5 papers
Numerical stability revisited: A family of benchmark problems for the analysis of explicit stochastic differential equation integrators
Thomas Hudson, Sarah Helfert, Xingjie Helen Li
We revisit the numerical stability of four well-established explicit stochastic integration schemes through a new generic benchmark stochastic differential equation designed to ass…
A Comprehensive Study of Covid 19 in Florida
Julian Bennett, Lauren Eriksen, Xingjie Helen Li
Within the likes of any highly contagious and unpredictable disease, lies a predictable and attainable growth rate that researchers can find in order to make logistical conclusions…
Automated construction of effective potential via algorithmic implicit bias
Xingjie Helen Li, Molei Tao
We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in , where . This approach leverages a recentl…
A One-Dimensional Symmetric Force-Based Blending Method for Atomistic-to-Continuum Coupling
Elaine Gorom-Alexander, Xingjie Helen Li
Inspired by the blending method developed by [P. Seleson, S. Beneddine, and S. Prudhome, \emph{A Force-Based Coupling Scheme for Peridynamics and Classical Elasticity}, (2013)] for…
Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism
Thomas Hudson, Xingjie Helen Li
The Mori-Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and it…