10 citations · 25 across the 13 of their papers we have counts for
16 papers
Scalable Unbalanced Sobolev Transport for Measures on a Graph
Tam Le, Truyen Nguyen, Kenji Fukumizu
Optimal transport (OT) is a popular and powerful tool for comparing probability measures. However, OT suffers a few drawbacks: (i) input measures required to have the same mass, (i…
Dynamic Flows on Curved Space Generated by Labeled Data
Xinru Hua, Truyen Nguyen, Tam Le +2
The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to ge…
Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics
Tam Le, Truyen Nguyen, Dinh Phung +1
Optimal transport (OT) is a popular measure to compare probability distributions. However, OT suffers a few drawbacks such as (i) a high complexity for computation, (ii) indefinite…
Adversarial Regression with Doubly Non-negative Weighting Matrices
Tam Le, Truyen Nguyen, Makoto Yamada +2
Many machine learning tasks that involve predicting an output response can be solved by training a weighted regression model. Unfortunately, the predictive power of this type of mo…
Entropy Partial Transport with Tree Metrics: Theory and Practice
Tam Le, Truyen Nguyen
Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious draw…
On the Convergence of Gradient Descent in GANs: MMD GAN As a Gradient Flow
Youssef Mroueh, Truyen Nguyen
We consider the maximum mean discrepancy () GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized $\mathr…
Boundary regularity for quasilinear elliptic equations with general Dirichlet boundary data
Truyen Nguyen
We study global regularity for solutions of quasilinear elliptic equations of the form $÷\A(x,u,\nabla u) = ÷\F $ in rough domains in with nonhomogeneous Dirichlet bound…
Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations
Giuseppe Di Fazio, Truyen Nguyen
We study regularity for solutions of quasilinear elliptic equations of the form $÷\A(x,u,\nabla u) = ÷\F $ in bounded domains in . The vector field $\A$ is assumed to be cont…
Interior Calderón-Zygmund estimates for solutions to general parabolic equations of -Laplacian type
Truyen Nguyen
We study general parabolic equations of the form whose principal part depends on the solution itself. The vector field is assume…
Interior gradient estimates for quasilinear elliptic equations
Truyen Nguyen, Tuoc Phan
We study quasilinear elliptic equations of the form in bounded domains in , . The vector field…
Local gradient estimates for degenerate elliptic equations
Luan Hoang, Truyen Nguyen, Tuoc Phan
This paper is focused on the local interior -regularity for weak solutions of degenerate elliptic equations of the form $\text{div}[\mathbf{a}(x,u, \nabla u)] +b(x, u…
Global magnetic confinement for the 1.5D Vlasov-Maxwell system
Toan T. Nguyen, Truyen V. Nguyen, Walter A. Strauss
We establish the global-in-time existence and uniqueness of classical solutions to the "one and one-half" dimensional relativistic Vlasov--Maxwell systems in a bounded interval, su…
Non-existence and Non-uniqueness for Multidimensional Sticky Particle Systems
Alberto Bressan, Truyen Nguyen
The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cau…
Self-diffusion and cross-diffusion equations: -estimates and global existence of smooth solutions
Luan T. Hoang, Tuoc V. Phan, Truyen V. Nguyen
We investigate the global time existence of smooth solutions for the Shigesada-Kawasaki-Teramoto system of cross-diffusion equations of two competing species in population dynamics…
Interior second derivative estimates for solutions to the linearized Monge--Ampère equation
Cristian E. Gutiérrez, Truyen Nguyen
Let be a bounded convex domain and be a convex function such that is sufficiently smooth on and the Monge--Ampère measure $\det D^2ϕ…
Geometric properties of boundary sections of solutions to the Monge--Ampère equation and applications
Nam Q. Le, Truyen Nguyen
In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge-Ampère equations: the engulfing and separating properties and volume…