JIAYU ZHAI (JERRY)
Visiting Assistant Professor

RESEARCH INTERESTS:

Numerical Analysis: Minimum action methods for large deviation principle, Numerical methods for invariant probability measures, Machine learning methods and analysis, Numerical methods for stochastic differential equations and stochastic modeling, Uncertainty quantification.

Stochastic Analysis: Stochastic Integration, White Noise Theory, Stochastic differential equations.


WORK EXPERIENCE:

Visiting Assistant Professor:

University of Massachusetts Amherst, Sep.2018–Present

Research Assistant:

Louisiana State University, Feb.2016–May.2018

NSF Mathematical Sciences Graduate Internship Program:

Pacific Northwest National Laboratory, May.2017-Jul.2017

Teaching Assistant:

Louisiana State University, Aug.2012–Feb.2016

Teaching Assistant:

Shanghai University, Sep.2011–Jan.2012


FUNDS, AWARDS AND HONORS:

NSF Funding, Co-PI.

Analysis and Data-Driven Computation for Nonequilibrium Thermodynamic Models

(Award Number: 2108628, PI: Dr. Yao Li, NSF Organization: DMS, Total Award Amount: $225,549.00), 2021-2024.

MSP Research Support Funds

University of Massachusetts Amherst, 2018-2021

Pasquale Porcelli Graduate Student Academic Excellence Award

Louisiana State University, 2013

Graduate School Enrichment

Louisiana State University, 2012-2016

Innovation Fund of Academic Research for Graduate Students

Shanghai University, 2011-2012


PUBLICATIONS:

1. 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).

2. 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.

3. 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.

4. Matthew Dobson, Yao Li and Jiayu Zhai, An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis, Accepted, Communications in Mathematical Sciences (2021), arXiv:1906.02600.

5. Xiaoliang Wan, Haijun Yu and Jiayu Zhai, Convergence analysis of a finite element approximation of minimum action methods, SIAM J. Numer. Anal., 56(3), 1597–1620.

6. Hui-Hsiung Kuo, Sudip Sinha and Jiayu Zhai, Stochastic Differential Equations with Anticipating Initial Conditions, Communications on Stochastic Analysis 12, no. 4 (2018) 473–485.

7. Chii-Ruey Hwang, Hui-Hsiung Kuo, Kimiaki Saitô and Jiayu Zhai, Near-martingale property of anticipating stochastic integration, Communications on Stochastic Analysis 11 (2017), no. 4, 491-504.

8. Chii-Ruey Hwang, Hui-Hsiung Kuo, Kimiaki Saitô and Jiayu Zhai, A general Itô formula for adapted and instantly independent stochastic processes, Communications on Stochastic Analysis 10, no.3 (2016) 341–362.

9. Zhongrui Shi and Jiayu Zhai, λ-point and λ-property in generalized Orlicz spaces with Luxemburg norm, Journal of East China Normal University (Natural Science), 1 (2012), 63–73.


PREPRINTS AND WORKS IN PROGRESS:

1. Jiayu Zhai, Quantify the dynamics from invariant distribution using GANs, Work in progress (2021).

2. Jiayu Zhai, Xiaoliang Wan, Yao Li, A flow-GANs for dynamics quantification via block-triangular mapping, Work in progress (2021).

3. Yao Li, Jiayu Zhai, Matthew Dobson, Yaping Yuan, A hybrid reinforcement method for injection measure in low density regions, Work in progress (2021).

4. Yulong Lu, Jiayu Zhai, Yao Li, Neural network representation of solutions to convection–diffusion equations in Barron Spaces, Work in progress (2021).

5. Jiayu Zhai and Liwen Ouyang,, A data-driven method for invariant probability measures of nonlinear dynamical systems driven by non-Gaussian Lévy processes, Work in progress (REU program as a supervisor at UMass Amherst).

6. Jiayu Zhai, Xiaoliang Wan and Bin Zheng, Multigrid minimum action method, In preparation.

7. Jiayu Zhai and Xiaoliang Wan, A minimum action method by augmented Lagrange multipliers for delayed stochastic dynamical systems, In preparation.

8. Jiayu Zhai, Huan Lei and Xiaoliang Wan, MAM for systems with degenerated noises, In preparation.

9. Hui-Hsiung Kuo, Sudip Sinha and Jiayu Zhai, A Black-Scholes model with anticipating initial conditions, Preprint to be submitted (2021).


CONFERENCES, WORKSHOPS AND SUMMER SCHOOLS:

Mathematical and Scientific Machine Learning (MSML21)

Presented Talk: A Deep Learning Method for Solving Fokker-Planck Equations

Zoom virtual conference, August 16–19, 2021.

SIAM Conference on Applications of Dynamical Systems (DS21)

Presented Talk: A Neural Network Approximation for Invariant Measures in Stochastic Dynamical Systems

Zoom virtual conference, May 23–27, 2021.

The Second Northeast Conference on Dynamical Systems

Presented Talk: A Data-Driven Solver for Steady State Distributions of Stochastic Dynamical Systems

University of Massachusetts Amherst, Amherst, MA, November 15–17, 2019.

SIAM Conference on Computational Science and Engineering (CSE18)

Presented Talk:Transitions as Rare Events in Stochastic Delayed Systems

Spokane, WA, February 25– March 1 2019.

SIAM Conference on Uncertainty Quantification (UQ18)

Presented Talk: Temporal Minimum Action Method for Delayed System

Orange County, CA, April 16-19, 2018.

The Finite Element Rodeo 2018

Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, February 23-24, 2018.

Scientific Computing Around Louisiana (SCALA 2018)

Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, February 2-3, 2018.

Joint Mathematics Meeting (JMM 2018)

San Diego Convention Center, San Diego, CA, January 10-13, 2018.

The Finite Element Circus 2017

Presented Talk: Convergence Analysis of Finite Element Approximation of Large Deviation Principle

College of Natural and Mathematical Sciences, UMBC, Baltimore, MD, October 20-21, 2017.

Scientific Computing Around Louisiana (SCALA2017)

Presented Talk: Convergence Analysis of Finite Element Approximation of Large Deviation Principle

Scientific Computing Around Louisiana (SCALA2016)

Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, February 12-13, 2016.

The 8th International Congresson Industrial and Applied Mathematics (ICIAM2015)

Beijing, China, August 10-14, 2015.

The 3rd International Conference on Analytic Mathematics and its Application

Presented Talk: λ-Point and λ-Property in Generalized Orlicz Spaces

Xinyang, China, August 8-12, 2011.

The 16th National Summer School of Mathematics for Graduate Students

Chern Institute of Mathematics, Nankai University, Tianjin, China, August 1-19, 2011

International Conference on Convex Geometric Analysis, Integral Geometry and Related Topics

Shanghai University, Shanghai, China, June 21-24, 2011.


INVITED LOCAL TALKS:

Deep Density Estimation via Invertible Block-Triangular Mappings

Seminar on Mathematics of Machine Learning

University of Massachusetts Amherst, Nov. 2021.

A Neural Network Approximation for Invariant Measures in Stochastic Dynamical Systems

Nanjing University, May 2021.

Data-Driven Methods for Fokker–Planck Partial Differential Equations

CCMA Seminar on Mathematics of Data and Computation

Pennsylvania State University and Peking University Jointly, Zoom presentation, Dec. 2021.

Minimum Action Methods for Transitions in Stochastic Dynamical Systems

Applied Mathematics Seminar

Northeast Normal University, Zoom presentation, Oct. 2020.

Data-Driven Methods for Fokker–Planck Partial Differential Equations

Scientific Computing and Numerical Analysis Seminar

Center for Computation and Technology, Louisiana State University, Cancelled due to COVID-19, Mar. 2020.

A Data-Driven Solver for Steady State Distributions of Stochastic Dynamical Systems

Applied Mathematics Seminar

Nanjing, China, Dec. 2019.

A Data-Driven Solver for Steady State Distributions of Stochastic Dynamical Systems

Applied Mathematics and Computation Seminar

University of Massachusetts Amherst, Sep. 2019.

Convergence Analysis of a Finite Element Approximation of Minimum Action Methods

Numerical Methods Seminar

Worcester Polytechnic Institute, Nov. 2018.

Multilevel Convergence Analysis of a Finite Element Approximation of Minimum Action Methods

Applied Mathematics and Computation Seminar

University of Massachusetts Amherst, Oct. 2018.

Markov Property (Series Talks)

Weekly Group Seminar

University of Massachusetts Amherst, Fall 2018.

Multilevel Monte Carlo Methods for PDE

Weekly Computational Group Seminar

Louisiana State University, Oct. 2017.

Banach Spaces, Orlicz Spaces and Related Theories (Series Talks)

Weekly Graduate Student Seminar on Functional Analysis

Shanghai University, Sep. 2009-May. 2011.

Linear Topological Spaces

Graduate Student Seminar

Shanghai University, Dec. 2009.

Convex Bodies: The Brunn-Minkowski Theory

Graduate Student Seminar

Shanghai University, Dec. 2009.


SUPERVISION EXPERIENCE:

Research Experiences for Undergraduates (REU), Summer 2020

Student: Liwen Ouyang

Topic: A data-driven method for invariant probability measures of nonlinear dynamical systems driven by non-Gaussian Lévy processes (paper in preparation)

University of Massachusetts Amherst