Projects
- Defense Threat Reduction Agency (DTRA).
Neural-Net/Deep Learning Based Chemical Reaction Package.
April 2020 – April 2021. - Department of Navy, Naval PostGraduate School – N00244-20-1-0005.
Constrained Optimization and Machine Learning.
January 2020 – December 2021. - NSF DMS – 1913004
Collaborative Research: Multilevel Methods for Optimal Control of Partial Differential Equations and Optimization-Based Domain Decomposition.
July 2019-June 2022. - Air Force Office of Scientific Research (AFOSR) – FA9550-19-1-0036.
Structure Exploiting Trust Regions for Bilevel and Risk-Averse Optimization. January 2019-December 2021. - NSF DMS – 1907412
East Coast Optimization Meeting (ECOM). March 2019-August 2020. - NSF DMS – 1818772
Partial Differential Equation Constrained Optimization: Algorithms, Numerics, and Applications. August 2018-July 2021. - Department of Energy, Sandia National Laboratories
Fractional differential operators for features detection in the subsurface. January-May 2019. - Department of Energy, Sandia National Laboratories
Fractional operators in Geophysics. January-May 2018 - NSF DMS – 1521590
Numerical Analysis of Partial Differential Equation Constrained Optimization Problems. July 2015-May 2019.
Publications
2020
- H. Antil, T.S. Brown, D. Verma and M. Warma.
Moreau-Yosida Regularization for Optimal Control of Fractional PDEs with State Constraints: Parabolic Case.
Submitted 2020. Preprint - H. Antil and T.N.T. Quyen.
Optimal Control of Parameterized Maxwell’s System: Reduced Basis, Convergence Analysis, and A Posteriori Error Estimates.
Submitted 2020. Preprint - H. Antil, C.N. Rautenberg, and A. Schikorra.
On a Fractional Version of a Murat Compactness Result and Applications.
Submitted 2020. Preprint - H. Antil, R. Khatri, R. Loehner, and D. Verma.
Fractional Deep Neural Network via Constrained Optimization.
Submitted 2020. Preprint - H. Antil, D.P. Kouri, and J. Pfefferer.
Fractional diffusion and uncertainty.
Submitted 2020. - R. Vaughn, T. Berry, H. Antil
Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs.
Submitted 2020. Preprint - H. Antil, S. Kubota, K. Shirakawa, and N. Yamazaki
Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems.
Submitted 2020. Preprint - H. Antil, M. D’Elia, C. Glusa, B van Bloemen Waanders, and C.J. Weiss
A fast solver for the fractional Helmholtz equation.
Submitted 2020. Preprint - H. Antil, D. Verma, and M. Warma
Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the dual of Fractional Order Sobolev Spaces.
Accepted in Journal of Optimization Theory and Applications (JOTA) 2020. Preprint - H. Antil, Z. (Wendy) Di, and R. Khatri
Bilevel optimization, deep learning and fractional Laplacian with applications in tomography.
Inverse Problems, 36 – 064001 (22pp), (2020). Preprint - R. Lohner and H. Antil
Revisiting Calderon’s Problem.
International Journal of Numerical Methods for Heat and Fluid Flow. 2020.
DOI: https://doi.org/10.1108/HFF-12-2019-0931. Preprint - H. Antil, D. Verma, and M. Warma.
External optimal control of fractional parabolic PDEs.
ESAIM: Control, Optimisation and Calculus of Variations (CoCV), Volume: 26, Article Number: 20, Pages: 33, Year: 2020. Preprint - C.J. Weiss, B.G. van Bloemen Waanders, and H. Antil.
Fractional Operators Applied to Geophysical Electromagnetics.
Geophysical Journal International, 220(2), 1242-1259, 2020. Preprint - H. Antil and M. Warma.
Optimal control of fractional semilinear PDEs.
ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), Volume: 26, Article Number : 5, Pages: 30. 2020. Preprint
2019
- H. Antil, T.S. Brown, and D. Verma
Moreau-Yosida Regularization for Optimal Control of Fractional Elliptic Problems with State and Control Constraints.
Submitted 2019. Preprint - H. Antil, U. Biccari, R. Ponce, M. Warma, and S. Zamorano
Controllability properties from the exterior under positivity constraints for a 1–D fractional heat equation.
Submitted 2019. Preprint - H. Antil, C. Lizama, R. Ponce, and M. Warma
Convergence of solutions of discrete semi-linear space-time fractional evolution equations.
Submitted 2019. Preprint - Z. Zou , S. Mukherjee, H. Antil, and W. Aquino
Adaptive particle-based approximations of the Gibbs posterior for inverse problems.
Submitted 2019. Preprint - H. Dinh, H. Antil, Y. Chen, E. Cherkaev, and A. Narayan
Model reduction for fractional elliptic problems using the Kato’s formula.
Submitted 2019. Preprint - H. Antil, T. Berry, and J. Harlim.
Fractional Diffusion Maps.
Submitted 2019. Preprint - H. Antil, Y. Chen, and A. Narayan.
Reduced basis methods for fractional Laplace equations via extension.
SIAM J. of Sci. Computing 41(6), pp. A3552-A3575, 2019. Preprint - H. Antil, T. Brown, and F.J. Sayas.
A problem in control of elastodynamics with piezoelectric effects.
DOI: https://doi.org/10.1093/imanum/drz047. IMA Journal of Numerical Analysis, 2019. Preprint - 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. Preprint - H. Antil, R. Khatri, and M. Warma.
External optimal control of nonlocal PDEs.
Inverse Problems 35(8) 2019. Preprint - H. Antil and M. Warma.
Optimal control of the coefficient for regional fractional p-Laplace equation: Approximation and convergence.
Mathematical Control & Related Fields, 9(1), pp 1-38, 2019. Preprint
Among the 10 most downloaded article in this journal. Years 2018-19. - A. Hazra, V. Maggioni, P. Houser, H. Antil and M. Noonan.
A monte carlo-based multi-objective optimization approach to merge different precipitation estimates for land surface modeling.
Journal of Hydrology 570, 454–462, 2019.