6 citations · 12 across the 9 of their papers we have counts for
12 papers
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…
A Neural Network Approach for Stochastic Optimal Control
Xingjian Li, Deepanshu Verma, Lars Ruthotto
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value fun…
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…
Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints
Harbir Antil, Rafael Arndt, Carlos N. Rautenberg +1
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint i…
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…
Novel Deep neural networks for solving Bayesian statistical inverse
Harbir Antil, Howard C Elman, Akwum Onwunta +1
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MC…
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…
Fractional Deep Neural Network via Constrained Optimization
Harbir Antil, Ratna Khatri, Rainald Löhner +1
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into th…
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…
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…
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…