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.
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**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.
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**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.
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**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.
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**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.
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**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.
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**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.
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**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.
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**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.
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**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.
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**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.
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**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”.
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**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.
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**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.
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**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.
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**LIU Hao**
* SIAM Conference on Applied Linear Algebra (LA24), 2024. Organized minisymposium “Exploiting Low-dimensional Structures in Data Science”.
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**PAN Junjun**
* SIAM Conference on Applied Linear Algebra (LA24), 2024.
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**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”.