447 citations · 733 across the 44 of their papers we have counts for
44 papers
High-dimensional Optimal Density Control with Wasserstein Metric Matching
Shaojun Ma, Mengxue Hou, Xiaojing Ye +1
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable age…
Parameterized Wasserstein Hamiltonian Flow
Hao Wu, Shu Liu, Xiaojing Ye +1
In this work, we propose a numerical method to compute the Wasserstein Hamiltonian flow (WHF), which is a Hamiltonian system on the probability density manifold. Many well-known PD…
RRCNN: A novel signal decomposition approach based on recurrent residue convolutional neural network
Feng Zhou, Antonio Cicone, Haomin Zhou
The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decompositio…
Why Shallow Networks Struggle to Approximate and Learn High Frequencies
Shijun Zhang, Hongkai Zhao, Yimin Zhong +1
In this work, we present a comprehensive study combining mathematical and computational analysis to explain why a two-layer neural network struggles to handle high frequencies in b…
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Nathan Gaby, Xiaojing Ye, Haomin Zhou
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order mode…
Optimal control for stochastic nonlinear Schrodinger equation on graph
Jianbo Cui, Shu Liu, Haomin Zhou
We study the optimal control formulation for stochastic nonlinear Schrodinger equation (SNLSE) on a finite graph. By viewing the SNLSE as a stochastic Wasserstein Hamiltonian flow…
Discrete Langevin Sampler via Wasserstein Gradient Flow
Haoran Sun, Hanjun Dai, Bo Dai +2
It is known that gradient-based MCMC samplers for continuous spaces, such as Langevin Monte Carlo (LMC), can be derived as particle versions of a gradient flow that minimizes KL di…
New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: the IMFogram algorithm
Antonio Cicone, Wing Suet Li, Haomin Zhou
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have…
Wasserstein Hamiltonian flow with common noise on graph
Jianbo Cui, Shu Liu, Haomin Zhou
We study the Wasserstein Hamiltonian flow with a common noise on the density manifold of a finite graph. Under the framework of stochastic variational principle, we first develop t…
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…
Time-frequency representation of nonstationary signals: the IMFogram
Philippe Barbe, Antonio Cicone, Wing Suet Li +1
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they pres…
Time Discretizations of Wasserstein-Hamiltonian Flows
Jianbo Cui, Luca Dieci, Haomin Zhou
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the -Wasserstein metric. Based on discrete optimal transport theory, several…
Numerical Solution of Inverse Problems by Weak Adversarial Networks
Gang Bao, Xiaojing Ye, Yaohua Zang +1
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomogra…
Neural Parametric Fokker-Planck Equations
Shu Liu, Wuchen Li, Hongyuan Zha +1
In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a for…
Learning Cost Functions for Optimal Transport
Shaojun Ma, Haodong Sun, Xiaojing Ye +2
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained con…
Learning Stochastic Behaviour from Aggregate Data
Shaojun Ma, Shu Liu, Hongyuan Zha +1
Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one tim…
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…