![[arjun.jpeg|300]] <span class="profile-links"> <a href="https://github.com/avj-jpg" class="circle-icon github" title="GitHub" target="_blank"></a> <a href="https://orcid.org/0000-0001-5391-5560" class="circle-icon orcid" title="ORCID" target="_blank"></a> <a href="https://scholar.google.com/citations?user=_fcSwDYAAAAJ&hl=en" class="circle-icon scholar" title="Google Scholar" target="_blank"></a> <a href="https://www.researchgate.net/profile/Arjun-Vijaywargiya?ev=hdr_xprf" class="circle-icon rg" title="ResearchGate" target="_blank"></a> <a href="https://www.linkedin.com/in/arjunveejay/" class="circle-icon linkedin" title="LinkedIn" target="_blank"></a> </span> # About Me I am a Peter O'Donnell Jr. Postdoctoral Fellow at the [Oden Institute for Computational Engineering and Sciences](https://oden.utexas.edu/) 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](https://www.cosmicai.org/). My postdoctoral mentor is [Prof. George Biros](https://www.oden.utexas.edu/people/1056/), and within Cosmic AI, I am part of the *Accelerated Universe* working group led by [Prof. Stella Offner](https://sites.google.com/view/stellaoffner/home). I earned my Ph.D. in Applied Mathematics from the University of Notre Dame under the guidance of [Prof. Guosheng Fu](https://sites.nd.edu/gfu/). 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](https://www3.nd.edu/~zxu2/). 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](https://www.sandia.gov/-ikalash/staff/irina-tezaur/) and [Dr. Anthony Gruber](https://adeyemiadeoye.github.io/) on structure-preserving reduced order models, contributing to the Department of Energy funded [M2dt](https://m2dt.oden.utexas.edu/) 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](https://www.mathworks.com/products/new_products/release2024a.html). # 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 $\subset$ Computer Science Research Institute | Year-round intern | Anthony Gruber | Irina Tezaur | | February 2021–May 2025 | University of Notre Dame | Applied and Computational Mathematics and Statistic | Research and Teaching Assistant | Guosheng Fu | Guosheng Fu | | May 2023–August 2023 | MathWorks | MATLAB Data Analysis $\subset$ MATLAB Math and PDE | Summer Intern | Cosmin Ionita | Cosmin Ionita | | May 2022–August 2022 | MathWorks | Simscape Language and Execution | Summer Intern | Peng Cheng | Jacek Kierzenka | # 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](https://www.siam.org/conferences-events/past-event-archive/cse25/) | | 2024 | Student Travel Award | Society for Industrial and Applied Mathematics | [Travel support for MDS24](https://www.siam.org/conferences-events/past-event-archive/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 [[Errata]] ## Dissertation - **A. Vijaywargiya**, *High order computation of gradient flows and barycenters in generalized Wasserstein spaces*, University of Notre Dame, 2025. 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. [https://arxiv.org/abs/2502.10888](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](https://doi.org/10.1016/j.jcp.2025.113772). - **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](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](https://meetings.ams.org/math/spring2023c/meetingapp.cgi/Paper/24462), 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*](https://web.ma.utexas.edu/users/drp/projects.html), 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](https://icerm.brown.edu/programs/sp-s24/w2/) 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](https://science.nd.edu/events/2023/12/08/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 - April 04, 2025: I successfully defended my PhD dissertation titled "High-Order Computation of Gradient Flows and Barycenters in Generalized Wasserstein Spaces".