31 citations · 64 across the 11 of their papers we have counts for
12 papers
Front location determines convergence rate to traveling waves
Jing An, Christopher Henderson, Lenya Ryzhik
We propose a novel method for establishing the convergence rates of solutions to reaction-diffusion equations to traveling waves. The analysis is based on the study of the travelin…
Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks
Jing An, Jianfeng Lu
We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local Łojas…
Voting models and semilinear parabolic equations
Jing An, Christopher Henderson, Lenya Ryzhik
We present probabilistic interpretations of solutions to semi-linear parabolic equations with polynomial nonlinearities in terms of the voting models on the genealogical trees of b…
Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts
Jing An, Christopher Henderson, Lenya Ryzhik
We uncover a seemingly previously unnoticed algebraic structure of a large class of reaction-diffusion equations and use it, in particular, to study the long time behavior of the s…
Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation
Jing An, Christopher Henderson, Lenya Ryzhik
We consider the long time behavior of the solutions to the Burgers-FKPP equation with advection of a strength . This equation exhibits a transition from pulled to p…
Combining resampling and reweighting for faithful stochastic optimization
Jing An, Lexing Ying
Many machine learning and data science tasks require solving non-convex optimization problems. When the loss function is a sum of multiple terms, a popular method is the stochastic…
Why resampling outperforms reweighting for correcting sampling bias with stochastic gradients
Jing An, Lexing Ying, Yuhua Zhu
A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proporti…
On the gradient flow structure of the isotropic Landau equation
Jing An, Lexing Ying
We prove that the isotropic Landau equation equipped with the Coulomb potential introduced by Krieger-Strain and Gualdani-Guillen can be identified with the gradient flow of the en…
Searching for correlations in GAIA DR2 unbound star trajectories
Francesco Montanari, David Barrado, Juan García-Bellido
Scattering events with compact objects are expected in the primordial black hole (PBH) cold dark matter (CDM) scenario due to close encounters between stars and PBH in the dense en…
Global well-posedness for the Euler alignment system with mildly singular interactions
Jing An, Lenya Ryzhik
We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutio…
Stochastic modified equations for the asynchronous stochastic gradient descent
Jing An, Jianfeng Lu, Lexing Ying
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more infor…
Fast algorithms for integral formulations of steady-state radiative transfer equation
Yuwei Fan, Jing An, Lexing Ying
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a s…