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I am a Researcher and Lecturer at the Institute of Research and Development, Duy Tan University, Da Nang, Vietnam, in a role broadly comparable to Assistant Professor in the US system.
I am also an External Affiliate of the Institute for Scientific Computation (ISC), Texas A&M University (TAMU) (with homepage https://sites.google.com/tamu.edu/tina-mai/home), where I make regular research visits, often for one to two months at a time. During these visits, I am also hosted as a Visiting Scholar in the Department of Mathematics.
I was a Postdoctoral Research Associate at the ISC, TAMU, mentored by Yalchin Efendiev. Over the course of this appointment, I also undertook invited research visits to the University of Minnesota and short-term research visits to the University of Texas at Austin.
I obtained my Ph.D. in Mathematics from TAMU, with a dissertation on convexity in nonlinear elasticity under the guidance of Jay R. Walton.
I received a B.S. in Mathematics–Informatics Teaching at University of Education, The University of Da Nang, Vietnam.
Email: tinagdi<at>gmail.com; maitina<at>duytan.edu.vn; tinamai<at>tamu.edu
My publications can be found on my Google Scholar Profile
Multiscale Modeling and Computation
Research Interests
Analysis of nonlinear PDEs and kinetic theory
Multiscale and structure-preserving numerical methods
Scientific machine learning and data-driven techniques for multiscale systems
Research Overview
My research develops multiscale modeling and computation for complex systems arising in physics, biology, and engineering.
My analytical work includes a recent sole-authored paper in Kinetic and Related Models on the hydrodynamic limit of the Kuramoto–Sakaguchi equation with inertia and noise, together with a substantially revised preprint on entropic convergence and the linearized limit for the Boltzmann equation with external force.
In parallel, my computational research develops and analyzes frameworks based on the generalized multiscale finite element method (GMsFEM) and its constraint energy minimizing variant (CEM-GMsFEM) for strain-limiting models of nonlinear elasticity, Cosserat (micropolar) elasticity, poroelasticity, and multi-continuum Richards equations describing soil-moisture dynamics. I have also integrated deep learning with homogenization and online GMsFEM to predict effective coefficients, multiscale basis functions, and coarse-scale solutions for Richards flow.
Across both strands, the interaction between theory, computation, and data is central. Rigorous analysis provides insight into the structure and limiting behavior of nonlinear and kinetic PDEs through asymptotic limits, entropy-based arguments, and semigroup and evolution-family techniques. Functional-analytic and variational estimates also provide the foundation for the stability and convergence analysis of my multiscale schemes. In turn, multiscale numerical methods and scientific machine learning connect these analytical insights with computationally effective approaches for complex heterogeneous and stochastic systems in which direct fine-scale simulation is prohibitively expensive.
Note. In the publication lists below, an asterisk (*) denotes corresponding authorship, and my name is shown in bold.
Selected Publications
Tina Mai*. Hydrodynamic limit of the Kuramoto–Sakaguchi equation with inertia and noise effects. Kinetic and Related Models, 24 (2026) 75–108.
Journal: https://www.aimsciences.org/article/doi/10.3934/krm.2026020
arXiv: https://arxiv.org/abs/2410.05113
Rigorously derives the hydrodynamic limit of the kinetic Kuramoto equation with inertia and noise using generalized collision invariants, supported by a Hardy-type inequality.
Tina Mai*. Entropic convergence and the linearized limit for the Boltzmann equation with external force. Preprint, arXiv:1612.05096v2 (2025).
https://arxiv.org/abs/1612.05096v2
Extends Levermore’s entropic-convergence framework to the nonlinear Boltzmann equation with external forces, showing that the strong linearized limit persists under physically meaningful force fields. The key technical ingredients are new force-regularity assumptions and careful treatment of test-function regularity, which support the semigroup and evolution-family constructions, enable the dissipation equality in the forced setting, and provide the compactness needed for the limit.
Dmitry Ammosov, Tina Mai*, Juan Galvis. Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model. Journal of Computational Physics, 519 (2024) 113428.
https://doi.org/10.1016/j.jcp.2024.113428
https://arxiv.org/abs/2403.14178
Develops a generalized multiscale finite element framework for nonlinear strain-limiting Cosserat elasticity, establishing convergence and demonstrating efficiency and robustness in heterogeneous media.
Tina Mai, Siu Wun Cheung, and Jun Sur Richard Park. Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations. Journal of Computational Physics, 477 (2023) 111915.
https://doi.org/10.1016/j.jcp.2023.111915
https://arxiv.org/abs/2205.11294
Extends the CEM-GMsFEM to a sample-informed model-reduction approach for coupled nonlinear multi-continuum Richards equations, enabling efficient simulation of flow in heterogeneous fractured porous media and providing a rigorous convergence analysis of the Picard iteration.
Denis Spiridonov, Sergei Stepanov, Tina Mai*. Prediction of discretization of online GMsFEM using deep learning for Richards equation. Journal of Computational and Applied Mathematics, 454 (2025) 116167.
https://doi.org/10.1016/j.cam.2024.116167
https://arxiv.org/abs/2403.14177
Combines deep learning with online GMsFEM to rapidly predict multiscale basis functions and efficiently compute coarse-scale solutions for the nonlinear Richards equation in heterogeneous, non-periodic media with uncertainty.
Publications
Kinetic Theory and Nonlinear PDEs
Tina Mai*. Hydrodynamic limit of the Kuramoto–Sakaguchi equation with inertia and noise effects. Kinetic and Related Models, 24 (2026) 75–108.
Journal: https://www.aimsciences.org/article/doi/10.3934/krm.2026020
arXiv: https://arxiv.org/abs/2410.05113
Tina Mai*. Entropic convergence and the linearized limit for the Boltzmann equation with external force. Preprint, arXiv:1612.05096v2 (2025).
arXiv: https://arxiv.org/abs/1612.05096v2
Multiscale Numerical Methods
Dmitry Ammosov, Tina Mai*, Juan Galvis. Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model, Journal of Computational Physics, 519 (2024) 113428.
https://doi.org/10.1016/j.jcp.2024.113428
https://arxiv.org/abs/2403.14178
Tina Mai, Siu Wun Cheung, and Jun Sur Richard Park. Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations, Journal of Computational Physics, 477 (2023) 111915.
https://doi.org/10.1016/j.jcp.2023.111915
https://arxiv.org/abs/2205.11294
Jun Sur Richard Park, Siu Wun Cheung, Tina Mai*. Multiscale simulations for multi-continuum Richards equations, Journal of Computational and Applied Mathematics, 397 (2021) 113648.
https://doi.org/10.1016/j.cam.2021.113648
https://arxiv.org/abs/2010.09181
Jun Sur Richard Park, Siu Wun Cheung, Tina Mai*, Viet Ha Hoang. Multiscale simulations for upscaled multi-continuum flows, Journal of Computational and Applied Mathematics, 374 (2020) 112782.
https://doi.org/10.1016/j.cam.2020.112782
https://arxiv.org/abs/1909.04722
Shubin Fu, Eric Chung, Tina Mai*. Constraint energy minimizing generalized multiscale finite element method for nonlinear poroelasticity and elasticity, Journal of Computational Physics, 417 (2020) 109569.
https://doi.org/10.1016/j.jcp.2020.109569
https://arxiv.org/abs/1909.13267
Shubin Fu, Eric Chung, Tina Mai*. Generalized multiscale finite element method for a strain-limiting nonlinear elasticity model, Journal of Computational and Applied Mathematics, 359 (2019) 153–165.
https://doi.org/10.1016/j.cam.2019.03.047
https://arxiv.org/abs/1812.09347
Scientific Machine Learning and Data-Driven Multiscale Methods
Denis Spiridonov, Sergei Stepanov, Tina Mai*. Prediction of discretization of online GMsFEM using deep learning for Richards equation, Journal of Computational and Applied Mathematics, 454 (2025) 116167.
https://doi.org/10.1016/j.cam.2024.116167
https://arxiv.org/abs/2403.14177
Sergei Stepanov, Denis Spiridonov, Tina Mai*. Prediction of numerical homogenization using deep learning for the Richards equation, Journal of Computational and Applied Mathematics, 424 (2023) 114980.
https://doi.org/10.1016/j.cam.2022.114980
https://arxiv.org/abs/2208.12161
Continuum Mechanics
Tina Mai*, Jay R. Walton. On monotonicity for strain-limiting theories of elasticity, Journal of Elasticity, 120 (I) (2015) 39–65.
https://doi.org/10.1007/s10659-014-9503-4
Tina Mai, Jay R. Walton. On strong ellipticity for implicit and strain-limiting theories of elasticity, Mathematics and Mechanics of Solids, 20 (II) (2015) 121–139.
https://doi.org/10.1177/1081286514544254
Optimization / Computational Mathematics
Tina Mai*, Daniele Mortari. Theory of functional connections applied to quadratic and nonlinear programming under equality constraints, Journal of Computational and Applied Mathematics, 406 (2022) 113912.
https://doi.org/10.1016/j.cam.2021.113912
https://arxiv.org/abs/1910.04917
Research Grants
RFBR Research Grant, 2021–2022: Russian Foundation for Basic Research (RFBR)
on Cooperation with Vietnam Academy of Science and Technology (VAST),
a principal investigator (co-PI), grant number RFBR-VAST 21-51-54001,
“New mathematical models for multiscale infiltration process using machine learning approaches”,
with Aleksandr Grigorev (co-PI), Denis Spiridonov, Sergei Stepanov, and Hieu Nguyen (members)
NAFOSTED Research Grant, 2020–2022: Vietnam National Foundation for Science and Technology Development (NAFOSTED),
a principal research member, grant number 101.99-2019.326,
“Methods for solving multiscale partial differential equations”,
with Nguyen Trung Hieu (PI) and Chu Van Tiep (principal research member)
Welcome
August 2 – 7, 2027, the 22nd ICMP (International Congress of Mathematical Physics),
taking place at Duy Tan University, Da Nang, Vietnam
Invited Talks
April 9, 2026, Invited Speaker, Stochastic Process Seminar, Department of Mathematics, Texas A&M University, College Station, USA
"Prediction of discretization of online GMsFEM using deep learning for Richards equation"
(paper with Denis Spiridonov and Sergei Stepanov; invited by Patricia Ning)
April 8, 2025, Invited Speaker, Nonlinear PDE Seminar, Department of Mathematics, Texas A&M University, College Station, USA
"Hydrodynamic limit of the Kuramoto–Sakaguchi equation with inertia and noise effects"
(slides; paper; invited by Edriss Titi)
Contributed Talks
February 27–28, 2026, Contributed Speaker, Finite Element Rodeo,
"Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model"
The University of Texas at Austin, USA
(paper with Dmitry Ammosov and Juan Galvis)
April 13–14, 2023, Contributed Speaker, The 4th East Coast Optimization Meeting (Virtual),
George Mason University, Fairfax, VA, USA
“Optimization and Game Theory”
Video of my talk: Prediction of numerical homogenization for Richards equation using deep learning
(paper with Sergei Stepanov and Denis Spiridonov)
Selected Activities
April 10–12, 2025, Participant, Frontiers in Computational Mathematics,
A conference in honor of Bjorn Engquist's 80th birthday,
The University of Texas at Austin, USA
February 6–10, 2023, Invited Participant, Workshop 1: Multiscale analysis and methods for PDEs: fluids and active matter dynamics,
Program Multiscale Analysis and Methods for Quantum and Kinetic Problems,
Institute for Mathematical Sciences (IMS), National University of Singapore (NUS)
Teaching
I enjoy teaching across levels and mentoring students through guided reading and research projects
Selected teaching evaluations:
https://sites.google.com/view/tina-mai/mai_evaluations
At Duy Tan University (DTU), Da Nang, Vietnam
Adjunct Instructor of Troy University at DTU
(American Degree Program jointly offered by DTU and Troy University)
MTH 1126 Calculus II (lectures in English to Computer Science students)
Primary instructor: teaching in person, co-teaching some sessions Spring 2026
(15 students)
Selected students' evaluations Spring 2026
Primary instructor: teaching in person, co-teaching some sessions Spring 2025
(19 students)
Selected students' evaluations Spring 2025
Primary instructor: course design, assessment, and grading, Spring 2024
with colleagues delivering lectures (29 students)
Primary instructor: course design, assessment, and grading, Summer 2022
with colleagues delivering lectures (15 students)
Lecturer at DTU: STA 151 Probability and Statistics, Fall 2018,
four sections, approximately 100 students each
(bilingual lectures in Vietnamese and English)
At Texas A&M University (TAMU), College Station, USA
Instructor of Record at TAMU: Math 142 Business Mathematics II, Summer 2014
(lectures in English)
Selected students' evaluations Summer 2014
Honors and Awards (Selected)
SIAM Early Career Travel Award, Society for Industrial and Applied Mathematics (SIAM), USA, 2021.
Awarded to support my participation and contributed presentation at the Virtual SIAM Conference on Computational Science and Engineering (CSE21), March 1–5, 2021.
(paper with Shubin Fu and Eric Chung).
Mathematical Work Award (twice), National Program for the Development of Mathematics,
Ministry of Education and Training (MOET) and Vietnam Institute for Advanced Study in Mathematics (VIASM),
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