13 citations · 18 across the 5 of their papers we have counts for
8 papers
Deep Neural Nets with Fixed Bias Configuration
Harbir Antil, Thomas S. Brown, Rainald Löhner +2
For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `…
Optimal Control, Numerics, and Applications of Fractional PDEs
Harbir Antil, Thomas S. Brown, Ratna Khatri +3
This article provides a brief review of recent developments on two nonlocal operators: fractional Laplacian and fractional time derivative. We start by accounting for several appli…
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Thomas S. Brown, Harbir Antil, Rainald Löhner +2
Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the num…
Moreau-Yosida regularization for optimal control of fractional PDEs with state constraints: parabolic case
Harbir Antil, Thomas S. Brown, Deepanshu Verma +1
This paper considers optimal control of fractional parabolic PDEs with both state and control constraints. The key challenge is how to handle the state constraints. Similarly, to t…
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…
Analysis of models for viscoelastic wave propagation
Thomas Brown, Shukai Du, Hasan Eruslu +1
We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time ver…
A problem in control of elastodynamics with piezoelectric effects
Harbir Antil, Thomas S. Brown, Francisco-Javier Sayas
We consider an optimal control problem where the state equations are a coupled hyperbolic-elliptic system. This system arises in elastodynamics with piezoelectric effects -- the el…
Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
Thomas S. Brown, Tonatiuh Sánchez-Vizuet, Francisco-Javier Sayas
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear…