About Me
I am a Peter O’Donnell Jr. Postdoctoral Fellow at the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin, and concurrently a Cosmic AI Fellow at the NSF–Simons AI Institute for the Study of Cosmic Origins. My postdoctoral mentor is Prof. George Biros, and within Cosmic AI, I am part of the Accelerated Universe working group led by Prof. Stella Offner.
I earned my Ph.D. in Applied Mathematics from the University of Notre Dame under the guidance of Prof. Guosheng Fu. My doctoral research focused on developing high-order variational methods for computing gradient flows and barycenters in generalized Wasserstein spaces. I was co-advised by Prof. Zhiliang Xu.
During my graduate studies, I completed three internships: one at Sandia National Laboratories and two at MathWorks. At Sandia, I worked within the Computer Science Research Institute under Dr. Irina Tezaur and Dr. Anthony Gruber on structure-preserving reduced order models, contributing to the Department of Energy funded M2dt initiative. At MathWorks, I interned with the MATLAB Math & PDE and Simscape Language & Execution teams, where I contributed to the development and enhancement of core features—two of which were included in the release notes of MATLAB R2024a.
Research Interests
- Reduced Order Modeling
- Finite Element Analysis
- Mean-Field Control
- Optimal Transport
Education
- PhD Applied Mathematics (University of Notre Dame ‘25).
- BS Pure Mathematics (University of Texas at Austin ‘19).
- BS Computational Physics (University of Texas at Austin ‘19).
Experience
| Tenure | Institute/Company | Division/Department | Position | Mentor/Manager | PI |
|---|---|---|---|---|---|
| June 2024–May 2025 | Sandia National Laboratories | Computational Mathematics Computer Science Research Institute | Year-round intern | Anthony Gruber | Irina Tezaur |
| February 2021–May 2025 | University of Notre Dame | Applied and Computational Mathematics and Statistics | Research and Teaching Assistant | Guosheng Fu | Guosheng Fu |
| May 2023–August 2023 | MathWorks | MATLAB Data Analysis MATLAB Math and PDE | Summer Intern | Cosmin Ionita | Cosmin Ionita |
| May 2022–August 2022 | MathWorks | Simscape Language and Execution | Summer Intern | Jacek Kierzenka | Peng Cheng |
Awards
| Year | Award | Awarded By | Awarded For |
|---|---|---|---|
| 2025 | The Peter O’Donnell Jr. Fellowship | The Oden Institute for Computational Engineering and Sciences | Postdoctoral research |
| 2025 | Cosmic AI Fellowship | NSF–Simons AI Institute for the Study of Cosmic Origins | Postdoctoral research |
| 2024 | Student Travel Award | Society for Industrial and Applied Mathematics | Travel support for CSE25 |
| 2024 | Student Travel Award | Society for Industrial and Applied Mathematics | Travel support for MDS24 |
| 2019 | magna cum laude | The University of Texas at Austin | High academic achievement in Mathematics |
| 2019 | cum laude | The University of Texas at Austin | High academic achievement in Physics |
| 2018 | Departmental Scholarship | Department of Physics, The University of Texas at Austin | Academic excellence |
| 2018 | Robert E. Boyer Endowed Presidential Scholarship for Natural Sciences | College of Natural Sciences, The University of Texas at Austin | Academic excellence and leadership potential in the natural sciences |
| 2018 | Phi Beta Kappa Junior Year Inductee | Phi Beta Kappa, Alpha of Texas, The University of Texas at Austin | Being in the top 2% of the graduating class. |
| 2017 | John W. Cox Endowment for Advanced Studies in Astronomy | Department of Astronomy, The University of Texas at Austin | Undertaking an advanced summer research project in astronomy |
Publications
Dissertation
- A. Vijaywargiya, High-Order Computation of Gradient Flows and Barycenters in Generalized Wasserstein Spaces, Dataset, University of Notre Dame. Available at https://doi.org/10.7274/28766591.v1
Papers
- A. Vijaywargiya, G. Fu, W. Pazner, and W. Li, High order spacetime computation of Wasserstein gradient flows using a mean field control approach, in preparation, 2025.
- A. Vijaywargiya, S. McQuarrie, and A. Gruber, Tensor parametric Hamiltonian operator inference, arXiv preprint arXiv:2502.10888, 2025. Available at: https://arxiv.org/abs/2502.10888.
- A. Vijaywargiya, G. Fu, S. Osher, and W. Li, Efficient computation of mean field control based barycenters from reaction-diffusion systems, J. Comput. Phys., 2025, 113772. https://doi.org/10.1016/j.jcp.2025.113772.
- A. Vijaywargiya, S. McQuarrie, and A. Gruber, Tensor Parametric Operator Inference with Hamiltonian Structure, in Computer Science Research Institute Summer Proceedings 2024, M. B. P. Adams, T. A. Casey, and B. W. Reuter, eds., Technical Report SAND2024-16688O, Sandia National Laboratories, 2024, pp. 172–194.
- A. Vijaywargiya and G. Fu, Two finite element approaches for the porous medium equation that are positivity preserving and energy stable, J. Sci. Comput., 100 (2024), 86. https://doi.org/10.1007/s10915-024-02642-x.
Presentations
Talks
- A. Vijaywargiya, Tensor parametric operator inference with Hamiltonian structure, presented (by co-author A. Gruber) at the Mini-symposium on Structure-Preserving Model Order Reduction for Large-Scale Systems, SIAM Conference on Computational Science and Engineering (CSE25), Fort Worth, TX, March 6, 2025.
- A. Vijaywargiya, High-order computation of gradient flows and generalized barycenters in the Wasserstein-2 space, presented at the MCS/LANS Seminar, Argonne National Laboratory, Argonne, IL, December 17, 2024.
- A. Vijaywargiya, High-order computation of Wasserstein barycenters with reaction-diffusion, presented at the 2024 SIAM Great Lakes Sectional Meeting, Purdue University Northwest, Hammond, IN, October 12, 2024.
- A. Vijaywargiya, Two finite element approaches for the porous medium equation that are positivity preserving and energy stable, presented at the AMS Special Session on Recent Advances in Finite Element Methods: Theory and Applications I, University of Cincinnati, Cincinnati, OH, April 15, 2023.
- A. Vijaywargiya, Isometries, gluing, and tessellating polygons, presented at the DRP Project Symposium, University of Texas at Austin, Austin, TX, November 30, 2017.
- A. Vijaywargiya, Modeling the spectra of exoplanetary atmospheres in the near-infrared region, presented at the Texas Astronomy Undergraduate Research Symposium, Rice University, Houston, TX, October 13, 2017.
Posters
- A. Vijaywargiya, Tensor parametric Hamiltonian operator inference, presented at the Computational Learning for Model Reduction Workshop, ICERM, Providence, RI, January 7, 2025.
- A. Vijaywargiya, Tensor parametric operator inference with structure information, presented at the NM SIP Intern Symposium, Sandia National Laboratories, National Museum of Nuclear Science & History, Albuquerque, NM, August 1, 2024.
- A. Vijaywargiya, Efficient computation of higher-dimensional mean field control-based barycenters from reaction-diffusion systems, presented at PDEs and Geometry: Numerical Aspects workshop, Brown University, Providence, RI, March 13, 2024.
- A. Vijaywargiya, Efficient computation of higher-dimensional Wasserstein barycenters with reaction-diffusion dynamics via mean field control and high-order finite elements, presented at the COSE Research Horizons Symposium, University of Notre Dame, Notre Dame, IN, December 8, 2023.
Lightning Talks
- A. Vijaywargiya, High-order computation of MFC barycenters with MFEM, presented at the MFEM Community Workshop, Lawrence Livermore National Laboratory (LLNL) + Virtual, October 22, 2024.
- A. Vijaywargiya, Tensor parametric operator inference with structure information, presented at CSRI Lightning Talks, Sandia National Laboratories, Albuquerque, NM, July 31, 2024.
News
- May 17, 2025: I was honored to be hooded by my Ph.D. advisor and officially received my doctoral degree during the Notre Dame Graduate School Commencement Ceremony.
- April 04, 2025: I successfully defended my PhD dissertation titled “High-Order Computation of Gradient Flows and Barycenters in Generalized Wasserstein Spaces.”