6 citations · 8 across the 4 of their papers we have counts for
11 papers
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems
Tingwei Meng, Zhen Zhang, Jérôme Darbon +1
Solving high-dimensional optimal control problems in real-time is an important but challenging problem, with applications to multi-agent path planning problems, which have drawn in…
Connecting Hamilton--Jacobi partial differential equations with maximum a posteriori and posterior mean estimators for some non-convex priors
Jérôme Darbon, Gabriel P. Langlois, Tingwei Meng
Many imaging problems can be formulated as inverse problems expressed as finite-dimensional optimization problems. These optimization problems generally consist of minimizing the s…
A Caputo fractional derivative-based algorithm for optimization
Yeonjong Shin, Jérôme Darbon, George Em Karniadakis
We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a ge…
Optimal Trajectories of a UAV Base Station Using Hamilton-Jacobi Equations
Marceau Coupechoux, Jérôme Darbon, Jean-Marc Kélif +1
We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given i…
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
Yeonjong Shin, Jerome Darbon, George Em Karniadakis
Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Gu…
On Bayesian posterior mean estimators in imaging sciences and Hamilton-Jacobi Partial Differential Equations
Jerome Darbon, Gabriel P. Langlois
Variational and Bayesian methods are two approaches that have been widely used to solve image reconstruction problems. In this paper, we propose original connections between Hamilt…