37 citations · 162 across the 25 of their papers we have counts for
26 papers
Coadjoint averaging and cross-scale fluxes in a fast-slow stochastic Euler-Arnold system on
Wenqing Hu
We study the emergence of (cross-scale) fluxes associated with energy and enstrophy in a stochastic version of Zeitlin's approximation of 2-d Euler dynamics. Motivated by t…
Wave propagation for 1-dimensional reaction-diffusion equations with nonzero random drift
Dihang Guan, Hui He, Wenqing Hu +1
We consider the wave propagation for a reaction-diffusion equation on the real line, with a random drift and Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) type nonlinear reaction.…
On the Posterior Distribution of a Random Process Conditioned on Empirical Frequencies of a Finite Path: the i.i.d and finite Markov chain case
Wenqing Hu, Hong Qian
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the…
Stochastic Recursive Momentum Method for Non-Convex Compositional Optimization
Huizhuo Yuan, Wenqing Hu
We propose a novel stochastic optimization algorithm called STOchastic Recursive Momentum for Compositional (STORM-Compositional) optimization that minimizes the composition of exp…
Wave propagation for reaction-diffusion equations on infinite random trees
Wai-Tong Louis Fan, Wenqing Hu, Grigory Terlov
The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provide…
On the Noisy Gradient Descent that Generalizes as SGD
Jingfeng Wu, Wenqing Hu, Haoyi Xiong +3
The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and t…
Quasi-potential as an implicit regularizer for the loss function in the stochastic gradient descent
Wenqing Hu, Zhanxing Zhu, Haoyi Xiong +1
We interpret the variational inference of the Stochastic Gradient Descent (SGD) as minimizing a new potential function named the \textit{quasi-potential}. We analytically construct…
On the long-time behavior of a perturbed conservative system with degeneracy
Wenqing Hu
We consider in this work a model conservative system subject to dissipation and Gaussian-type stochastic perturbations. The original conservative system possesses a continuous set…
On the Global Convergence of Continuous-Time Stochastic Heavy-Ball Method for Nonconvex Optimization
Wenqing Hu, Chris Junchi Li, Xiang Zhou
We study the convergence behavior of the stochastic heavy-ball method with a small stepsize. Under a change of time scale, we approximate the discrete method by a stochastic differ…
Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations
Wenqing Hu, Michael Salins, Konstantinos Spiliopoulos
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow comp…
A convergence analysis of the perturbed compositional gradient flow: averaging principle and normal deviations
Wenqing Hu, Chris Junchi Li
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of t…
On the fast convergence of random perturbations of the gradient flow
Jiaojiao Yang, Wenqing Hu, Chris Junchi Li
We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse…
FWDA: a Fast Wishart Discriminant Analysis with its Application to Electronic Health Records Data Classification
Haoyi Xiong, Wei Cheng, Wenqing Hu +2
Linear Discriminant Analysis (LDA) on Electronic Health Records (EHR) data is widely-used for early detection of diseases. Classical LDA for EHR data classification, however, suffe…
Itô's formula, the stochastic exponential and change of measure on general time scales
Wenqing Hu
We provide an Itô's formula for stochastic dynamical equation on general time scales. Based on this Itô's formula we give a closed form expression for stochastic exponential on gen…
On 2d incompressible Euler equations with partial damping
Tarek Elgindi, Wenqing Hu, Vladimir Sverak
We consider various questions about the 2d incompressible Navier-Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.
Dynamics of geodesic flows with random forcing on Lie groups with left-invariant metrics
Wenqing Hu, Vladimir Sverak
We consider stochastic perturbations of geodesic flow for left-invariant metrics on finite-dimensional Lie groups and study the Hörmander condition and some properties of the solut…
Hypoelliptic multiscale Langevin diffusions: Large deviations, invariant measures and small mass asymptotics
Wenqing Hu, Konstantinos Spiliopoulos
We consider a general class of non-gradient hypoelliptic Langevin diffusions and study two related questions. The first one is large deviations for hypoelliptic multiscale diffusio…
Wave front propagation for a reaction-diffusion equation in narrow random channels
Mark Freidlin, Wenqing Hu
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making…
On diffusion in narrow random channels
Mark Freidlin, Wenqing Hu
We consider in this paper a solvable model for the motion of molecular motors. Based on the averaging principle, we reduce the problem to a diffusion process on a graph. We then ca…
On stochasticity in nearly-elastic systems
Mark Freidlin, Wenqing Hu
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that inst…
Smoluchowski-Kramers approximation in the case of variable friction
Mark Freidlin, Wenqing Hu
We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classic…
On perturbations of generalized Landau-Lifshitz dynamics
Mark Freidlin, Wenqing Hu
We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in . The Landau-Lifshitz equation for the magnetization dynamics in ferroma…
On second order elliptic equations with a small parameter
Mark Freidlin, Wenqing Hu
The Neumann problem with a small parameter is considered in this paper.…
Random perturbations of dynamical systems with reflecting boundary and corresponding PDE with a small parameter
Wenqing Hu, Lucas Tcheuko
We study the asymptotic behavior of a diffusion process with small diffusion in a domain . This process is reflected at with respect to a co-normal direction pointi…