Research area: Numerical Analysis, Inverse Problems, Optimal Transportation, Machine Learning, and Nonconvex Optimization
My research focuses on computational mathematics, especially developing numerical methods for computational inverse problems, machine learning, PDE-constrained optimization, global optimization, and computational optimal transport with data science applications.
- Efficient natural gradient descent methods for large-scale PDE-based optimization problems (with L. Nurbekyan and W. Lei), in press for SIAM Journal on Scientific Computing (2023).
- Neural Inverse Operators for Solving PDE Inverse Problems (with R. Molinaro, B. Engquist, and S. Mishra), The 40th International Conference on Machine Learning (2023).
- Optimal transport for parameter identification of chaotic dynamics via invariant measures (with L. Nurbekyan, E. Negrini, R. Martin, and M. Pasha), SIAM Journal on Applied Dynamical Systems 22, no. 1 (2023): 269-310.
- Optimal transport based seismic inversion: Beyond cycle skipping (with B. Engquist), Communications on Pure and Applied Mathematics 75, no. 10 (2022): 2201-2244.
- Adjoint DSMC for nonlinear Boltzmann equation constrained optimization (with R. Caflisch and D. Silantyev), Journal of Computational Physics 439 (2021): 110404.
- The quadratic Wasserstein metric for inverse data matching (with B. Engquist and K. Ren), Inverse Problems 36, no. 5 (2020): 055001.
- Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion (with B. Engquist, J. Sun, and B. F. Hamfeldt), Geophysics 83, no. 1 (2018): R43-R62.
MATH Courses - Fall 2023
- MATH 4250 : Numerical Analysis and Differential Equations
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
- MATH 5250 : Numerical Analysis and Differential Equations