2 citations · 2 across the 6 of their papers we have counts for
7 papers
A Unified Variational Framework for Optimal Transport with Lagrangian Costs
Hailiang Liu
We investigate optimal transport distances induced by general Lagrangian action functionals. Extending the classical Monge - Kantorovich and Benamou - Brenier theories, we derive a…
A Primal-Dual Level Set Method for Computing Geodesic Distances
Hailiang Liu, Laura Zinnel
The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance…
A Generalized Energy-Based Adaptive Gradient Method for Optimization
Lin Feng, Hailiang Liu
Adaptive Gradient Descent with Energy (AEGD) is a variant of Gradient Descent (GD) designed to address step size sensitivity through an energy-based formulation. AEGD is notable fo…
Variational structure of Fokker-Planck equations with variable mobility
Hailiang Liu, Athanasios E. Tzavaras
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced…
The Onsager principle and structure preserving numerical schemes
Huangxin Chen, Hailiang Liu, Xianmin Xu
We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial d…
Data-driven optimal control with neural network modeling of gradient flows
Xuping Tian, Baskar Ganapathysubramanian, Hailiang Liu
Extracting physical laws from observation data is a central challenge in many diverse areas of science and engineering. We propose Optimal Control Neural Networks (OCN) to learn th…
Adaptive Preconditioned Gradient Descent with Energy
Hailiang Liu, Levon Nurbekyan, Xuping Tian +1
We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied…