48 citations · 252 across the 96 of their papers we have counts for
12 papers · 1 filter
Well-Posedness of Pseudo-Parabolic Gradient Systems with State-Dependent Dynamics
Harbir Antil, Daiki Mizuno, Ken Shirakawa +1
This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fi…
Convection Effects and Optimal Insulation: Modelling and Analysis
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount of insulating material coating an insulated boundary part $Γ_…
Optimal Boundary Control of Diffusion on Graphs via Linear Programming
Harbir Antil, Rainald Löhner, Felipe Pérez
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a we…
Well-Posedness and Approximation of Weak Solutions to Time Dependent Maxwell's Equations with -Data
Harbir Antil
We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and -data. Our first…
Randomized Matrix Sketching for Neural Network Training and Gradient Monitoring
Harbir Antil, Deepanshu Verma
Neural network training relies on gradient computation through backpropagation, yet memory requirements for storing layer activations present significant scalability challenges. We…
OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Case
Ratna Khatri, Anthony Kolshorn, Colin Olson +1
This paper presents a novel, mathematically rigorous framework for autoencoder-type deep neural networks that combines optimal control theory and low-rank tensor methods to yield m…
A smoothed proximal trust-region algorithm for nonconvex optimization problems with -regularization,
Harbir Antil, Anna Lentz
We investigate a trust-region algorithm to solve a nonconvex optimization problem with -regularization for . The algorithm relies on descent properties of a so-call…
A posteriori and a priori error estimates for linearized thin sheet folding
Harbir Antil, Sean P. Carney, Rohit Khandelwal
We describe a posteriori error analysis for a discontinuous Galerkin method for a fourth order elliptic interface problem that arises from a linearized model of thin sheet folding.…
Optimal Control of Pseudo-Parabolic KWC Systems for Grain Boundary Motion
Harbir Antil, Daiki Mizuno, Ken Shirakawa
The KWC system is a well-known generic framework for phase-field models of grain boundary motion, whose original formulation is given as a parabolic gradient flow of a free energy.…
Duality-Based Algorithm and Numerical Analysis for Optimal Insulation Problems on Non-Smooth Domains
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
This article develops a numerical approximation of a convex non-local and non-smooth minimization problem. The physical problem involves determining the optimal distribution, given…
Modeling and Analysis of an Optimal Insulation Problem on Non-Smooth Domains
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount of insulating material coating an insulated boundary $Γ_I\subseteq \partia…
On Techniques for Barely Coupled Multiphysics
Rainald Löhner, Harbir Antil, Sebastian Schöps
A technique to combine codes to solve barely coupled multiphysics problems has been developed. Each field is advanced separately until a stop is triggered. This could be due to a p…