Recent Research Interests

• optimization algorithms for problems governed by nonlinear, large-scale (infinite dimensional) physical models given by partial differential equations (PDEs);
• free boundary problems;
• calculus of variations;
• inverse problems;
• numerical analysis;
• scientific computing and software development;
• dimensional reduction;
• deep learning.

Sponsored Research

Selected research grants, see Curriculum Vitae (.PDF) for more details.

Current

• National Science Foundation (NSF) DMS - 2110263
  Algorithms and Numerics for Optimization Problems with PDEs.
  August 2021-July 2024.

• Air Force Office of Scientific Research (AFOSR) - FA9550-21-1-0181.
  Defense University Research Instrumentation Program (DURIP).
  Optimization, Control, Networks and Learning from Data.
  May 2021-April 2022.

• Defense Threat Reduction Agency (DTRA).
  Neural-Net/Deep Learning Based Chemical Reaction Package.
  April 2020 - September 2021.

• Department of Navy, Naval PostGraduate School - N00244-20-1-0005.
  Constrained Optimization and Machine Learning.
  January 2020 - December 2021.

• National Science Foundation (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.

• National Science Foundation (NSF) DMS - 1907412
  East Coast Optimization Meeting (ECOM).
  March 2019-August 2022.

Recently Ended

• National Science Foundation (NSF) DMS - 1818772
  Partial Differential Equation Constrained Optimization: Algorithms, Numerics, and Applications.
  August 2018-July 2021.

• National Institute of Standards and Technology (NIST).
  Algorithms for Image and Shape Analysis in 3d.
  August - December 2020.

• 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

• National Science Foundation (NSF) DMS - 1521590
  Numerical Analysis of Partial Differential Equation Constrained Optimization Problems.
  July 2015-May 2019.

Outcomes

• See Publications for a complete list of latest work
• Software written link
• Mentoring of students and postdocs link