6 citations · 8 across the 4 of their papers we have counts for
8 papers · 1 filter
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…
Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architectures
Jerome Darbon, Gabriel P. Langlois, Tingwei Meng
We propose new and original mathematical connections between Hamilton-Jacobi (HJ) partial differential equations (PDEs) with initial data and neural network architectures. Specific…
On Decomposition Models in Imaging Sciences and Multi-time Hamilton-Jacobi Partial Differential Equations
Jérôme Darbon, Tingwei Meng
This paper provides new theoretical connections between multi-time Hamilton-Jacobi partial differential equations and variational image decomposition models in imaging sciences. We…