Career • 2022.09-present Assistant Professor, ShanghaiTech University • 2018.09-2022.09 Visiting Assistant Professor, University of Massachusetts Amherst, USA • 2017.05-2017.08 NSF Mathematical Sciences Graduate Internship Program, Pacific Northwest National Laboratory, USA Education
• 2018.05, Ph.D. in Mathematics, Louisiana State University, USA • 2012.07, Master in Pure Mathematics, Shanghai University • 2009.07, Bachelor in Mathematics, Ludong University
Research Interest
My research interests include computational methods and stochastic analysis. In computational methods and their numerical analysis, my research emphasizes on the computations of long-term behaviours in stochastic dynamical systems. To be precise, my works focus on the numerical approximations for the invariant probability measures and transitions as rare events. In particular, my current interest focuses on solving these and related problems using machine learning methods, as well as their applications. The works are interdisciplinary, involving Fokker–Planck PDEs, large deviation theory, uncertainty quantification, coupling methods, machine learning methods. In stochastic analysis, I focus on stochastic integration and white noise theory and their applications in (particularly non-adapted) stochastic differential equations.
Selected Publications
• Jiayu Zhai, Matthew Dobson and Yao Li, A deep learning method for solving Fokker–Planck partial differential equations, Proceeding of Mathematical and Scientific Machine Learning (MSML21) (2021). • Xiaoliang Wan and Jiayu Zhai, A minimum action method for dynamical systems with constant time delays, SIAM Journal on Scientific Computing, (2021), 41(1), A541–A565. •Matthew Dobson, Yao Li and Jiayu Zhai, Using coupling methods to estimate sample quality for stochastic differential equations, SIAM/ASA Journal on Uncertainty Quantification (2021), 9(1), 135–162. • Matthew Dobson, Yao Li and Jiayu Zhai, An efficient data-driven solver for Fokker–Planck equations: algorithm and analysis, Communications in Mathematical Sciences (2022), 20(3), 803 – 827. • Xiaoliang Wan, Haijun Yu and Jiayu Zhai, Convergence analysis of a finite element approximation of minimum action methods, SIAM J. Numer. Anal., (2018), 56(3), 1597–1620. • Zhongrui Shi and Jiayu Zhai, $\lambda$ point and $\lambda$ property in generalized Orlicz spaces with |
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