Research

Background

I graduated from Tsinghua in 2016 (BSc), and HKU in 2020 (PhD). Dr. Zhang Zhiwen is my PhD supervisor. Title of my PhD thesis is Robust Lagrangian Numerical Schemes in Computing Effective Diffusivities for Chaotic and Random Flows. The draft can be downloaded here.

Academic Positions

I worked as the William H. Kruskal Instructor at the University of Chicago from fall of 2020 to fall of 2023. Since August of 2023, I joined the Division of Mathematical Sciences at Nanyang Technological University as a Tenure-Track Assistant Professor.

Interests

Applied analysis and computational methods for physics and engineering problems, currently including but not limited to,

  • structure preserving algorithms: Lagrangian approach for effective diffusivities, KPP front wave speed, chemotaxis; scattering in topological insulators.

  • data-driven reduced order models: density estimation in filtering, inverse problems.

  • neuron net models: generative models, mesh free approximation to physics problems, neural operators.

I am currently excited about

  • computation of Wasserstein distance,

  • assymetric transport in TI,

  • neural operators,

  • math foundation of diffusion models,

  • effective diffusivities, KPP front speed, chemotaxis,

  • interacting particle (field) methods,

  • convection Enhanced phenomenon in large Peclet regime,

  • POD/Tensor-Train,

  • non-linear filtering,

  • …

Publications

  1. Mooney C., Wang Z., Xin J., Yu Y., Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates. International Conference on Learning Representations, 2025. [arXiv]

  2. Zhang T., Wang Z., Xin J., Zhang Z., A convergent interacting particle method for computing KPP front speeds in random flows. SIAM-ASA Journal on Uncertainty Quantification, 2025 [arXiv]

  3. Lu Y., Wang Z., Bal G., Mathematical analysis of singularities in the diffusion model under the submanifold assumption. East Asian Journal on Applied Mathematics, 2025. [arXiv]

  4. Wang Z., Xin J., Zhang Z., A Novel Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Chemotaxis System. Journal of Scientific Computing, 2025. [doi]

  5. Xie Y., Wang Z., Zhang Z., Random block coordinate descent methods for computing optimal transport and convergence analysis. Journal of Scientific Computing, 2024. [doi]

  6. Bal G., Wang Z., Z2 classification of FTR symmetric differential operators and obstruction to Anderson localization. Journal of Physics A: Mathematical and Theoretical, 2024 [doi]

  7. Wang Z., Zhang Z., A class of robust numerical methods for solving dynamical systems with multiple time scales. Communications on Analysis and Computation, 2024. [doi]

  8. Wang Z., Xin J., Zhang Z., A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems. Physica D: Nonlinear Phenomena, 2024. [doi]

  9. Bal G., Hoskins J., Wang Z., Asymmetric transport computations in Dirac models of topological insulators. Journal of Computational Physics, 2023. [doi]

  10. Wang Z., Zhang W., Zhang Z., A data-driven model reduction method for parabolic inverse source problems and its convergence analysis. Journal of Computational Physics, 2023. [doi]

  11. Cui T., Wang Z., Zhang Z., A variational neural network approach for glacier modelling with nonlinear rheology. Communications in Computational Physics, 2023. [doi]

  12. Li S., Wang Z., Yau S.S.T., Zhang Z., Solving Nonlinear Filtering Problems Using a Tensor Train Decomposition Method. IEEE Transactions on Automatic Control, 2022. [doi]

  13. Wang Z., Xin J., Zhang Z., Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method. ESAIM: Mathematical Modelling and Numerical Analysis, 2022. [doi]

  14. Wang Z., Xin J., Zhang Z., DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method. Journal of Computational Physics, 2022. [doi]

  15. Lyu J., Wang Z., Xin J., Zhang Z., A convergent interacting particle method and computation of KPP front speeds in chaotic flows. SIAM Journal on Numerical Analysis, 2022. [doi]

  16. Wang Z, Xin J, Zhang Z. Sharp error estimates on a stochastic structure-preserving scheme in computing effective diffusivity of 3D chaotic flows. Multiscale Model and Simulation, 2021. [doi]

  17. Lyu J., Wang Z., Xin J., Zhang Z. Convergence analysis of stochastic structure-preserving schemes for computing effective diffusivity in random flows. SIAM Journal on Numerical Analysis, 2020. [doi]

  18. Wang Z., Zhang Z., A mesh-free method for interface problems using the deep learning approach. Journal of Computational Physics, 2020. [doi]

  19. Wang Z., Luo X., Yau S.S.T., Zhang Z. Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension. IEEE Transactions on Automatic Control, 2020. [doi]

  20. Wang Z., Xin J., Zhang Z., Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes. SIAM Journal on Numerical Analysis, 2018. [doi]

(Names in Math papers are arranged in alphabetical order.)

Preprints

  • Wang X., Wang Z., Wasserstein Bounds for generative diffusion models with Gaussian tail targets. [arXiv]

  • Bal G., Chen B., Wang Z., Long time asymptotics of mixed-type Kimura diffusions. [arXiv]

  • Zhang T., Wang Z., Xin J., Zhang Z., A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows [arXiv]

  • Hu B., Wang Z., Xin J., Zhang Z., A Stochastic Interacting Particle-Field Algorithm for a Haptotaxis Advection-Diffusion System Modeling Cancer Cell Invasion [arXiv]

  • Wang Z., Zhang Z., Zhang Z., Stochastic convergence of regularized solutions for backward heat conduction problems [arXiv]

Vita

It can be found here. A updated version will be avaialbe upon request.