8 citations · 20 across the 6 of their papers we have counts for
6 papers
Dissipation enhancement of planar helical flows and applications to three-dimensional Kuramoto-Sivashinsky and Keller-Segel equations
Yuanyuan Feng, Binbin Shi, Weike Wang
We introduce the planar helical flows on three dimensional torus and study the dissipation enhancement of such flows. We then use such flows as transport flows to solve the three d…
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection
Yuanyuan Feng, Anna L. Mazzucato
We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence…
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Yuanyuan Feng, Tingran Gao, Lei Li +2
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the back…
Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
Yuanyuan Feng, Lei Li, Jian-Guo Liu
We study the Markov semigroups for two important algorithms from machine learning: stochastic gradient descent (SGD) and online principal component analysis (PCA). We investigate t…
A note on one-dimensional time fractional ODEs
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of…
Continuous and discrete one dimensional autonomous fractional ODEs
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
In this paper, we study 1D autonomous fractional ODEs , where is the unknown function and is the generalized Caputo de…