Research by Themes

Update Non-frequently, see the research page for the most recent ones.

Diffusion/Generative Models

• Wang A., Nair A., Wang Z., Bal G., ML-based approach to classification and generation of structured light propagation in turbulent media. [arXiv]

• Cheng Z., Wang L., Wang Z., Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces. [arXiv]

• Luu H., Wang Z., DC-LA: Difference-of-Convex Langevin Algorithm. [arXiv]

• Shen Z., Wang Z., Xin J., Zhang Z., Two-Step Diffusion: Fast Sampling and Reliable Prediction for 3D Keller–Segel and KPP Equations in Fluid Flows. [arXiv]

• Meng X., Wang Z., Pathway to O(√d) Complexity bound under Wasserstein metric of flow-based models. [arXiv]

• Song F., Wang Z., Sun J., Physics-Informed Design of Input Convex Neural Networks for Consistency Optimal Transport Flow Matching. [arXiv]

• Li Y., Wang A., Wang Z., DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee. [arXiv]

• Zhang T., Wang Z., Xin J., Zhang Z., A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems. [arXiv]

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

• 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. [OpenReview] [arXiv]

• 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]

• 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. [arXiv]

• 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. [arXiv]

PDE related Machine Learning

• Wang A., Nair A., Wang Z., Bal G., ML-based approach to classification and generation of structured light propagation in turbulent media. [arXiv]

• Cheng Z., Wang Z., Wang L., Azaiez M., PODNO: Proper Orthogonal Decomposition Neural Operators. SIAM Journal on Scientific Computing. [arXiv]

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

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

Interactive Particles

• Hu J., Wang Z., Xin J., Zhang Z., A fast stochastic interacting particle-field method for 3D parabolic parabolic Chemotaxis systems: numerical algorithms and error analysis. [arXiv]

• Hu B., Wang Z., Xin J., Zhang Z., A Stochastic Genetic Interacting Particle Method for Reaction-Diffusion-Advection Equations. [arXiv]

• Hu B., Wang Z., Xin J., Zhang Z., Convergence Analysis of a Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Systems. [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]

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

• 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. [arXiv]

• 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]

• 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. [arXiv]

• 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. [arXiv]

• 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. [arXiv]

• 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. [arXiv]

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

Reduced Order Models and Fast Algorithms

• Meng Y., Wang Z., Yau S.S.T., Zhang Z., Regularity estimate and sparse approximation of pathwise robust Duncan-Mortensen-Zakai equation. [arXiv]

• Cheng Z., Wang Z., Wang L., Azaiez M., PODNO: Proper Orthogonal Decomposition Neural Operators. SIAM Journal on Scientific Computing. [arXiv]

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

• 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. [arXiv]

• 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. [arXiv]

• 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.

Applied Analysis

• Bal G., Wang X., Wang Z., Inverse scattering for waveguides in topological insulators. [arXiv]

• Meng Y., Wang Z., Yau S.S.T., Zhang Z., Regularity estimate and sparse approximation of pathwise robust Duncan-Mortensen-Zakai equation. [arXiv]

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

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

• Bal G., Chen B., Wang Z., Long time asymptotics of mixed-type Kimura diffusions. Communications in Mathematical Sciences, 2026. [arXiv]

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

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