48 citations · 252 across the 96 of their papers we have counts for
12 papers · 1 filter
Moreau-Yosida Regularization for Optimal Control of Fractional Elliptic Problems with State and Control Constraints
Harbir Antil, Thomas S. Brown, Deepanshu Verma
Recently the authors have studied a state and control constrained optimal control problem with fractional elliptic PDE as constraints. The goal of this paper is to continue that pr…
Revisiting Calderon's Problem
Rainald Löhner, Harbir Antil
A finite element code for heat conduction, together with an adjoint solver and a suite of optimization tools was applied for the solution of Calderon's problem. One of the question…
Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs
Ryan Vaughn, Tyrus Berry, Harbir Antil
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equ…
Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation
Harbir Antil, Umberto Biccari, Rodrigo Ponce +2
We study the controllability to trajectories, under positivity constraints on the control or the state, of a one-dimensional heat equation involving the fractional Laplace operator…
Convergence of solutions of discrete semi-linear space-time fractional evolution equations
Harbir Antil, Carlos Lizama, Rodrigo Ponce +1
Let be the realization of the fractional Laplace operator on the space of continuous functions , and let denote the discrete fractional Lapla…
Optimal Control of Parameterized Maxwell's System: Reduced Basis, Convergence Analysis, and A Posteriori Error Estimates
Harbir Antil, Tran Nhan Tam Quyen
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnet…
Bilevel Optimization, Deep Learning and Fractional Laplacian Regularization with Applications in Tomography
Harbir Antil, Zichao Di, Ratna Khatri
In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction…
Adaptive particle-based approximations of the Gibbs posterior for inverse problems
Zilong Zou, Sayan Mukherjee, Harbir Antil +1
In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The G…
Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the dual of Fractional Order Sobolev Spaces
Harbir Antil, Deepanshu Verma, Mahamadi Warma
This paper introduces the notion of state constraints for optimal control problems governed by fractional elliptic PDEs of order . There are several mathematical tools…
Model reduction for fractional elliptic problems using Kato's formula
Huy Dinh, Harbir Antil, Yanlai Chen +2
We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. O…
External optimal control of fractional parabolic PDEs
Harbir Antil, Deepanshu Verma, Mahamadi Warma
In this paper we introduce a new notion of optimal control, or source identification in inverse, problems with fractional parabolic PDEs as constraints. This new notion allows a so…
Fractional Operators Applied to Geophysical Electromagnetics
Chester J. Weiss, Bart G. van Bloemen Waanders, Harbir Antil
A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the a…