5 citations · 12 across the 14 of their papers we have counts for
16 papers
Data-driven computation for periodic stochastic differential equations
Yao Li, Jiatong Sun
Many stochastic differential equations in various applications like coupled neuronal oscillators are driven by time-periodic forces. In this paper, we extend several data-driven co…
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions
Max Kreider, Peter J. Thomas, Yao Li
For a stochastic differential equation (SDE) that is an Itô diffusion or Langevin equation, the Fokker-Planck operator governs the evolution of the probability density, while its a…
Non-equilibrium steady state for a three-mode energy cascade model
Zaher Hani, Yao Li, Andrea Nahmod +1
Motivated by the central phenomenon of energy cascades in wave turbulence theory, we construct non-equilibrium statistical steady states (NESS), or invariant measures, for a simpli…
Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events
Long Le, Yao Li
The firing dynamics of biological neurons in mathematical models is often determined by the model's parameters, representing the neurons' underlying properties. The parameter estim…
Entropy, mutual information, and systematic measures of structured spiking neural networks
Wenjie Li, Yao Li
The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that based on mutual information…
From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equation
Yao Li
This paper consider the mesoscopic limit of a stochastic energy exchange model that is numerically derived from deterministic dynamics. The law of large numbers and the central lim…
Thermal conductivity and local thermodynamic equilibrium of stochastic energy exchange models
Yao Li, Wenbo Xie
In this paper we study macroscopic thermodynamic properties of a stochastic microscopic heat conduction model that is reduced from deterministic problems. Our goal is to numericall…
Firing rate and spatial correlation in a stochastic neural field model
Yao Li, Hui Xu
This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons…
A data-driven method for the steady state of randomly perturbed dynamics
Yao Li
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condit…
From billiards to thermodynamic laws: I. Stochastic energy exchange model
Yao Li, Lingchen Bu
This paper studies a billiards-like microscopic heat conduction model, which describes the dynamics of gas molecules in a long tube with thermalized boundary. We numerically invest…
Numerical simulation of polynomial-speed convergence phenomenon
Yao Li, Hui Xu
We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on th…
On the polynomial convergence rate to nonequilibrium steady-states
Yao Li
We consider a stochastic energy exchange model that models the 1D microscopic heat conduction in the nonequilibrium setting. In this paper, we prove the existence and uniqueness of…
Systematic Measures of Biological Networks, Part II: Degeneracy, Complexity and Robustness
Yao Li, Yingfei Yi
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this par…
Systematic Measures of Biological Networks, Part I: Invariant measures and Entropy
Yao Li, Yingfei Yi
This paper is Part I of a two-part series devoting to the study of systematic measures in a complex biological network modeled by a system of ordinary differential equations. As th…
Local thermal equilibrium for certain stochastic models of heat transport
Yao Li, Peter Nandori, Lai-Sang Young
This paper is about nonequilibrium steady states (NESS) of a class of stochastic models in which particles exchange energy with their "local environments" rather than directly with…
Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities
Rui Che, Wen Huang, Yao Li +1
In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When is the number of vertic…