357 citations · 875 across the 60 of their papers we have counts for
10 papers · 1 filter
The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term
Shi Jin, Yuhua Zhu, Enrique Zuazua
We consider the Vlasov-Fokker-Planck equation with random electric field where the random field is parametrized by countably many infinite random variables due to uncertainty. At t…
Convergence of a first-order consensus-based global optimization algorithm
Seung-Yeal Ha, Shi Jin, Doheon Kim
Global optimization of a non-convex objective function often appears in large-scale machine-learning and artificial intelligence applications. Recently, consensus-based optimizatio…
An Uncertainty Quantification Approach to the Study of Gene Expression Robustness
Pierre Degond, Shi Jin, Yuhua Zhu
We study a chemical kinetic system with uncertainty modeling a gene regulatory network in biology. Specifically, we consider a system of two equations for the messenger RNA and mic…
Error estimate of a bi-fidelity method for kinetic equations with random parameters and multiple scales
Irene M. Gamba, Shi Jin, Liu Liu
In this paper, we conduct uniform error estimates of the bi-fidelity method for multi-scale kinetic equations. We take the Boltzmann and the linear transport equations as important…
A consensus-based global optimization method for high dimensional machine learning problems
José A. Carrillo, Shi Jin, Lei Li +1
We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183--204, 2017…
On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation
Esther S. Daus, Shi Jin, Liu Liu
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time beha…
Collective dynamics of opposing groups with stochastic communication
Shi Jin, Ruiwen Shu
We propose models describing the collective dynamics of two opposing groups of individuals with stochastic communication. Individuals from the same group are assumed to align in a…
On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime
François Golse, Shi Jin, Thierry Paul
By using the pseudo-metric introduced in [F. Golse, T. Paul: Archive for Rational Mech. Anal. 223 (2017) 57-94], which is an analogue of the Wasserstein distance of exponent be…
Sharp Decay Estimates in Local Sensitivity Analysis for Evolution Equations with Uncertainties: from ODEs to Linear Kinetic Equations
Anton Arnold, Shi Jin, Tobias Wöhrer
We review the Lyapunov functional method for linear ODEs and give an explicit construction of such functionals that yields sharp decay estimates, including an extension to defectiv…
Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs
Shi Jin, Liu Liu, Giovanni Russo +1
In this work, we study the semi-classical limit of the Schrödinger equation with random inputs, and show that the semi-classical Schrödinger equation produces osci…