Antil studying algorithms and numerical methods for optimization with partial differential equation constraints

Harbir Antil, Professor, Mathematical Sciences; Director, Center for Mathematics and Artificial Intelligence, is studying optimization problems with partial differential equation (PDE) constraints.  

He and his collaborators aim to create new optimization methods Deep Learning frameworks to solve several currently intractable optimization problems constrained by: fractional harmonic maps, advection dominated (also limiting transport equations) arising in magnetic targeted drug delivery, general inequality and equality constraints such as contact or complementarity. All these problems are nonlinear, nonconvex, and nonsmooth in nature. 

Antil received $340,000 from the National Science Foundation for this project. Funding began in August 2021 and will end in late July 2024.