447 citations · 733 across the 44 of their papers we have counts for
7 papers · 1 filter
Stochastic Wasserstein Hamiltonian Flows
Jianbo Cui, Shu Liu, Haomin Zhou
In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, the probability density space equipped with -Wasserstein metric tensor, via the Wong--Zakai ap…
One or two frequencies? The Iterative Filtering answers
Antonio Cicone, Stefano Serra-Capizzano, Haomin Zhou
The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade…
Neural Monge Map estimation and its applications
Jiaojiao Fan, Shu Liu, Shaojun Ma +2
Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network base…
A continuation multiple shooting method for Wasserstein geodesic equation
Jianbo Cui, Luca Dieci, Haomin Zhou
In this paper, we propose a numerical method to solve the classic -optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continu…
Mean Field Game GAN
Shaojun Ma, Haomin Zhou, Hongyuan Zha
We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a pr…
Learning High Dimensional Wasserstein Geodesics
Shu Liu, Shaojun Ma, Yongxin Chen +2
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagran…
What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
Jianbo Cui, Shu liu, Haomin Zhou
We present a definition of stochastic Hamiltonian process on finite graph via its corresponding density dynamics in Wasserstein manifold. We demonstrate the existence of stochastic…