Applied and Computational Mathematics Group

*People*

DON Wai Sun, FAN Jun, HON Yu Sing Sean, HOU Liangshao, LAM Kei Fong Andrew, LIAO Lizhi, LING Leevan, LIU Hao, NG Kwok Po Michael, PAN Junjun, TANG Xindong, YU Zhan

*Overview*

The Applied and Computational Mathematics group is dedicated to developing and analyzing mathematical models and algorithms to address significant challenges in applied sciences. The members' board research interests encompass applied mathematics, numerical analysis, numerical PDEs, scientific computing, optimization, and deep learning approaches. These methodologies have been successfully applied in image processing, healthcare, computational fluid dynamics, robotic control, and continuum mechanics.

*Research Interests*

* **Numerical Methods**, including high-performance computing, artificial neural networks, discontinuous Galerkin methods, meshless collocation methods, operator splitting, preconditioners for large matrices, fast solvers, high-order WENO schemes, spectral methods.
* **Deep Learning Approach**, including artificial neural networks to solve PDEs, approximation theory, PDE learning from noisy data.
* **Optimization**, including matrix factorizations, optimization on manifolds, optimization with PDE constraints, optimal control, polynomial optimization, Nash equilibrium, tensor computation.
* **Applications**, including image processing and denoising, inverse problems, healthcare, fluid dynamics, continuum mechanics, robotics control.

*Publications*

**DON Wai Sun**
* **Don, W. S.**, Li, R., Wang, B. S., & Wang, Y. (2022). A novel and robust scale-invariant WENO scheme for hyperbolic conservation laws. _Journal of Computational Physics_, _448_, 110724.
* Borges, R., Carmona, M., Costa, B., & **Don, W. S.** (2008). An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. _Journal of Computational Physics_, _227_(6), 3191-3211.
<br>
**FAN Jun**
* **Fan, J.**, & Lei, Y. (2024). High-probability generalization bounds for pointwise uniformly stable algorithms. _Applied and Computational Harmonic Analysis_, _70_, 101632.
* Feng, Y., **Fan, J.**, & Suykens, J. A. (2020). A statistical learning approach to modal regression. _Journal of Machine Learning Research_, _21_(2), 1-35.
<br>
**HON Yu Sing Sean**
* **Hon, S.**, Dong, J., & Serra-Capizzano, S. (2023). A preconditioned MINRES method for optimal control of wave equations and its asymptotic spectral distribution theory. _SIAM Journal on Matrix Analysis and Applications_, _44_(4), 1477-1509.
* Ferrari, P., Furci, I., **Hon, S.**, Ayman-Mursaleen, M., & Serra-Capizzano, S. (2019). The eigenvalue distribution of special 2-by-2 block matrix-sequences with applications to the case of symmetrized Toeplitz structures. _SIAM Journal on Matrix Analysis and Applications_, _40_(3), 1066-1086.
<br>
**HOU Liangshao**
* **Hou, L.**, Chu, D., & Liao, L. Z. (2023). A progressive hierarchical alternating least squares method for symmetric nonnegative matrix factorization. _IEEE Transactions on Pattern Analysis and Machine Intelligence_, _45_(5), 5355-5369.
* **Hou, L.**, Qian, X., Liao, L. Z., & Sun, J. (2022). An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming. _Journal of Scientific Computing_, _90_(3), 95.
<br>
**LAM Kei Fong Andrew**
* Garcke, H., **Lam, K. F.**, Nürnberg, R., & Signori, A. (2023). Phase field topology optimisation for 4D printing. _ESAIM: Control, Optimisation and Calculus of Variations_, _29_, 24.
* Garcke, H., **Lam, K. F.**, Sitka, E., & Styles, V. (2016). A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport. _Mathematical Models and Methods in Applied Sciences_, _26_(06), 1095-1148.
<br>
**LIAO Lizhi**
* Qian, X., **Liao, L. Z.**, & Sun, J. (2020). A strategy of global convergence for the affine scaling algorithm for convex semidefinite programming. _Mathematical Programming_, _179_(1-2), 1-19.
* Qian, X., **Liao, L. Z.**, Sun, J., & Zhu, H. (2018). The convergent generalized central paths for linearly constrained convex programming. _SIAM Journal on Optimization_, _28_(2), 1183-1204.
<br>
**LING Leevan**
* Chen, M., Cheung, K. C., & **Ling, L.** (2023). A kernel-based least-squares collocation method for surface diffusion. _SIAM Journal on Numerical Analysis_, _61_(3), 1386-1404.
* Sun, Z., & **Ling, L.** (2022). A kernel-based meshless conservative Galerkin method for solving Hamiltonian wave equations. _SIAM Journal on Scientific Computing_, _44_(4), A2789-A2807.
<br>
**LIU Hao**
* He, Y., Kang, S. H., Liao, W., **Liu, H.**, & Liu, Y. (2022). Robust identification of differential equations by numerical techniques from a single set of noisy observation. _SIAM Journal on Scientific Computing_, _44_(3), A1145-A1175.
* He, Y., Kang, S. H., & **Liu, H.** (2020). Curvature regularized surface reconstruction from point clouds. _SIAM Journal on Imaging Sciences_, _13_(4), 1834-1859.
<br>
**NG Kwok Po Michael**
* Gu, Y., & **Ng, M. K.** (2023). Deep neural networks for solving large linear systems arising from high-dimensional problems. _SIAM Journal on Scientific Computing_, _45_(5), A2356-A2381.
* Chen, J., & **Ng, M. K.** (2023). Signal reconstruction from phase-only measurements: Uniqueness condition, minimal measurement number and beyond. _SIAM Journal on Applied Mathematics_, _83_(4), 1341-1365.
<br>
**PAN Junjun**
* **Pan, J.**, & Gillis, N. (2021). Generalized separable nonnegative matrix factorization. _IEEE Transactions on Pattern Analysis and Machine Intelligence_, _43_(5), 1546-1561.
* **Pan, J.**, Ng, M. K., Liu, Y., Zhang, X., & Yan, H. (2021). Orthogonal nonnegative tucker decomposition. _SIAM Journal on Scientific Computing_, _43_(1), B55-B81.
<br>
**TANG Xindong**
* Qu, Z., & **Tang, X.** (2024). A Correlatively Sparse Lagrange Multiplier Expression Relaxation for Polynomial Optimization. _SIAM Journal on Optimization_, _34_(1), 127-162.
* Nie, J., & **Tang, X.** (2023). Convex generalized Nash equilibrium problems and polynomial optimization. _Mathematical Programming_, _198_(2), 1485-1518.
<br>
**YU Zhan**
* **Yu, Z.**, Ho, D. W., & Yuan, D. (2022). Distributed randomized gradient-free mirror descent algorithm for constrained optimization. _IEEE Transactions on Automatic Control_, _67_(2), 957-964.
* **Yu, Z.**, Ho, D. W., Shi, Z., & Zhou, D. X. (2021). Robust kernel-based distribution regression. _Inverse Problems_, _37_(10), 105014.

*Related Academic Activities*

**DON Wai Sun**
* Shenzhen International Center for Mathematics, SUSTech, 2024. “Development of High-Order Methods for Hyperbolic PDEs”.
* Mini-course for the Special Program on Numerical Methods for Nonlinear Hyperbolic PDEs, 2024. “A Person Journey in the World of WENO”.
* Symposium on Recent Developments in Numerical Methods for Computational Fluid Dynamics, 2024.
* Advances in High-Order Methods-fluid dynamics, biomedical science, and exascale computing, 2024.
* Shenzhen International Center for Mathematics, SUSTech, 2023. “Recent Advances in Numerical Methods for Hyperbolic Conservation Laws”.
<br>
**FAN Jun**
* The sixth Institute of Mathematical Statistics Asia Pacific Rim Meeting (IMS-APRM), 2024.
* The 16th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2023), 2023.
* The 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), 2023.
* International Conference on Applied Mathematics, 2023.
<br>
**HON Yu Sing Sean**
* SIAM Conference on Applied Linear Algebra (LA24), 2024.
* Exploiting Algebraic and Geometric Structure in Time-Integration Methods, 2024.
* “数值代数的机遇与挑战”学术研讨会, 2024.
* The 5th International Workshop on Numerical Analysis and Applications of Fractional Differential Equations, Shenzhen, 2023.
* The Hong Kong Laureate Forum, 2023.
* The 10th International Congress on Industrial and Applied Mathematics, 2023.
<br>
**LAM Kei Fong Andrew**
* RIMS Workshop "Evolution equations and related Topics - Energy Structures and Quantitative Analysis", 2023.
* The International Council for Industrial and Applied Mathematics (ICIAM), 2023.
* The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications in Wilmington, 2023.
<br>
**LIU Hao**
* SIAM Conference on Applied Linear Algebra (LA24), 2024. Organized minisymposium “Exploiting Low-dimensional Structures in Data Science”.
<br>
**PAN Junjun**
* SIAM Conference on Applied Linear Algebra (LA24), 2024.
<br>
**TANG Xindong**
* 25th International Symposium on Mathematical Programming (ISMP 2024), 2024. Session Chair of “Moment, Polynomial and Tensor Optimization”.
* 2023 INFORMS Annual Meeting, 2023. “A correlatively sparse Lagrange multiplier expression relaxation for polynomial optimization”.
* SIAM Conference on Optimization (OP23), 2023. “Rational generalized Nash equilibrium problems”.

Foundation in AI and Applications Group

*People*

DON Wai Sun, FAN Jun, LIAO Lizhi, LING Leevan, LIU Hao, NG Kwok Po Michael, PAN Junjun, PENG Heng, XU Yi Da, ZHOU Le

*Overview*

The Foundation in AI and Applications group focuses on developing mathematical and statistical theories and algorithms, catering to the field of artificial intelligence and its associated applications. Our research encompasses formulating mathematical and statistical frameworks to explicate the efficacy of deep learning techniques and pioneering new deep learning algorithms grounded in robust mathematical and statistical principles.

*Research Interests*

* **Data Science**, including dimension reduction, model reduction, high-dimensional data analysis.
* **Deep Learning Theories**, including approximation and generalization theory, graph neural networks, deep generative models.
* **Machine Learning and Deep Learning Applications**, including object recognition, deep dictionary learning, operator learning, image processing.

*Publications*

**DON Wai Sun**
* Gao, Z., Liu, Q., Hesthaven, J. S., Wang, B. S., **Don, W. S.**, & Wen, X. (2021). Non-intrusive reduced order modeling of convection dominated flows using artificial neural networks with application to Rayleigh–Taylor instability. _Communications in Computational Physics_, _30_(1), 97-123.
* Wen, X., **Don, W. S.**, Gao, Z., & Hesthaven, J. S. (2020). An edge detector based on artificial neural network with application to hybrid compact-WENO finite difference scheme. _Journal of Scientific Computing_, _83_(49), 1-21.
<br>
**FAN Jun**
* Zhang, Y., Fang, Z., & **Fan, J.** (2024). Generalization analysis of deep CNNs under maximum correntropy criterion. _Neural Networks_, _174_, 106226.
* Song, L., **Fan, J.**, Chen, D. R., & Zhou, D. X. (2023). Approximation of nonlinear functionals using deep ReLU networks. _Journal of Fourier Analysis and Applications_, _29_(4), 50.
<br>
**LIAO Lizhi**
* Hou, L., Chu, D., & **Liao, L. Z.** (2024). Convergence of a Fast Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization. _IEEE Transactions on Knowledge and Data Engineering_, _36_(1), 77-89.
* Hou, L., Chu, D., & **Liao, L. Z.** (2023). A progressive hierarchical alternating least squares method for symmetric nonnegative matrix factorization. _IEEE Transactions on Pattern Analysis and Machine Intelligence_, _45_(5), 5355-5369.
<br>
**LING Leevan**
* Chiu, S. N., **Ling, L.**, & McCourt, M. (2020). On variable and random shape Gaussian interpolations. _Applied Mathematics and Computation_, _377_, 125159.
<br>
**LIU Hao**
* **Liu, H.**, Havrilla, A., Lai, R., & Liao, W. (2024). Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness. _Applied and Computational Harmonic Analysis_, _68_, 101602.
* **Liu, H.**, Yang, H., Chen, M., Zhao, T., & Liao, W. (2024). Deep nonparametric estimation of operators between infinite dimensional spaces. _Journal of Machine Learning Research_, _25_(24), 1-67.
<br>
**NG Kwok Po Michael**
* Wu, H., Yip, A., Long, J., Zhang, J., & **Ng, M. K.** (2024). Simplicial complex neural networks. _IEEE Transactions on Pattern Analysis and Machine Intelligence_, _46_(1), 561-575.
* Gao, Y., **Ng, M. K.**, & Zhou, M. (2023). Approximating probability distributions by using Wasserstein generative adversarial networks. _SIAM Journal on Mathematics of Data Science_, _5_(4), 949-976.
<br>
**PAN Junjun**
* Liu, Y., **Pan, J.**, & Ng, M. K. (2023). Tucker network: Expressive power and comparison. _Neural Networks_, _160_, 63-83.
* **Pan, J.**, & Ng, M. K. (2023). Coseparable nonnegative matrix factorization. _SIAM Journal on Matrix Analysis and Applications_, _44_(3), 1393-1420.
<br>
**PENG Heng**
* Pei, Y., **Peng, H.**, & Xu, J. (2024). A latent class Cox model for heterogeneous time-to-event data. _Journal of Econometrics_, _239_, 105351.
* Hu, X., Zhao, J., Lin, Z., Wang, Y., **Peng, H.**, Zhao, H., Wang, X. & Yang, C. (2022). Mendelian randomization for causal inference accounting for pleiotropy and sample structure using genome-wide summary statistics. _Proceedings of the National Academy of Sciences_, _119_(28), e2106858119.
<br>
**XU Yi Da**
* Huang, W., Liu, C., Chen, Y., **Xu, R. Y. D.**, Zhang, M., & Weng, T. W. (2023). Analyzing deep PAC-Bayesian learning with neural tangent kernel: Convergence, analytic generalization bound, and efficient hyperparameter selection. _Transactions on Machine Learning Research_.
* Huang, W., Du, W., & **Xu, R. Y. D.** (2021). On the neural tangent kernel of deep networks with orthogonal initialization. _International Joint Conference on Artificial Intelligence_.
<br>
**ZHOU Le**
* **Zhou, L.**, Wang, B., & Zou, H. (2023). Sparse convoluted rank regression in high dimensions. _Journal of the American Statistical Association_, _119_(546), 1500-1512.
* Wang, B., **Zhou, L.**, Gu, Y., & Zou, H. (2022). Density-convoluted support vector machines for high-dimensional classification. _IEEE Transactions on Information Theory_, _69_(4), 2523-2536.

*Related Academic Activities*

**LIU Hao**
* SIAM Conference on Applied Linear Algebra (LA24), 2024. Organized minisymposium “Exploiting Low-dimensional Structures in Data Science”. Gave talk “Deep Learning Theories for Problems with Low–Dimensional Structures”.
* SIAM Conference on Imaging Science (IS24), 2024. Gave talk “A Mathematical Explanation of Encoder-Decoder Based Neural Networks”.
<br>
**NG Kwok Po Michael**
* SIAM Conference on Imaging Science (IS24), 2024. Invited Presentation “Signal Reconstruction from Phase-only Measurements, Dithered Quantization or Quantized Corrupted Sensing”.
<br>
**PAN Junjun**
* SIAM Conference on Applied Linear Algebra (LA24), 2024.

Statistics and Data Science Group

*People*

CHENG Ming-Yen, CHIU Sung Nok, FAN Jun, HOU Liangshao, NG Kwok Po Michael, PENG Heng, TONG Tiejun, XU Yi Da, YAO Shunan, YU Zhan, ZHOU Le, ZHU Lixing

*Overview*

The statisticians in the Mathematics Department form a strong team, whose research is remarkably influential. Our people won the Humboldt research award, the State Natural Science award, IMS fellowship, ASA fellowship and ISI elected membership. Many of our publications have high citation numbers and most of us are serving as associate editors of leading journals. The HKBU Statistics and Data Science group has been recognized internationally. Because of the wide applicability nature of statistics and data science and the diversified expertise among our team members, we have been very successful in various interdisciplinary research. Our work is not only on the development of innovative theory and methodology, but also on innovative applications, leading to publications in prestigious journals in statistics, data science and other disciplines. As a platform, the University's Statistics Research and Consultancy Centre (SRCC) engages in both theoretical and applied research in statistics and data science and provides statistical consultancy, sponsors academic exchange, and organizes international conferences and workshops.

*Research Interests*

* **Applied Probability**, including stochastic geometry and Voronoi diagrams.
* **Big Data**, including big data in biomedicine, big data analytics and applications in online education.
* **Biostatistics and Bioinformatics**, including clinical trial design, health informatics, meta-analysis, pattern recognition, and statistical genomics.
* **Finance**, including credit risk modeling, financial econometrics, financial risk management, and industrial engineering.
* **High-dimensional Data Analysis**, including covariance matrix estimation, dimension reduction, machine learning, heteroscedastic regression, model-adaptive dimension reduction testing for regressions, pivotal variable detection in factor models, shrinkage estimation, variable selection, and their scientific applications.
* **Regression and Classification**, including econometrics related regression analysis, goodness-of-fit tests, model selection, nonparametric and semiparametric regression, shrinkage estimation, variable selection, robust regression, asymmetric classification and tensor classification.
* **Spatial Statistics**, including statistics for spatial point processes and random set models.
* **Miscellanea**, including data-analytic modeling, design of experiments, design methods for time-to-event data, efficient estimation and sampling, nonparametric and robust methods, resampling techniques, and survival analysis.

*Publications*

**CHENG Ming-Yen**
* **Cheng, M. Y.**, Wang, S., Xia, L., & Zhang, X. (2024). Testing specification of distribution in stochastic frontier analysis. _Journal of Econometrics_, _239_, 105280.
* Wang, S., Huang, T., You, J., & **Cheng, M. Y.** (2022). Robust Inference for Nonstationary Time Series with Possibly Multiple Changing Periodic Structures. _Journal of Business & Economic Statistics_, _40_(4), 1718-1731.
<br>
**CHIU Sung Nok**
* Stoyan, D., & **Chiu, S. N.** (2024). Statistics did not prove that the Huanan Seafood Wholesale Market was the early epicentre of the COVID-19 pandemic. _Journal of the Royal Statistical Society Series A: Statistics in Society_, qnad139.
* Feng, S., Tong, T., & **Chiu, S. N.** (2023). Statistical Inference for Partially Linear Varying Coefficient Spatial Autoregressive Panel Data Model. _Mathematics_, _11_(22), 4606.
<br>
**FAN Jun**
* **Fan, J.**, & Lei, Y. (2024). High-probability generalization bounds for pointwise uniformly stable algorithms. _Applied and Computational Harmonic Analysis_, _70_, 101632.
* Feng, Y., **Fan, J.**, & Suykens, J. A. (2020). A statistical learning approach to modal regression. _Journal of Machine Learning Research_, _21_(2), 1-35.
<br>
**HOU Liangshao**
* **Hou, L.**, Chu, D., & Liao, L. Z. (2024). Convergence of a Fast Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization. _IEEE Transactions on Knowledge and Data Engineering_, _36_(1), 77-89.
* **Hou, L.**, Chu, D., & Liao, L. Z. (2023). A progressive hierarchical alternating least squares method for symmetric nonnegative matrix factorization. _IEEE Transactions on Pattern Analysis and Machine Intelligence_, _45_(5), 5355-5369.
<br>
**NG Kwok Po Michael**
* Luo, Y., Zhao, X., Li, Z., **Ng, M. K.**, & Meng, D. (2024). Low-rank tensor function representation for multi-dimensional data recovery. _IEEE Transactions on Pattern Analysis and Machine Intelligence_, _46_(5), 3351-3369.
* Chen, J., **Ng, M. K.**, & Wang, D. (2024). Quantizing heavy-tailed data in statistical estimation: (near) minimax rates, covariate quantization, and uniform recovery. _IEEE Transactions on Information Theory_, _70_(3), 2003-2038.
<br>
**PENG Heng**
* Pei, Y., **Peng, H.**, & Xu, J. (2024). A latent class Cox model for heterogeneous time-to-event data. _Journal of Econometrics_, _239_, 105351.
* Pei, Y., Huang, T., **Peng, H.**, & You, J. (2022). Network-based clustering for varying coefficient panel data models. _Journal of Business & Economic Statistics_, _40_(2), 578-594.
<br>
**TONG Tiejun**
* Hu, Z., **Tong, T.**, & Genton, M. G. (2024). A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors. _Statistica Sinica_, _34_, 229-256.
* Shi, J., Luo, D., Wan, X., Liu, Y., Liu, J., Bian, Z., & **Tong, T.** (2023). Detecting the skewness of data from the five-number summary and its application in meta-analysis. _Statistical Methods in Medical Research_, _32_(7), 1338-1360.
<br>
**XU Yi Da**
* Fan, X., **Xu, R. Y. D.**, Cao, L., & Song, Y. (2017). Learning Hidden Structures with Relational Models by Adequately Involving Rich Information in A Network. _IEEE Transaction on Cybernetics_, _47_(3), 589-599.
* Fan, X., **Xu, R. Y. D.**, & Cao, L. (2016, January). Copula mixed-membership stochastic block model. In _IJCAI International Joint Conference on Artificial Intelligence_.
<br>
**YAO Shunan**
* **Yao, S.**, Rava, B., Tong, X., & James, G. (2022). Asymmetric Error Control Under Imperfect Supervision: A Label-Noise-Adjusted Neyman–Pearson Umbrella Algorithm. _Journal of the American Statistical Association_, _118_(543), 1824-1836.
<br>
**YU Zhan**
* **Yu, Z.**, & Ho, D. W. (2024). Estimates on learning rates for multi-penalty distribution regression. _Applied and Computational Harmonic Analysis_, _69_, 101609.
* **Yu, Z.**, Ho, D. W., Shi, Z., & Zhou, D. X. (2021). Robust kernel-based distribution regression. _Inverse Problems_, _37_(10), 105014.
<br>
**ZHOU Le**
* **Zhou, L.**, Wang, B., & Zou, H. (2023). Sparse convoluted rank regression in high dimensions. _Journal of the American Statistical Association_, _119_(546), 1500-1512.
* **Zhou, L.**, & Zou, H. (2021). Cross-Fitted Residual Regression for High-Dimensional Heteroscedasticity Pursuit. _Journal of the American Statistical Association_, _118_(542), 1056-1065.
<br>
**ZHU Lixing**
* Li, L., Zhu, X., & **Zhu, L.** (2023). Adaptive-to-model hybrid of tests for regressions. _Journal of the American Statistical Association_, _118_(541), 514-523.
* Tan, F., & **Zhu, L.** (2022). Integrated conditional moment test and beyond: when the number of covariates is divergent. _Biometrika_, _109_(1), 103-122.

*Related Academic Activities*

* “Probabilistic Forecasting for Daily Electricity Loads” by Professor Qiwei Yao, SRCC Distinguished Lecture Series, June 2024.
* SRCC Workshop on Advanced Statistical and Machine Learning Methods, April 2024.
* SRCC Workshop on Advanced Statistical Methods and Their Applications, July 2023.
* SRCC Workshop on Statistical Learning with Medical Applications, July 2023.
* SRCC Workshop on Statistics and Mediation Analysis, May 2023.
* AAAS fellowship, ZHU Lixing.
* AAIA fellowship, NG Kwok Po Michael.

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DetailsThe Department has a distinguished record in teaching and research. A number of faculty members have been recipients of relevant awards.

Learn MoreWe warmly welcome any interested parties/individuals to contact us for further information about our Department.

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