Welcome to my homepage.

I am currently an Assistant Professor of Mathematics at the Department of Mathematics and Statistics, Missouri University of Science and Technology (formerly University of Missouri, Rolla).

During 2013-2016 I worked as a Postdoctoral Associate at the School of Mathematics, University of Minnesota, Twin Cities, sponsored by Professor Vladimir Sverak (wikipage).

From 2008-2013 I completed a Ph.D. in Mathematics at the Department of Mathematics, University of Maryland, College Park, under the supervision of Professor Mark Freidlin (wikipage). Before that, during 2004-2008, I got my B.S. degree at the School of Mathematical Sciences, Peking University, under the supervision of Professor Yong Liu.

Here is A history of Dynkin's school.

At Missouri University of Science and Technology (formerly University of Missouri, Rolla):

Spring 2021. MATH 5325. Partial Differential Equations. Section 101 (online asynchronous class via zoom due to COVID-19).

Spring 2021. MATH 6001. Nonlinear Optimization in Machine Learning. Section 101 (online asynchronous class via zoom due to COVID-19). Course Flyer. Course Syllabus. Lecture Notes. Source Code.

At Missouri University of Science and Technology (formerly University of Missouri, Rolla):

Fall 2020. MATH 3304. Elementary Differential Equations. Section 101 (online synchronous class via zoom due to COVID-19). Course Video. Teaching Evaluation. Student Comments.

Fall 2020. MATH 5351. Introduction to Complex Variables. Section 101 (online asynchronous class via zoom due to COVID-19). Teaching Evaluation. Student Comments.

Spring 2020. MATH 6001. Nonlinear Optimization in Machine Learning. Sections 106 and 107 (distant section). Course Flyer. Course Syllabus. Lecture Notes. Source Code. Distance Education. Teaching Evaluation. Student Comments. Teaching Evaluation. Student Comments.

Spring 2020. MATH 3304. Elementary Differential Equations. Section 111. Teaching Evaluation. Student Comments.

Fall 2019. MATH 3304. Elementary Differential Equations. Section 103. Teaching Evaluation. Student Comments.

Fall 2019. MATH 5351. Introduction to Complex Variables. Section 101. Teaching Evaluation. Student Comments.

Spring 2019. MATH 6001B. Nonlinear Optimization in Machine Learning. Section 1B. (New course developed at Missouri S&T!) Course Flyer. Course Syllabus. Lecture Notes. Teaching Evaluation. Student Comments.

Fall 2018. MATH 3304. Elementary Differential Equations. Section 1C. Teaching Evaluation. Student Comments.

Fall 2018. MATH 5351. Introduction to Complex Variables. Section 1A. Teaching Evaluation. Student Comments.

Spring 2018. MATH 3304. Elementary Differential Equations. Section 1L. Teaching Evaluation. Student Comments.

Fall 2017. MATH 5351. Introduction to Complex Variables. Section 1A. Teaching Evaluation. Student Comments.

Fall 2017. MATH 3304. Elementary Differential Equations. Section 1D. Teaching Evaluation. Student Comments.

Spring 2017. MATH 3304. Elementary Differential Equations. Section 1A. Teaching Evaluation. Student Comments.

Fall 2016. MATH 3304. Elementary Differential Equations. Section 1B. Teaching Evaluation. Student Comments.

Fall 2016. MATH 3304. Elementary Differential Equations. Section 1E. Teaching Evaluation. Student Comments.

At University of Minnesota, Twin Cities:

Spring 2016. MATH 4242. Applied Linear Algebra. Teaching Evaluation. Student Comments.

Fall 2015. MATH 5652. Introduction to Stochastic Processes. Lecture Notes. Teaching Evaluation. Student Comments.

Fall 2015. MATH 5651. Basic Theory of Probability and Statistics. Teaching Evaluation. Student Comments.

Spring 2015. MATH 5651. Basic Theory of Probability and Statistics. Teaching Evaluation. Student Comments.

Fall 2014. MATH 5651. Basic Theory of Probability and Statistics. Teaching Evaluation. Student Comments.

Fall 2013. MATH 4603. Advanced Calculus I. Teaching Evaluation. Student Comments.

Spring 2018. MATH 3304H-1L. Elementary Differential Equations - Honors Program. Lotka-Volterra models of Predator-Prey Relationships.

Spring 2016. MATH 4995. Senior project for independent study. An overview of linear model selection methods.

Spring 2016. MATH 4997W. Senior project for independent study. VaR (Value at Risk) estimation and extreme value theory. paper1, paper2.

Fall 2015. MATH 4997W. Senior project for independent study. An overview of Modern Portfolio Theory.

[1] Miner Alumni Association's Class of '42 Excellence in Teaching Award. June 20, 2018. [award document] [award] [photo] [moment] [moment on youku]

[1] Elementary Differential Equations. Course Video. (This is a compulsary class numbered MATH 3304 for all engineering students at Missouri University of Science and Technology, or formerly University of Missouri, Rolla.)

I enjoy both the mathematical beauty and the practical power of **probability theory**. By making effective use of *stochastic analysis*, I analyzed problems in stochastic processes, differential equations, dynamical systems, and mathematical physics. These problems include 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.

I also have interests in **statistical methodology**. I have been working on problems in *data sciences*, *statistical machine learning* and *optimization*. In particular, I got involved in 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.

My profile on MathSciNet, Google Scholar, ORCID, ResearchGate and GitHub.

[3] Yuan, H., **Hu, W.**, Stochastic Recursive Momentum Method for Non-Convex Compositional Optimization.
[arXiv]
[source code]

[2] **Hu, W.**, Sun, Z., Yang, J., Steimeister, L., Xu, K., Joint Control of Manufacturing and Onsite Microgrid System via Novel
Neural-Network Integrated Reinforcement Learning Algorithms.
[preprint]
[source code]

[1] **Hu, W.**, Zhu, Z., Xiong, H., Huan, J., Quasi-potential as an implicit regularizer for the loss function in the stochastic gradient descent.
[arXiv]
[media report 1]
[media report 2]

[22] Fan, W., **Hu, W.**, Terlov, G., Wave propagation for reaction-diffusion equations on infinite random trees.
*Communications in Mathematical Physics*,
online first, 2021.
[arXiv]
[journal paper]

[21] Islam, Md M., Sun, Z., Qin, R., **Hu, W.**, Xiong, H., Xu, K.,
Flexible energy load identification in intelligent manufacturing for demand response using a neural network integrated particle swarm optimization.
*Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*, online first, 2020.
[journal paper]

[20] Yang, J., **Hu, W.**, Li, C.J., On the fast convergence of random perturbations of the gradient flow.
*Asymptotic Analysis*, Volume **122**, 2021, pages 371-393.
[arXiv]
[journal paper]

[19] Islam, Md M., Zhong, X., Sun, Z., Xiong, H., **Hu, W.**,
Real-Time Frequency Regulation Using Aggregated Electric Vehicles in Smart Grid.
*Computers & Industrial Engineering*, Volume **134**, August 2019, pages 11-26.
[journal paper]

[18] **Hu, W.**, On the long time behavior of a perturbed conservative system with degeneracy.
*Journal of Theoretical Probability*, Volume **33**, pp.1266-1295, 2020. (Published online on 11, May 2019.)
[arXiv]
[journal paper]

[17] **Hu, W.**, Salins, M., Spiliopoulos, K., Large deviations and averaging for systems of slow-fast stochastic reaction-diffusion equations.
*Stochastics and Partial Differential Equations: Analysis and Computations*, December 2019, Volume **7**, Issue 4, pp. 808-874.
[arXiv]
[journal paper]

[16] **Hu, W.**, Li, C.J., Li, L., Liu, J., On the diffusion approximation of nonconvex stochastic gradient descent.
*Annals of Mathematical Science and Applications*, Vol. **4**, No. 1 (2019), pp. 3-32.
[arXiv]
[journal paper]

[15] **Hu, W.**, Li, C.J., A convergence analysis of the perturbed compositional gradient flow: averaging principle and normal deviations.
*Discrete and Continuous Dynamical Systems, Series A*, **38**, 10, October 2018, pp. 4951-4977.
[arXiv]
[journal paper]

[14] Xiong, H., Cheng, W., Bian, J., **Hu, W.**, Sun, Z., Guo, Z.,
DBSDA: Lowering the Bound of Misclassification Rate for Sparse Linear Discriminant Analysis via Model Debiasing.
*IEEE Transactions on Neural Networks and Learning Systems*, Volume **30**, Issue 3, pp. 707-717, March 2019.
[journal paper]

[13] **Hu, W.**, Sverak, V., Dynamics of geodesic flows with random forcing on Lie groups with left-invariant metrics.
*Journal of Nonlinear Science*, **28**(6):2249-2274, December 2018.
[arXiv]
[journal paper]

[12] **Hu, W.**, Ito's formula, the stochastic exponential and change of measure on general time scales.
*Abstract and Applied Analysis*, Vol. 2017, Article ID 9140138, 2017.
[arXiv]
[journal paper]

[11] **Hu, W.**, Spiliopoulos, K., Hypoelliptic multiscale Langevin diffusions: Large deviations, invariant measures and small mass asymptotics.
*Electronic Journal of Probability*, **22** (2017), paper no. 55, pp. 1-38.
[arXiv]
[journal paper]

[10] Elgindi, T., **Hu, W.**, Sverak, V., On 2d incompressible Euler equations with partial damping.
*Communications in Mathematical Physics*, **355**, Issue 1, October 2017, pp. 145-159.
[arXiv]
[journal paper]

[9] **Hu, W.**, Tcheuko, L., Random perturbations of dynamical systems with reflecting boundary and corresponding PDE with a small parameter.
*Asymptotic Analysis*, **87**, 1-2, 2014, pp. 43-56.
[arXiv]
[journal paper]

[8] Freidlin, M., **Hu, W.**, Wave front propagation for a reaction-diffusion equation in narrow random channels.
*Nonlinearity*, **26**, 8, 2013, pp. 2333-2356.
[arXiv]
[journal paper]

[7] Freidlin, M., **Hu, W.**, On diffusion in narrow random channels.
*Journal of Statistical Physics*, **152**, 2013, pp. 136-158.
[arXiv]
[journal paper]

[6] Freidlin, M., **Hu, W.**, On second order elliptic equations with a small parameter.
*Communications in Partial Differential Equations*, **38**, 10, 2013, pp. 1712-1736.
[arXiv]
[journal paper]

[5] Freidlin, M., **Hu, W.**, Wentzell, A., Small mass asymptotic for the
motion with vanishing friction.
*Stochastic Processes and their Applications*, **123** (2013), pp. 45-75.
[arXiv]
[journal paper]

[4] Freidlin, M., **Hu, W.**, Smoluchowski-Kramers approximation in the case of variable friction.
*Journal of Mathematical Sciences*, **79**, 1, November 2011, translated from
*Problems in Mathematical Analysis*, **61**, October 2011 (in Russian).
[arXiv]
[journal paper]

[3] **Hu, W.**, On metastability in nearly-elastic systems.
*Asymptotic Analysis*, **79**, 1-2, 2012, pp. 65-86.
[arXiv]
[journal paper]

[2] Freidlin, M., **Hu, W.**, On perturbations of generalized Landau-Lifshitz dynamics.
*Journal of Statistical Physics*, **144**, 2011, pp. 978-1008.
[arXiv]
[journal paper]

[1] Freidlin, M., **Hu, W.**, On stochasticity in nearly-elastic systems.
*Stochastics and Dynamics*, **12**, 3, 2012.
[arXiv]
[journal paper]

[9] Wu, J., **Hu, W.**, Xiong, H., Huan, J., Braverman, V., Zhu, Z., On the Noisy Gradient Descent that Generalizes as SGD.
*ICML 2020 (37th International Conference on Machine Learning), virtual conference due to COVID-19, July 12-18, 2020*.
[arXiv]

[8] Yuan, H., Lian, X., Li, C.J., Liu, J., **Hu, W.**,
Efficient Smooth Non-Convex Stochastic Compositional Optimization via Stochastic Recursive Gradient Descent.
*NeurIPS 2019 (Thirty-third Conference on Neural Information Processing Systems), Vancouver, Canada, December 8-14, 2019*.
[conference paper]

[7] **Hu, W.**, Li, C.J., Zhou, X., On the Global Convergence of Continuous-Time Stochastic Heavy-Ball Method for Nonconvex Optimization.
*IEEE Big Data 2019 (2019 IEEE International Conference on Big Data), Los Angeles, California, USA, December 9-12, 2019*.
[arXiv]
[conference paper]

[6] Islam, Md M., Sun, Z., **Hu, W.**, Dagli, C., A Framework of Integrating Manufacturing Plants
in Smart Grid Operation: Manufacturing Flexible Load Identification.
*ICPR 2019 (the 25th International Conference on Production Research), Chicago, Illinois, USA, August 10-14, 2019*.
[conference paper]

[5] **Hu, W.**, Sun, Z., Zhang, Y., Li, Y., Joint Manufacturing and Onsite Microgrid
System Control Using Markov Decision Process and Neural Network Integrated Reinforcement Learning.
*ICPR 2019 (the 25th International Conference on Production Research), Chicago, Illinois, USA, August 10-14, 2019*.
[conference paper]

[4] Xiong, H., Cheng, W., Fu, Y., Bian, J., **Hu, W.**, Guo, Z.,
De-Biasing Covariance-Regularized Discriminant Analysis.
*IJCAI-ECAI 2018 (the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence),
Stockholm, Sweden, July 13-19, 2018*.
[conference paper]

[3] Bian, J., Xiong, H., Cheng, W., Fu, Y., **Hu, W.**, Guo, Z., Multi-Party Sparse Discriminant Learning.
*ICDM 2017 (2017 IEEE International Conference on Data Mining), New Orleans, Louisiana, USA, November 8-21, 2017*.
[conference paper]

[2] Xiong, H., Cheng, W., Bian, J., **Hu, W.**, Guo, Z., AWDA: Adapted Wishart Discriminant Analysis.
*ICDM 2017 (2017 IEEE International Conference on Data Mining), New Orleans, Louisiana, USA, November 8-21, 2017*.
[conference paper]

[1] Wang, P., Liu, G., Fu, Y., **Hu, W.**, Aggarwal, C., Human Mobility Synchronization and Trip Purpose Detection with Mixture of Hawkes Processes. *KDD 2017 (Knowledge, Discovery and Data Mining), Halifax, Nova Scotia, Canada, August 13-17, 2017*. Accepted paper ID=fp1019.
[conference paper]
[abstract and video]

[4] Nonlinear Optimization in Machine Learning. (A new graduate-level topic course that I developed at Missouri S&T.) Lecture Notes.

[3] Lectures on Nonlinear Optimization in Machine Learning. (A series of lectures that I gave at the School of Mathematics and Statistics, Anhui Normal University in June 27-July 8, 2018.) Lecture 1. Lecture 2. Lecture 3. Lecture 4.

[2] Lectures on the Nature of Statistical Learning Theory. (A series of lectures that I gave at the Computer Science Department, Missouri S&T in the Spring semester of 2017.) Lecture 1. Lecture 2. Lecture 3. Lecture 4. Lecture 5.

[1] Lectures on Stochastic Fluid Mechanics. (A series of lectures that I gave at the School of Mathematical Sciences, Peking University in July 9-17, 2015.) Poster. Abstract. Lecture Notes.

[18] Wave propagation for reaction-diffusion equation on infinite random trees.

[17] Some Probabilistic Understandings of the Effects of Noise in the Stochastic Gradient Descent.

[15] On 2d Euler equations with partial damping and some related model problems.

[14] On the long time behavior of a perturbed conservative system with degeneracy.

[13] Hypoelliptic multiscale Langevin diffusions and Slow-fast stochastic reaction-diffusion equations.

[12] A random perturbation approach to some stochastic approximation algorithms in optimization.

[11] Large deviations and averaging for systems of slow-fast reaction-diffusion equations.

[10] Fast convergence of random perturbations of the gradient flow.

[9] Ito's formula on general time scales.

[8] 2-d incompressible Euler equations with partial damping.

[7] Hypoelliptic multiscale Langevin diffusions.

[6] Stochastically perturbed geodesic flows on Lie groups.

[5] Dynamics of geodesic flows with random forcing on Lie groups with left invariant metrics.

[4] Diffusion and wave front propagation in narrow random channels.

[3] Second order elliptic equations with a small parameter.

[2] Small mass asymptotic for the motion with variable and vanishing friction.

[1] Stochastic behavior in nearly-elastic billiard systems.

I acknowledge the generous support of my research from the following funding opportunities:

[4] Simons Foundation Collaboration Grants for Mathematicians, 2020-2025. [award document].

[3] NSF sponsored AMS Travel Support to the International Congress of Mathematicians (ICM) in Rio de Janeiro, Brazil, in August of 2018. [award document].

[2] University of Missouri Research Board. June 1, 2017-May 31, 2018. Topic: Multiscale Stochastic Differential Equations. [award document].

[1] AMS Simons Travel Grant. July 1, 2015-June 30, 2017. [award document].

**Contact Information.**

Wenqing Hu.

112 Rolla Building,

Department of Mathematics and Statistics,

Missouri University of Science and Technology (formerly University of Missouri, Rolla).

400W, 12th Street, Rolla, MO, 65409-0020, USA.

Email address 1: huwen "at" mst "dot" edu

Email address 2: huwenqing"dot"pku "at" gmail "dot" com

**Useful Links.**

American Mathematical Society, American Statistical Association, Society of Industrial and Applied Mathematics, INFORMS Applied Probability Society, The Bachelier Finance Society, Society of Actuaries, Institute of Electrical and Electronics Engineers, Association for Computing Machinery, Association for the Advancement of Artificial Intelligence, Missouri Institute for Computational and Applied Mathematical Sciences, Applied Computational Intelligence Laboratory, Intelligent Systems Center.

Last updated: 04/2021.