Single-cell sequencing technologies provide unprecedented resolution for studying the dynamic process of cell-state transitions during development and complex disease. In this talk, I will discuss how machine learning has enabled us to overcome this challenge and use dynamical systems techniques to analyze scRNA-seq data. I will introduce the low-dimensional dynamical manifold to identify attractor basins and transition probabilities in snapshot data. I will also present the usage of non-equilibrium dynamical systems theory to analyze attractor stability and identify transition-driving genes in gene expression and splicing processes. Finally, I will discuss our efforts to construct a time-varying landscape, which interpolates non-stationary time-series scRNA-seq data using Wasserstein-Fisher-Rao metric, unbalanced optimal transport and its neural network-based partial differential equation implementations.
