Publications

Journal Publications

[25] Wang, H., Gan, X., Hu, W., Ao, P., The generalized Lyapunov function as Ao’s potential function: Existence in dimensions 1 and 2, Journal of Applied Analysis and Computation, Volume 13, Number 1, February 2023, pp. 359-375. [journal paper]

[24] Wang, H., Gan, X., Hu, W., Ao, P., Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case, Journal of Mathematics, Volume 2022 Article ID 2596074. [journal paper]

[23] Yang, J., Sun, Z., Hu, W., Steimeister, L., Joint Control of Manufacturing and Onsite Microgrid System via Novel Neural-Network Integrated Reinforcement Learning Algorithms. Applied Energy, Volume 315, 1 June 2022, 118982. [manuscript] [journal paper] [source code]

[22] Fan, W., Hu, W., Terlov, G., Wave propagation for reaction-diffusion equations on infinite random trees. Communications in Mathematical Physics, 384, Issue 1, April 2021, pages 109-163. [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]

Conference Publications

[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] [conference paper]

[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]

Unpublished Manuscript

[2] Yuan, H., Hu, W., Stochastic Recursive Momentum Method for Non-Convex Compositional Optimization. [arXiv] [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]

Expository Notes

[5] Introductory Lectures on Machine Learning, Nonlinear Optimization and Reinforcement Learning. (Zu-Chongzhi Lectures at Duke-Kunshan University, July-August, 2020.) Poster. Lecture notes: Part 1. Part 2. Part 3.

[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.

Selected slides of talks and presentations

[20] 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.

[19] Joint Control of Manufacturing and Onsite Microgrid System via Markov Decision Processes and Reinforcement Learning.

[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.

[16] Stochastic Approximations, Diffusion Limit and Small Random Perturbations of Dynamical Systems – a probabilistic approach to machine learning.

[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.

Support Acknowledgement

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].