3 papers
math.OC2021
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…
math.ST2020
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…
math.OC2019
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…