8 papers
QH-GEM: Quantum-Hydrodynamic Generative Modeling
Harbir Antil, Alex Kaltenbach, Sarswati Shah
In this paper, we develop a deterministic, physically constrained generative framework based on the Madelung formulation of the free-particle Schrödinger equation. A reference Born…
Duality-Based Error Identities for Subgradient Flows Based on the Brézis-Ekeland-Nayroles Principle
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
We derive duality-based error identities for a broad class of subgradient flows induced by time-dependent convex integral functionals. Starting from the Bré…
A Finite Element Approximation of an Optimal Insulation Problem with Convective Heat Transfer
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
A finite element discretization of an optimal insulation problem with convective heat transfer is considered. The model is formulated as a non-smooth, two-variable convex minimizat…
A Priori and A Posteriori Error Identities for Vectorial Problems via Convex Duality
P. A. Gazca-Orozco, A. Kaltenbach
Convex duality has been leveraged in recent years to derive a posteriori error estimates and identities for a wide range of non-linear and non-smooth scalar problems. By employing…
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_…
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…
Note on the existence theory for non-induced evolution equations
Alex Kaltenbach
In this note we develop a framework which allows to prove an abstract existence result for non-linear evolution equations involving so-called non-induced operators, i.e., operators…