447 citations · 733 across the 44 of their papers we have counts for
7 papers · 1 filter
New methodology based on energy flux similarity for large-eddy simulation of transitional and turbulent flows
Han Qi, Xinliang Li, Hao Zhou +1
A new methodology based on energy flux similarity is suggested in this paper for large eddy simulation (LES) of transitional and turbulent flows. Existing knowledge reveals that th…
Path Planning in Unknown Environments Using Optimal Transport Theory
Haoyan Zhai, Magnus Egerstedt, Haomin Zhou
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity…
Weak Adversarial Networks for High-dimensional Partial Differential Equations
Yaohua Zang, Gang Bao, Xiaojing Ye +1
Solving general high-dimensional partial differential equations (PDE) is a long-standing challenge in numerical mathematics. In this paper, we propose a novel approach to solve hig…
Method of evolving junction on optimal path planning in flow fields
Haoyan Zhai, Mengxue Hou, Fumin Zhang +1
We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagra…
Collective motion planning for a group of robots using intermittent diffusion
Christina Frederick, Magnus Egerstedt, Haomin Zhou
In this work we establish a simple yet effective strategy, based on optimal transport theory, for enabling a group of robots to accomplish complex tasks, such as shape formation an…
Parametric Fokker-Planck equation
Wuchen Li, Shu Liu, Hongyuan Zha +1
We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite…
Wasserstein Hamiltonian flows
Shui-Nee Chow, Wuchen Li, Haomin Zhou
We establish kinetic Hamiltonian flows in density space embedded with the -Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces…