37 citations · 44 across the 11 of their papers we have counts for
13 papers
Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions
Gabriel P. Langlois, Akwum Onwunta, Jérôme Darbon
Linear and convex quadratic programs are fundamental problems in optimization. While many methods have been developed for solving these programs in large-scale applications, to our…
Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws
Gabriel P. Langlois, Jerome Darbon, Rongjie Lai +2
High-order numerical methods for conservation laws can generate spurious oscillations near discontinuities. We propose to suppress these oscillations by post-processing the numeric…
Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations
Oluwatosin Akande, Gabriel P. Langlois, Akwum Onwunta
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization…
A fast algorithm for solving the lasso problem exactly without homotopy using differential inclusions
Gabriel P. Langlois, Jérôme Darbon
We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selectio…
Topology optimization for inverse magnetostatics as sparse regression: application to electromagnetic coils for stellarators
Alan A. Kaptanoglu, Gabriel P. Langlois, Matt Landreman
Topology optimization, a technique to determine where material should be placed within a predefined volume in order to minimize a physical objective, is used across a wide range of…
Efficient and robust high-dimensional sparse logistic regression via nonlinear primal-dual hybrid gradient algorithms
Jérôme Darbon, Gabriel P. Langlois
Logistic regression is a widely used statistical model to describe the relationship between a binary response variable and predictor variables in data sets. It is often used in mac…
Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learning
Jérôme Darbon, Gabriel P. Langlois
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike t…
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…
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…
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…
Normal and pathological dynamics of platelets in humans
Gabriel P. Langlois, Morgan Craig, Antony R. Humphries +6
We develop a comprehensive mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo…
Explicit form of spatially linear Navier-Stokes velocity fields
Gabriel Provencher Langlois, George Haller
We show that a smooth linear unsteady velocity field solves the incompressible Navier--Stokes equation if and only if the matrix has zero trace, and $\do…
Asymptotic dynamics of inertial particles with memory
Gabriel Provencher Langlois, Mohammad Farazmand, George Haller
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial par…