87 citations · 276 across the 17 of their papers we have counts for
17 papers
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…
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…
In-Context Operator Learning with Data Prompts for Differential Equation Problems
Liu Yang, Siting Liu, Tingwei Meng +1
This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new…
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…
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…
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…
Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates
Liu Yang, Tingwei Meng, George Em Karniadakis
We propose a simple but effective modification of the discriminators, namely measure-conditional discriminators, as a plug-and-play module for different GANs. By taking the generat…
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…
TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds
Ting Wei Meng, Gary Pui-Tung Choi, Lok Ming Lui
In recent decades, the use of 3D point clouds has been widespread in computer industry. The development of techniques in analyzing point clouds is increasingly important. In partic…
The Theory of Computational Quasi-conformal Geometry on Point Clouds
Ting Wei Meng, Lok Ming Lui
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been…