277 citations · 461 across the 25 of their papers we have counts for
28 papers
Shape Alignment via Allen-Cahn Nonlinear-Convection
Daniel Solano, Laurent Younes, Jerome Darbon
This paper demonstrates the impact of a phase field method on shape registration to align shapes of possibly different topology. It yields new insights into the building of discrep…
Automatic selection of the best neural architecture for time series forecasting
Qianying Cao, Shanqing Liu, Alan John Varghese +3
Time series forecasting plays a pivotal role in a wide range of applications, including weather prediction, healthcare, structural health monitoring, predictive maintenance, energy…
Automatic discovery of optimal meta-solvers via multi-objective optimization
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi…
HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models
Tingwei Meng, Zongren Zou, Jérôme Darbon +1
The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic pro…
A time-dependent symplectic network for non-convex path planning problems with linear and nonlinear dynamics
Zhen Zhang, Chenye Wang, Shanqing Liu +2
We propose a novel neural network architecture (TSympOCNet) to address high--dimensional optimal control problems with linear and nonlinear dynamics. An important application of th…
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning
Zongren Zou, Tingwei Meng, Paula Chen +2
Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful predictive power of SciML with methods for quantifying the reliability of the learned m…
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
Paula Chen, Tingwei Meng, Zongren Zou +2
We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processe…
Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems
Paula Chen, Tingwei Meng, Zongren Zou +2
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By…
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…
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…
Hopf-type representation formulas and efficient algorithms for certain high-dimensional optimal control problems
Paula Chen, Jérôme Darbon, Tingwei Meng
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper,…
Lax-Oleinik-type formulas and efficient algorithms for certain high-dimensional optimal control problems
Paula Chen, Jérôme Darbon, Tingwei Meng
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable…
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…
On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise
Jérôme Darbon, Tingwei Meng, Elena Resmerita
We consider image denoising problems formulated as variational problems. It is known that Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise mode…
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
Jérôme Darbon, Peter M. Dower, Tingwei Meng
Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose tw…
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…
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton--Jacobi partial differential equations
Jérôme Darbon, Tingwei Meng
We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamilton…
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…
Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics
Marceau Coupechoux, Jérôme Darbon, Jean-Marc Kélif +1
In this paper, we consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). We consider a map characterized by a traffic intensity of…