Thuy T. Le
Thuy T. Le

Thuy T. Le

Assistant Professor
Department of Mathematics & Statistics · California State University, Long Beach

Applied mathematician working on inverse problems, numerical analysis for partial differential equations, and machine learning — developing globally convergent numerical methods with rigorous theory and real-world data.

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About

Background

I am an Assistant Professor in the Department of Mathematics and Statistics at California State University, Long Beach. My research focuses on developing and analyzing novel computational methods to solve scientific problems motivated by high-impact applications, such as the detection of underground explosive devices, optical imaging, and seismic exploration. My work is concentrated in three key areas of applied mathematics: inverse problems, which extract hidden information from indirect measurements; numerical analysis for nonlinear PDEs, which provides the theoretical foundation for robust algorithms; and machine learning, which leverages data to uncover new insights and solve problems intractable for traditional models.

Before joining CSULB, I was a Postdoctoral Research Scholar at North Carolina State University, mentored by Dr. Hien Tran, and earned my Ph.D. in Applied Mathematics at the University of North Carolina at Charlotte, advised by Dr. Loc Nguyen.

Education

Ph.D., Applied Mathematics
UNC Charlotte
M.S., Mathematical Finance
UNC Charlotte
Research

Overview

Inverse Problems Numerical Analysis Nonlinear PDEs Carleman Estimates Inverse Scattering Operator Learning Causal Bayesian Optimization
01

Inverse Problems

Recovering sources, coefficients, and initial conditions in PDEs from external, often one-sided measurements — motivated by explosive-device detection, seismic exploration, non-destructive testing, and biomedical imaging. I build globally convergent solvers and validate them on real experimental data.

02

Numerical Analysis for Nonlinear PDEs

Developing and analyzing methods for nonlinear PDEs that converge rapidly and relax the dependence on precise initial guesses.

03

Machine Learning

Data-driven methods for problems beyond the reach of classical models: operation networks for inverse problems, biologically informed neural networks, and causal Bayesian optimization for high-stakes decision-making.

Publications

Selected & Recent Work

Preprints & Submitted
  1. Zixuan Ma, Chenfeng Huang, Thuy T. Le, Hien Tran. Safe-Handover Causal Bayesian Optimization with Dynamic Expert Trust. Submitted, 2026.
Journal Papers
  1. Chenfeng Huang, Thuy T. Le, Zixuan Ma and Hien Tran. Causal Bayesian Optimization: Foundations, Methods, and Applications. Transactions on Machine Learning Research, 2835-8856, 2026.
  2. Thuy T. Le, Minh-Binh Tran, and Loc H. Nguyen. A globally convergent Carleman–Picard method for an inverse initial-value problem for a nonlinear diffusive coagulation–fragmentation equation. Inverse Problems, accepted for publication, 2026.
  3. Cong B. Van, Thuy T. Le, and Loc H. Nguyen. The inverse initial data problem for anisotropic Navier–Stokes equations via Legendre time reduction method. Communications in Nonlinear Science and Numerical Simulation, 161 (2026), 110074.
  4. Thuy T. Le, Cong B. Van, Trong D. Dang, and Loc H. Nguyen. Inverse initial data reconstruction for Maxwell's equations via time-dimensional reduction method. Journal of Computational Physics, 559 (2026), 114896.
  5. Thuy T. Le, Phuong M. Nguyen, and Loc H. Nguyen. Inverse scattering without phase: Carleman convexification and phase retrieval via the WKB approximation. Computer Methods in Applied Mechanics and Engineering, 448 (2026), 118439.
  6. R. Lawrence Ives, Michael Read, Jeff Neilson, Thuc Bui, David Marsden, Thuy T. Le, and Hien T. Tran. Gyrotrons for Fusion Power Plants. Fusion Science and Technology, 1–11, 2025.
  7. Ray Abney, Thuy T. Le, Loc H. Nguyen, and Cam Peters. A Carleman–Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data. Applied Mathematics and Computation, 494 (2025), 129286.
  8. Thuy T. Le, Linh V. Nguyen, Loc H. Nguyen, and Hyunha Park. The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients. Computers & Mathematics with Applications, 166, 77–90, 2024.
  9. Huynh P. N. Le, Thuy T. Le, and Loc H. Nguyen. The Carleman convexification method for Hamilton–Jacobi equations. Computers & Mathematics with Applications, 59:173–185, 2024.
  10. Anuj Abhishek, Thuy T. Le, Loc H. Nguyen, and Taufiquar Khan. The Carleman–Newton method to globally reconstruct a source term for nonlinear parabolic equations. Journal of Computational and Applied Mathematics, 445:115827, 2024.
  11. Dinh-Nho Hào, Thuy T. Le, and Loc H. Nguyen. The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data. Communications in Nonlinear Science and Numerical Simulation, 128:107679, 2024.
  12. Phuong M. Nguyen, Thuy T. Le, Loc H. Nguyen, and Michael V. Klibanov. Numerical differentiation by the polynomial-exponential basis. Journal of Applied and Industrial Mathematics, 17, 928–942, 2023.
  13. Thuy T. Le, Vo A. Khoa, Michael V. Klibanov, Loc H. Nguyen, Grant Bidney, and Vasily Astratov. Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data. Journal of Applied and Industrial Mathematics, 17, 908–927, 2023.
  14. Thuy T. Le. Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman–contraction method. Advances in Inverse Problems for PDEs, vol. 784, 145–167, Contemporary Mathematics, AMS, 2023.
  15. Thuy T. Le, Loc H. Nguyen, and Hung V. Tran. A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications. Computers & Mathematics with Applications, 125, 13–24, 2022.
  16. Thuy T. Le and Loc H. Nguyen. The gradient descent method for the convexification to solve boundary value problems of quasi-linear PDEs and a coefficient inverse problem. Journal of Scientific Computing, 91:74, 2022.
  17. Thuy T. Le, Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, and Lam Nguyen. Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data. Inverse Problems, 38, 045002, 2022.
  18. M. Hashemitaheri, Thuy T. Le, H. Cherukuri, and T. Khan. A multivariate Newton–Raphson method approach to extract structural dynamics parameters during milling operations. AeroMat 2022, Pasadena, CA, 2022.
  19. Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen, Anders Sullivan, and Lam Nguyen. Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data. Inverse Problems and Imaging, 16, 1579–1618, 2022.
  20. Thuy T. Le and Loc H. Nguyen. A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data. Journal of Inverse and Ill-posed Problems, 30, 256–286, 2022.
  21. Thuy T. Le, Loc H. Nguyen, Thi-Phong Nguyen, and William Powell. The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations. Journal of Scientific Computing, 87:90, 2021.
  22. Michael V. Klibanov, Thuy T. Le, and Loc H. Nguyen. Convergent numerical method for a linearized travel time tomography problem with incomplete data. SIAM Journal on Scientific Computing, 42, B1173–B1192, 2020.

A complete, up-to-date list is available on Google Scholar and MathSciNet.

Presentations

Invited Talks & Seminars

  1. Expert-guided Causal Bayesian Optimization. SIAM Minisymposium on Scientific Machine Learning, Joint Mathematics Meetings, Washington D.C., 2026.
  2. Inverse scattering without phase: Carleman convexification and phase retrieval via the WKB approximation. AMS Special Session on Theoretical and Numerical Control of PDEs, JMM, Washington D.C., 2026.
  3. The dimensional reduction method for a nonlinear inverse heat conduction problem with limited boundary data. 3rd UNCG Virtual PDE Conference, UNC Greensboro, 2025.
  4. Carleman–Picard approach for a coefficient inverse problem in parabolic equations using partial boundary data. AMS Spring Southeastern Sectional Meeting, Clemson University, 2025.
  5. An inverse scattering problem with experimental data. Fluid Mechanics and Waves Seminar, New Jersey Institute of Technology, 2024.
  6. A convexification approach for the 3D inverse scattering problem with experimental data. AMS Spring Southeastern Sectional Meeting, Florida State University, 2024.
  7. A globally convergent method based on a Carleman estimate and the contraction mapping principle for an inverse scattering problem in the time domain with experimental data. SEARCDE 2023, Florida A&M University, 2023.
  8. A Carleman-based numerical method for solving a 3D coefficient inverse problem. AMS Fall Eastern Sectional Meeting, University at Buffalo (SUNY), 2023.
  9. A globally convergent numerical method for a coefficient inverse problem for a hyperbolic equation with experimental data. UNC Greensboro PDE Conference, 2023.
  10. Global reconstruction of initial conditions for nonlinear parabolic equations via the Carleman–contraction method. SIAM Southeastern Atlantic Section Annual Meeting, Virginia Tech, 2023.
  11. Convexification-based globally convergent numerical method for a 3D coefficient inverse problem. AMS Spring Southeastern Sectional Meeting, Georgia Institute of Technology, 2023.
  12. Convexification method for the 3D inverse scattering problem in the frequency domain. CAAM 3, Saigon University, Ho Chi Minh City, Vietnam, 2022.
  13. The Carleman contraction mapping method for the 1D inverse scattering problem in the time domain with experimental data. International Conference on Differential Equations and Applications, Hanoi, Vietnam, 2022.
  14. A new Carleman estimate and the contraction principle for the 1D inverse scattering problem with experimental data. Workshop on PDE and Related Topics, VIASM, Hanoi, Vietnam, 2022.
  15. Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data. SIAM Conference on Imaging Science (IS22), 2022.
  16. A Carleman-based reconstruction method for a 1D coefficient inverse problem with time-dependent experimental data. AMS Fall Western Sectional Meeting, 2021.
  17. Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data. SIAM Southeastern Atlantic Section Conference, Auburn University, 2021.
  18. Reconstructing the initial condition of quasi-linear parabolic equations from lateral Cauchy data. AMS Spring Southeastern Virtual Sectional Meeting, 2021.
  19. The convexification method for systems of quasi-linear PDEs and its application to a coefficient inverse problem. Applied Math Seminar, Kansas State University, 2020.
  20. A convergent numerical method to reconstruct the initial condition of nonlinear parabolic equations from lateral Cauchy data. October Math Day Symposium, UNC Charlotte, 2020.
  21. A convergent numerical method to reconstruct the initial condition of nonlinear parabolic equations from lateral Cauchy data. 15th UNCG Regional Mathematics and Statistics Conference, 2019.
Teaching

Courses Taught

Instructor · California State University, Long Beach

Department of Mathematics and Statistics · 2026 – present
Fall 2026
Scientific Computing (MA 473) · Advanced Scientific Computing (MA 573)

Instructor · North Carolina State University

Department of Mathematics · 2023 – 2026
Fall 2023 – Fall 2025
Elements of Calculus · Precalculus I

Instructor · UNC Charlotte

Department of Mathematics and Statistics · 2020 – 2021
Fall 2020 – Fall 2021
Calculus 1 · Differential Equations

Teaching Assistant · UNC Charlotte

Department of Mathematics and Statistics · 2019 – 2022
Fall 2019 – Spring 2022
Differential Equations · Advanced Calculus of One Variable · Matrices & Linear Algebra

Instructor · Banking Academy of Vietnam

Department of Mathematics · 2012 – 2019
Fall 2012 – Spring 2019
Econometrics · Introduction to Probability & Statistics
Service & Mentorship

Professional Activities

Conference Organizer

  • Special Session on Modeling and Control of Dynamical Systems and its Applications — AMS Spring Southeastern Sectional Meeting, Clemson University, 2025
  • Special Session on Recent Advances in Inverse Problems for PDEs and Their Applications — AMS Spring Southeastern Sectional Meeting, Florida State University, 2024

Journal Reviewer

  • Journal of Computational Physics
  • Evolution Equations and Control Theory
  • Communications in Nonlinear Science and Numerical Simulation
  • Scientific Reports · BIT Numerical Mathematics · AMS Contemporary Mathematics

Mentorship

  • Advised 8+ graduate and undergraduate students, including NSF REU participants, with co-authored publications in Applied Mathematics and Computation, Computers & Mathematics with Applications, and the Journal of Scientific Computing.
Contact

Get in touch

I welcome inquiries about research collaborations, student opportunities, and talks. The best way to reach me is by email.

Department of Mathematics & Statistics · California State University, Long Beach