# 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`

.

## 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,

surrogate models for particle simulation,

math foundation of diffusion models,

effective diffusivities, KPP front speed, chemotaxis,

interacting particle (field) methods,

convection Enhanced phenomenon in large Peclet regime,

neural operators,

POD/Tensor-Train,

non-linear filtering,

…

## Publications¶

Xie Y., Wang Z., Zhang Z., Random block coordinate descent methods for computing optimal transport and convergence analysis. JSC, 2024. [doi]

Bal G., Wang Z., Z2 classification of FTR symmetric differential operators and obstruction to Anderson localization. JPA, 2024 [arXiv]

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

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

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

Cui T., Wang Z., Zhang Z., A variational neural network approach for glacier modelling with nonlinear rheology. CiCP, 2023. [doi]

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

Wang Z., Xin J., Zhang Z., Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method. ESAIM: M2AN, 2022. [doi]

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]

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]

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]

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]

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

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]

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 Z., Xin J., Zhang Z., A Novel Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Chemotaxis System. [arXiv]

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

Zhang T., Wang Z., Xin J., Zhang Z., A convergent interacting particle method for computing KPP front speeds in random flows. [arXiv]

Lu Y., Wang Z., Bal G., Understanding the diffusion models by conditional expectations. [arXiv]

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

Wang Z., Zhang Z., A class of robust numerical methods for solving dynamical systems with multiple time scales. [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.