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03/22/2023
Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep conne...
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01/14/2022
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems
Solving high-dimensional optimal control problems in real-time is an imp...
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11/30/2021
Efficient and robust high-dimensional sparse logistic regression via nonlinear primal-dual hybrid gradient algorithms
Logistic regression is a widely used statistical model to describe the r...
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09/24/2021
Accelerated nonlinear primal-dual hybrid gradient algorithms with applications to machine learning
The primal-dual hybrid gradient (PDHG) algorithm is a first-order method...
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05/28/2021
On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise
We consider image denoising problems formulated as variational problems....
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05/07/2021
Neural network architectures using min plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
Solving high dimensional optimal control problems and corresponding Hami...
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04/22/2021
Connecting Hamilton–Jacobi partial differential equations with maximum a posteriori and posterior mean estimators for some non-convex priors
Many imaging problems can be formulated as inverse problems expressed as...
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04/06/2021
A Caputo fractional derivative-based algorithm for optimization
We propose a novel Caputo fractional derivative-based optimization algor...
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02/04/2021
Optimal Trajectories of a UAV Base Station Using Hamilton-Jacobi Equations
We consider the problem of optimizing the trajectory of an Unmanned Aeri...
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04/03/2020
On the Convergence and generalization of Physics Informed Neural Networks
Physics informed neural networks (PINNs) are deep learning based techniq...
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03/12/2020
On Bayesian posterior mean estimators in imaging sciences and Hamilton-Jacobi Partial Differential Equations
Variational and Bayesian methods are two approaches that have been widel...
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02/22/2020
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
We propose novel connection between several neural network architectures...
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12/20/2018