Profile photo of Ning Jiang

Ning Jiang

Department of Mathematics & Statistics · University of Massachusetts Amherst
Email: ningjiang@umass.edu

About

I am a Ph.D. student in Mathematics at the University of Massachusetts Amherst. My research lies at the intersection of stochastic analysis, applied dynamical systems, and machine learning, with applications to epidemiology and opinion dynamics.

Education

  • Ph.D., Mathematics, University of Massachusetts Amherst — Expected May 2026
  • B.S., Mathematics, University of Massachusetts Amherst — May 2021

Research

My research interests are in machine learning and applied dynamical systems, including stochastic stability of stochastic processes, machine learning and data assimilation, and connections to epidemiological models and opinion dynamics.

  • Feynman–Kac–Lyapunov (FKL) framework: Extended a systematic method to construct Lyapunov functions for coupled "driving–driven" SDEs and proposed a neural network solver for the high-dimensional Feynman–Kac equation that yields the Lyapunov pre-factor.
  • Mobility-based SIRS: Introduced a mobility variable to explain overestimation of final size in classical SIR; proved smaller final size for fixed R0 and identifiability of the mobility distribution from infection time series; learned mobility via a feedforward network.
  • ANN prediction of true COVID-19 infections. Recovered daily infections via deconvolution using death counts and a time-varying IFR, then trained a biology-informed neural model mapping confirmed cases/testing/population features to true infections.

Publications

  1. Chu, W., Jiang, N., & Li, Y. Constructing Lyapunov functions of stochastic differential equations by solving the Feynman–Kac equation (2025). Preprint.
  2. Jiang, N., Chu, W., & Li, Y. Modeling, Inference, and Prediction in Mobility-Based Compartmental Models for Epidemiology. SIAM Journal on Applied Mathematics 85, 2355–2375 (2025). DOI
  3. Jiang, N., Kolozsvary, C., & Li, Y. Artificial Neural Network Prediction of COVID-19 Daily Infection Count. Bulletin of Mathematical Biology 86, 49 (2024). DOI

Presentations

  • Talk, October 2025, AMS Fall Southeastern Sectional Meeting, New Orleans, LA
  • Talk, May 2025, SIAM Conference on Applications of Dynamical Systems, Denver, CO
  • Poster, October 2024, SIAM Conference on Mathematics of Data Science, Atlanta, GA

Teaching

  • Instructor: Calculus I (Fall 2023, Fall 2025)
  • Teaching Assistant: Actuarial Financial Math; Calculus for Life & Social Sciences I; Calculus I & II (Fall 2021–Spring 2024)