding Poster, Joint Mathematics Meeting, Jan. 2018.
• Banneker-Key Scholarship, University of Maryland, College Park, May 2015.

Talks and Presentations

• A. N. Diaz, Y. Choi, M. Heinkenschloss. Nonlinear manifold reduced order models with domain decomposition. Poster, Machine Learning and the Physical Sciences Workshop, NeurIPS 2023, 15 Dec. 2023, New Orleans, LA.
• A. N. Diaz, Y. Choi, M. Heinkenschloss. Nonlinear manifold reduced order models with domain decomposition. Poster, Mathematical Opportunities in Digital Twins, 11 Dec. 2023, Fairfax, VA.
• A. N. Diaz, Nonlinear manifold reduced order models with domain decomposition. Presentation, 6th Annual Meeting of the SIAM Texas-Louisiana Section, 4 Nov. 2023, Lafayette, LA.
• A. N. Diaz, Neural network-based reduced-order models with domain decomposition. Seminar, Network, Cyber & Computational Sciences Division at Army Research Laboratory, 25 Oct. 2023, Aberdeen, MD.
• A. N. Diaz, Neural network-based reduced-order models with domain decomposition. Presentation, Research Training Group in Numerical Mathematics and Scientific Computing at Rice University Annual Workshop, 13 Oct. 2023, Houston, TX.
• A. N. Diaz, Nonlinear Manifold Reduced Order Models with Domain Decomposition. Poster presentation, NDSEG Fellowship Program 4th Annual Conference, 1 Aug. 2023, San Antonio, TX.
• A. N. Diaz, A fast and accurate domain-decomposition nonlinear reduced order model using shallow masked autoencoders. Presentation, 2023 SIAM Conference on Computational Science and Engineering (CSE23), 27 Feb. 2023, Amsterdam, The Netherlands.
• A. N. Diaz, A fast and accurate domain-decomposition nonlinear reduced order model using shallow masked autoencoders. Presentation, 5th Annual Meeting of the SIAM Texas-Louisiana Section, 4-6 Nov. 2022, Houston, TX.
• A. N. Diaz, Impact of the Convergence of Series Expansions on Model Reduction of Quadratic-Bilinear Systems. Presentation, 2022 Model Reduction and Surrogate Modeling Conference, 21 Sept. 2022, Berlin, Germany.
• A. N. Diaz Data-Driven Model Reduction using the Loewner Framework. Poster, 2021 Oil and Gas HPC Conference, 5 Mar. 2021, Houston, TX (virtual).
• A. N. Diaz Data-Driven Model Reduction using the Loewner Framework. Presentation, Model Order Reduction for Large-Scale Problems Minisymposium, SIAM Conference on Computational Science and Engineering, 4 Mar. 2021, Fort Worth, TX (virtual).
• A. N. Diaz, A. Kakkar The Least-Area Tetrahedral Tile of Space. Poster, MAA Undergraduate Student Poster Session, Joint Mathematics Meetings, 12 Jan. 2018, San Diego, CA.
• A. N. Diaz Existence and Boundedness of Isoperimetric Regions in Surfaces of Revolution with Density, Informal Geometric Analysis Seminar, 14 Nov. 2017, Math Department, University of Maryland, College Park. Seminar.
• A. N. Diaz The Log-Convex Density Conjecture in Hyperbolic Space. MAA Student Paper Sessions, MathFest. 28 Jul. 2017, Hilton Hotel, Chicago, IL. Student Presentation.

Teaching

• Grader, Department of Computational and Applied Mathematics, Rice University
  • CAAM 336, Fall 2019, Spring 2020
  • CAAM 453/550, Fall 2020
  • CAAM 554, Spring 2021
• Teaching Assistant, Department of Mathematics, University of Maryland, College Park
  • MATH 141, Spring 2019
  • MATH 140, Fall 2018

Service

• SIAM Student Chapter, Rice University
  • President, Aug. 2022 - Aug. 2023
  • Graduate Student Association Representative, Aug. 2021 - Aug. 2022
  • Treasurer, Aug. 2020 - Aug. 2021
• Graduate Student Mentor, Department of Computational and Applied Mathematics, Rice University, Aug. 2021 - Aug. 2022
• Graduate Student Advisory Committee, Rice University, Member, Aug. 2020 - May 2023
• Freshmen Math Mentorship Program, Rice University, Graduate Student Mentor, Aug. 2020 - Dec. 2020