Abstract: The rapid development of single-cell sequencing technologies provides unprecedented resolutions to study the dynamical process of cell-state transitions during development and complex disease. Mathematically, the transitions can be modeled as a (stochastic) dynamical system with a multi-scale structure.
In this talk, we will discuss how recent developments in machine learning have allowed us to use dynamical systems techniques to analyze scRNA-seq data. We will introduce the MuTrans algorithm, which uses a low-dimensional dynamical manifold to uncover the underlying attractor basins and transition probabilities in snapshot data. We will also present the scTT (single-cell transition tensor) and spliceJAC algorithms, which use non-equilibrium dynamical systems theory to analyze the stability of attractors within data and identify transition-driving genes in gene expression and splicing processes. Finally, we will discuss our efforts to interpolate non-stationary time-series scRNA-seq data using Wasserstein-Fisher-Rao-metric unbalanced optimal transport and its neural network-based PDE implementations.