Publications

2025

1. Review

   

   Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis

   Zhenyi Zhang^†, Yuhao Sun^†, Qiangwei Peng^†, and 2 more authors

   2025

   Abs DOI Bib

   Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schrödinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

   @misc{zhang2025integratingdynamicalsystemsmodeling,
     title = {Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis},
     author = {Zhang, Zhenyi and Sun, Yuhao and Peng, Qiangwei and Li, Tiejun and Zhou, Peijie},
     year = {2025},
     eprint = {2503.11347},
     archiveprefix = {arXiv},
     url = {https://arxiv.org/abs/2503.11347},
     doi = {https://doi.org/10.48550/arXiv.2503.11347},
   }

2. ICLR 2025 oral

   

   Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport

   Zhenyi Zhang^†, Tiejun Li^*, and Peijie Zhou^*

   In The Thirteenth International Conference on Learning Representations  (Oral) , 2025

   Abs DOI HTML

   Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. Based on the RUOT form, our method models these dynamics without requiring prior knowledge of growth and death processes or additional information, allowing them to be learnt directly from data. Theoretically, we explore the connections between the RUOT and Schrödinger bridge problem and discuss the key challenges and potential solutions. The effectiveness of our method is demonstrated with a synthetic gene regulatory network. Compared with other methods, our approach accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape.

2024

1. CiCP

   

   Uncertainty Quantification of Phase Transition Problems with an Injection Boundary

   Zhenyi Zhang^†, Shengbo Ma, and Zhennan Zhou^*

   Accepted by Communications in Computational Physics , Feb 2024

   Abs DOI Bib

   We develop an enthalpy-based modeling and computational framework to quantify uncertainty in Stefan problems with an injection boundary. Inspired by airfoil icing studies, we consider a system featuring an injection boundary inducing domain changes and a free boundary separating phases, resulting in two types of moving boundaries. Our proposed enthalpy-based formulation seamlessly integrates thermal diffusion across the domain with energy fluxes at the boundaries, addressing a modified injection condition for boundary movement. Uncertainty then stems from random variations in the injection boundary. The primary focus of our Uncertainty Quantification (UQ) centers on investigating the effects of uncertainty on free boundary propagation. Through mapping to a reference domain, we derive an enthalpy-based numerical scheme tailored to the transformed coordinate system, facilitating a simple and efficient simulation. Numerical and UQ studies in one and two dimensions validate the proposed model and the extended enthalpy method. They offer intriguing insights into ice accretion and other multiphysics processes involving phase transitions.

   @article{zhang2024uncertainty,
     title = {Uncertainty Quantification of Phase Transition Problems with an Injection Boundary},
     author = {Zhang, Zhenyi and Ma, Shengbo and Zhou, Zhennan},
     year = {2024},
     month = feb,
     publisher = {arxiv},
     doi = {10.48550/arXiv.2402.02806},
     url = {https://arxiv.org/abs/2402.02806},
   }