I am on MathSciNet, Google Scholar, ORCID, ResearchGate and GitHub.
Research Areas and Topics
Probability: stochastic analysis, small random perturbations of dynamical systems, large deviations, metastability, stochastic averaging principle, reaction-diffusion equations and wave front propagation in random media, stochastic fluid mechanics, turbulence models, small mass limit of the Langevin equation (Smoluchowski-Kramers approximation), homogenization and multiscale problems, system of fast-slow stochastic reaction diffusion equations.
Data Sciences/Machine Learning/Optimization: covariance matrix estimation under High-Dimensional-Low-Sample-Size (HDLSS) setting, with applications to regularized linear discriminant analysis in Electronic Health Records (EHR) data, variational inference of human mobility patterns via Hawkes processes, convergence analysis of stochastic approximation algorithms (e.g. stochastic gradient descent) that are used in solving stochastic optimization problems, real-world applications of Markov Decision Processes (MDP) and Reinforcement Learning.
Operations Research: Smart Grid, Energy Management, Reinforcement Learning applied to Intelligent and Digital Manufacturing Systems.
Math Biology: Molecular motor (Brownian rachet), Ao’s potential function and its relation with stochastic dynamical systems.
Research Team
PhD/Master’s student with research topics that are closely related to cutting-edge technology innovation. We hope these efforts could lead them to better adaptation for the job-market and the business-world in general.
Current Doctoral Students
- Jiali Zhang, 2022-now, currently working with me on reinforcement learning and advanced manufacturing.
Current Master’s Students
- Paul O’Conner, 2022-now, currently working with me on blockchain and cryptocurrency.
Alumni
- Louis Steinmeister, PhD, 2019-2020, has been working with me on reinforcement learning and advanced manufacturing (paper).
- Austin Vandegriffe, Master’s, 2019-2021, has been working with me on the asymptotic properties of wide neural networks (project).
- Theophile Abraham, Intern, 2020, has been working with me on data-analytic problems related to image processing (t-SNE) and Deep Learning (project).
- Jiaojiao Yang, Visiting Scholar, 2019-2020, has been working with me on stochastic dynamical systems (paper).
Preprints in Submission/Revision
- [2] Hu, W., Qian, H., On the Posterior Distribution of a Random Process Conditioned on Empirical Frequencies of a Finite Path: the i.i.d and finite Markov chain case. [arXiv]
- [1] Hu, W., Jiang, T., Kathariya, B., Abrol, V., Li, Z., Subspace Interpolation and Indexing on Stiefel and Grassmann Manifolds as a Lightweight Inference Engine. [preprint] [source code]