Biological & Soft Matter Seminar: Characterizing Nonlinear Dynamics via Smooth Prototype Equivalences

Abstract:

Recent progress in computational biology has allowed researchers to gain insight into the dynamical state of cells in the gene expression space of single-cell RNA-sequencing data. Such information has immense potential for revealing mechanisms driving a multitude of biological processes, such as the cell cycle, the circadian rhythm, differentiation and reprogramming. However, characterizing the long term behavior of these dynamical systems given the limited, noisy, and high-dimensional measurements is a challenging task.

In this talk, I will present smooth prototype equivalences (SPE), a probabilistic framework for matching sparse and noisy velocity observations to prototypical dynamical behaviors, through diffeomorphisms parameterized by invertible neural networks. Using SPE it is possible to localize the long-term behavior of the observed dynamics and simulate future cellular states in a hypothesis driven, interpretable manner. Furthermore, through principled probabilistic modeling of the dynamical system, SPE enables grounded model selection given noisy observations, even when only a small subset of the phase space is observed.