Yanzhao Cao | Auburn University (original) (raw)
Papers by Yanzhao Cao
SIAM Journal on Numerical Analysis, 2017
IMA Journal of Numerical Analysis, 2017
arXiv (Cornell University), Oct 21, 2021
Discrete and Continuous Dynamical Systems - S
We develop a backward stochastic differential equation based probabilistic machine learning metho... more We develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.
ArXiv, 2021
A splitting scheme for backward doubly stochastic differential equations is proposed. The main id... more A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic differential equation. The backward stochastic differential equation and the stochastic differential equation are then approximated by first order finite difference schemes, which results in a first order scheme for the backward doubly stochastic differential equation. Numerical experiments are conducted to illustrate the convergence rate of the proposed scheme.
The numerical solution of backward doubly stochastic differential equations (BDSDES) and the rela... more The numerical solution of backward doubly stochastic differential equations (BDSDES) and the related stochastic partial differential equations (Zakai equations) are considered. First order algorithms are constructed using a generalized Itô-Taylor formula for two-sided stochastic differentials. The convergence order is proved through rigorous error analysis. Numerical experiments are carried out to demonstrate the efficiency of the proposed numerical scheme.
Numerical Methods for Partial Differential Equations, 2019
SIAM/ASA Journal on Uncertainty Quantification, 2016
Communications in Computational Physics, 2014
Nonlinear filter problems arise in many applications such as communications and signal processing... more Nonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.
International Journal for Uncertainty Quantification, 2016
Stochastics and Dynamics, 2017
We propose an efficient algorithm to perform nonlinear data assimilation for Korteweg–de Vries so... more We propose an efficient algorithm to perform nonlinear data assimilation for Korteweg–de Vries solitons. In particular we develop a reduced particle filtering method to reduce the dimension of the problem. The method decomposes a solitonic pulse into a clean soliton and small radiative noise, and instead of inferring the complete pulse profile, we only infer the two soliton parameters with particle filter. Numerical examples are provided to demonstrate that the proposed method can provide rather accurate results, while being much more computationally affordable than a standard particle filter.
International Journal for Uncertainty Quantification, 2011
SIAM/ASA Journal on Uncertainty Quantification, 2014
Journal of Complexity, 2014
A shape design model that reduces the amount of noise radiated from aircraft turbofan engines is ... more A shape design model that reduces the amount of noise radiated from aircraft turbofan engines is studied in this paper. The model is formulated as shape control of the Helmholtz equation with radiation boundary conditions on part of the boundary and incoming waves specified as the source. Existence of optimal shape is proved to show that the model is appropriately established. A numerical experiment is conducted to demonstrate the efficiency of the model.
Abstract The distribution of larval subfossil chironomids in surface sediment samples obtained fr... more Abstract The distribution of larval subfossil chironomids in surface sediment samples obtained from Bosten lake was analysed, and ordination methods were used to identify the influences of physical and chemical parameters on the abundance and diversity of chironomids. A total of 18 chironomid taxa was identified across the 32 samples, 15 of which showed minimum abundance of> 1% and were present in more than one site.
The numerical solutions of decoupled forward backward doubly stochastic differential equations an... more The numerical solutions of decoupled forward backward doubly stochastic differential equations and the related stochastic partial differential equations (Zakai equations) are considered. Numerical algorithms are constructed using reference equations. Rate of convergence is obtained through rigorous error analysis. Numerical experiments are carried out to verify the rate of convergence results and to demonstrate the efficiency of the proposed numerical algorithms.
ABSTRACT In this paper we study the dynamics of a vector-transmitted disease under two assumption... more ABSTRACT In this paper we study the dynamics of a vector-transmitted disease under two assumptions. We first look at time dependent prevention and treatment efforts where optimal control theory is applied. Using analytical and numerical techniques, it is shown that there are control efforts for treatment of hosts and prevention of host-vector contacts with minimal cost and side effects. Then we considered the autonomous counter part of the first mode and here we calculated an epidemiological parameter.
SIAM Journal on Numerical Analysis, 2017
IMA Journal of Numerical Analysis, 2017
arXiv (Cornell University), Oct 21, 2021
Discrete and Continuous Dynamical Systems - S
We develop a backward stochastic differential equation based probabilistic machine learning metho... more We develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.
ArXiv, 2021
A splitting scheme for backward doubly stochastic differential equations is proposed. The main id... more A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic differential equation. The backward stochastic differential equation and the stochastic differential equation are then approximated by first order finite difference schemes, which results in a first order scheme for the backward doubly stochastic differential equation. Numerical experiments are conducted to illustrate the convergence rate of the proposed scheme.
The numerical solution of backward doubly stochastic differential equations (BDSDES) and the rela... more The numerical solution of backward doubly stochastic differential equations (BDSDES) and the related stochastic partial differential equations (Zakai equations) are considered. First order algorithms are constructed using a generalized Itô-Taylor formula for two-sided stochastic differentials. The convergence order is proved through rigorous error analysis. Numerical experiments are carried out to demonstrate the efficiency of the proposed numerical scheme.
Numerical Methods for Partial Differential Equations, 2019
SIAM/ASA Journal on Uncertainty Quantification, 2016
Communications in Computational Physics, 2014
Nonlinear filter problems arise in many applications such as communications and signal processing... more Nonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.
International Journal for Uncertainty Quantification, 2016
Stochastics and Dynamics, 2017
We propose an efficient algorithm to perform nonlinear data assimilation for Korteweg–de Vries so... more We propose an efficient algorithm to perform nonlinear data assimilation for Korteweg–de Vries solitons. In particular we develop a reduced particle filtering method to reduce the dimension of the problem. The method decomposes a solitonic pulse into a clean soliton and small radiative noise, and instead of inferring the complete pulse profile, we only infer the two soliton parameters with particle filter. Numerical examples are provided to demonstrate that the proposed method can provide rather accurate results, while being much more computationally affordable than a standard particle filter.
International Journal for Uncertainty Quantification, 2011
SIAM/ASA Journal on Uncertainty Quantification, 2014
Journal of Complexity, 2014
A shape design model that reduces the amount of noise radiated from aircraft turbofan engines is ... more A shape design model that reduces the amount of noise radiated from aircraft turbofan engines is studied in this paper. The model is formulated as shape control of the Helmholtz equation with radiation boundary conditions on part of the boundary and incoming waves specified as the source. Existence of optimal shape is proved to show that the model is appropriately established. A numerical experiment is conducted to demonstrate the efficiency of the model.
Abstract The distribution of larval subfossil chironomids in surface sediment samples obtained fr... more Abstract The distribution of larval subfossil chironomids in surface sediment samples obtained from Bosten lake was analysed, and ordination methods were used to identify the influences of physical and chemical parameters on the abundance and diversity of chironomids. A total of 18 chironomid taxa was identified across the 32 samples, 15 of which showed minimum abundance of> 1% and were present in more than one site.
The numerical solutions of decoupled forward backward doubly stochastic differential equations an... more The numerical solutions of decoupled forward backward doubly stochastic differential equations and the related stochastic partial differential equations (Zakai equations) are considered. Numerical algorithms are constructed using reference equations. Rate of convergence is obtained through rigorous error analysis. Numerical experiments are carried out to verify the rate of convergence results and to demonstrate the efficiency of the proposed numerical algorithms.
ABSTRACT In this paper we study the dynamics of a vector-transmitted disease under two assumption... more ABSTRACT In this paper we study the dynamics of a vector-transmitted disease under two assumptions. We first look at time dependent prevention and treatment efforts where optimal control theory is applied. Using analytical and numerical techniques, it is shown that there are control efforts for treatment of hosts and prevention of host-vector contacts with minimal cost and side effects. Then we considered the autonomous counter part of the first mode and here we calculated an epidemiological parameter.