Xiaoxu Zhong

Xiaoxu Zhong, Shijun Liao

In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs), including one with high dimensionality (up to 12 dimensions). By means of the HAM, convergent series solutions can be quickly obtained with high accuracy for a FBSDE in a 6 dimensional case, within less than $1\%$ CPU time used by a currently reported numerical method for the same case [34]. Especially, as dimensionality enlarges, the increase of computational complexity for the HAM is not as dramatic as this numerical method. All of these demonstrate the validity and high efficiency of the HAM for the backward/forward-backward stochastic differential equations in science, engineering and finance.

Xiaoxu Zhong, Yukun Ye

The spread of diseases has been studied for many years, but it receives a particular focus recently due to the outbreak and spread of COVID-19. Studies show that the spread of COVID-19 can be characterized by the Susceptible-Infectious-Recovered-Deceased (SIRD) model with containment coefficients (due to quarantine and keeping social distance). This project aims to apply the machine learning technique to predict the severity of COVID-19 and the effect of quarantine, keeping social distance, working from home, and wearing masks on the transmission of the disease. This work deepens our understanding of disease transmission and reveals the importance of following policies.