Faculty & Staff Directory
- Director, Center for Mathematics and Artificial Intelligence (CMAI)
- Associate Professor
PhD, Mathematics, University of Houston, (2009)
Postdoc, Rice University, (2010)
Postdoc, University of Maryland College Park, (2011-12)
Passion for involving students and postdocs in applied mathematics research with collaborations in academia, industry, and national labs.
Funded by National Science Foundation, Department of Energy, and Department of Defense.
Current research is focused on:
- Optimal control of PDEs
- Shape optimization
- Free boundary problems
- Deep learning
- Inverse problems
- Calculus of variations
- Numerical analysis
- Applications: fractional PDEs, fluid dynamics, imaging etc.
I regularly teach courses on Optimal Control, PDEs, Numerical Analysis, Calculus of Variations, Finite Element Methods, and Deep Learning. I also run a weekly seminar on related graduate research topics.
1. H. Antil, Z. Di, and R. Khatri. Bilevel optimization, deep learning and fractional Laplacian with applications in tomography. Inverse Problems, 2020. DOI: https://doi.org/10.1088/1361-6420/ab80d7
2. H. Antil and C.N. Rautenberg. Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications. SIAM Journal on Mathematical Analysis 51(3), 2479--2503, 2019.
3. H. Antil and S. Bartels. Spectral approximation of fractional PDEs in image processing and phase field modeling. Computational Methods in Applied Mathematics 17 (4), 2017.
4. H. Antil, S. Hardesty, and M. Heinkenschloss. Shape Optimization of Shell Structure Acoustics. SIAM J. Control Optim. 55 (3), 1347--1376, 2017.
5. K. Carlberg, M. Barone, and H. Antil. Galerkin v. discrete-optimal projection in nonlinear model reduction. Journal of Computational Physics, 330, 693-734, 2017.
6. H. Antil, and E. Otarola. A FEM for an optimal control problem of fractional powers of elliptic operators. SIAM Journal of Control and Optimization, 53(6), 3432--3456, 2015.
7. H. Antil, S. Field, F. Herrmann, R. H. Nochetto, and M. Tiglio. Two-step Greedy Algorithm for Reduced Order Quadratures. Journal of Scientific Computing, Springer, 57:604--637, 2013.
- Research Fellow at ICERM, Brown University (2020).
- Plenary speaker at international workshop on Nonlocal Models: analysis, optimization and implementation. Trier University, Germany. July 2020.
- Plenary speaker at DFG SPP 1962: Priority Programme on Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization. Berlin, Germany. October, 2020.
- Summer school teacher. Department of Mathematics, Technical University Munich, Germany. July 31-August 4, 2017.
- Dean's Early-Career Excellence Award, College of Science at George Mason University 2015.
Our group organizes two workshops each year.
- East Coast Optimization Meeting (ECOM): Joint venture between GMU and Sandia National Laboratories.
- Sayas Numerics Day - Joint venture between GMU, University of Maryland College Park, University of Maryland Baltimore County, and University of Delaware.