Deepanshu Verma
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View article: Regularity and error estimates in physics-informed neural networks for the Kuramoto-Sivashinsky equation
Regularity and error estimates in physics-informed neural networks for the Kuramoto-Sivashinsky equation Open
Due to its nonlinearity, bi-harmonic dissipation, and backward heat-like term in the absence of a divergence-free condition, the $2$-D/$3$-D Kuramoto-Sivashinsky equation poses significant challenges for both mathematical analysis and nume…
View article: Randomized Matrix Sketching for Neural Network Training and Gradient Monitoring
Randomized Matrix Sketching for Neural Network Training and Gradient Monitoring Open
Neural network training relies on gradient computation through backpropagation, yet memory requirements for storing layer activations present significant scalability challenges. We present the first adaptation of control-theoretic matrix s…
View article: Error estimates for viscous Burgers' equation using deep learning method
Error estimates for viscous Burgers' equation using deep learning method Open
The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value pr…
View article: Neural network approaches for parameterized optimal control
Neural network approaches for parameterized optimal control Open
Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offlin…
View article: Emerging Technologies in Global South Classrooms: Teachers Imagining Future of Education
Emerging Technologies in Global South Classrooms: Teachers Imagining Future of Education Open
View article: Diabetic Retinopathy Eye Disease Detection Using Machine Learning
Diabetic Retinopathy Eye Disease Detection Using Machine Learning Open
INTRODUCTION: Diabetic retinopathy is the name given to diabetes problems that harm the eyes. Its root cause is damage to the blood capillaries in the tissue that is light-sensitive in the rear of the eye. Over time, having excessive blood…
View article: Neural Network Approaches for Parameterized Optimal Control
Neural Network Approaches for Parameterized Optimal Control Open
We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stag…
View article: Learning Control Policies of Hodgkin-Huxley Neuronal Dynamics
Learning Control Policies of Hodgkin-Huxley Neuronal Dynamics Open
We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic outc…
View article: Widespread amyloid aggregates formation by Zika virus proteins and peptides
Widespread amyloid aggregates formation by Zika virus proteins and peptides Open
Viral pathogenesis typically involves numerous molecular mechanisms. Protein aggregation is a relatively unknown characteristic of viruses, despite the fact that viral proteins have been shown to form terminally misfolded forms. Zika virus…
View article: A mixed finite element method using a biorthogonal system for optimal control problems governed by a biharmonic equation
A mixed finite element method using a biorthogonal system for optimal control problems governed by a biharmonic equation Open
In this article, we consider an optimal control problem governed by a biharmonic equation with clamped boundary conditions. We use the Ciarlet--Raviart formulation combined with a biorthogonal system to obtain an efficient numerical scheme…
View article: Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference
Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference Open
We present two neural network approaches that approximate the solutions of static and dynamic $\unicode{x1D450}\unicode{x1D45C}\unicode{x1D45B}\unicode{x1D451}\unicode{x1D456}\unicode{x1D461}\unicode{x1D456}\unicode{x1D45C}\unicode{x1D45B}…
View article: Japanese Encephalitis Virus: A pan-proteome analysis for aggregation propensities and in vitro validation with Capsid anchor and 2K peptide
Japanese Encephalitis Virus: A pan-proteome analysis for aggregation propensities and in vitro validation with Capsid anchor and 2K peptide Open
Japanese encephalitis infection is a vector-borne disease caused by the flavivirus Japanese encephalitis virus (JEV). It is responsible for severe brain infections in humans worldwide. Given the ubiquitous nature of complications and tropi…
View article: A deep neural network approach for parameterized PDEs and Bayesian inverse problems
A deep neural network approach for parameterized PDEs and Bayesian inverse problems Open
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such proble…
View article: Reinforcement Learning for Adaptive Control of PDE-Constrained Environments
Reinforcement Learning for Adaptive Control of PDE-Constrained Environments Open
View article: Reinforcement Learning for PDE-Based Control Problems
Reinforcement Learning for PDE-Based Control Problems Open
View article: Data-Driven Control Strategies for PDE Environments using Reinforcement Learning.
Data-Driven Control Strategies for PDE Environments using Reinforcement Learning. Open
View article: A Neural Network Approach for Stochastic Optimal Control
A Neural Network Approach for Stochastic Optimal Control Open
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space l…
View article: Deep neural nets with fixed bias configuration
Deep neural nets with fixed bias configuration Open
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 'learn' the network are faced with a very large number (in t…
View article: Reinforcement Learning for PDE Control Problems.
Reinforcement Learning for PDE Control Problems. Open
View article: Nondiffusive variational problems with distributional and weak gradient constraints
Nondiffusive variational problems with distributional and weak gradient constraints Open
In this article, we consider nondiffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the sta…
View article: Deep Neural Nets with Fixed Bias Configuration
Deep Neural Nets with Fixed Bias Configuration Open
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 `learn' the network are faced with a very large number (in t…
View article: Optimal Control, Numerics, and Applications of Fractional PDEs
Optimal Control, Numerics, and Applications of Fractional PDEs Open
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 applications of these operators in imaging science, geophysics, …
View article: Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints
Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints Open
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 is either a function or a Borel measure, leading to the stat…
View article: Novel Deep neural networks for solving Bayesian statistical inverse
Novel Deep neural networks for solving Bayesian statistical inverse Open
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such proble…
View article: Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows Open
View article: Fractional deep neural network via constrained optimization
Fractional deep neural network via constrained optimization Open
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 the network—it ensures all layers are connected to one anothe…
View article: Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the Dual of Fractional-Order Sobolev Spaces
Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the Dual of Fractional-Order Sobolev Spaces Open
View article: Moreau-Yosida regularization for optimal control of fractional PDEs with state constraints: parabolic case
Moreau-Yosida regularization for optimal control of fractional PDEs with state constraints: parabolic case Open
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 the elliptic case, in this paper, we establish several new m…
View article: External optimal control of fractional parabolic PDEs
External optimal control of fractional parabolic PDEs Open
In [Antil et al. Inverse Probl. 35 (2019) 084003.] we introduced a new notion of optimal control and source identification (inverse) problems where we allow the control/source to be outside the domain where the fractional elliptic PDE is f…
View article: Moreau-Yosida Regularization for Optimal Control of Fractional Elliptic Problems with State and Control Constraints
Moreau-Yosida Regularization for Optimal Control of Fractional Elliptic Problems with State and Control Constraints Open
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 program forward and introduce an algorithm to solve such opti…