Unveil microscopic mechanism from collective behaviors*

In many-body systems, the interplay between single-particle dynamics and interparticle interaction gives rise to the emergence of collective behavior. For physical systems, condensed matter theory allows us to derive such collective behavior from microscopic details. But for biological systems, microscopic mechanisms are often unknown. In this talk, we will present a generic neural network architecture to solve the inverse problem---revealing dynamical mechanisms of individual cells from their collective behaviors that are easily accessible in experiment. It employs graph neural networks to learn complex intercellular interactions and normalizing flows to capture the intrinsic fluctuations of cells. We show that by training on a few experimental videos, this machine learning (ML) model can accurately predict the stochastic motion of epithelial cells, the deterministic growth of a fly wing, and the wave propagation of ERK signaling. In contrast to traditional ML methods that make deterministic predictions, our probabilistic design makes it possible to reveal the stochasticity of a biological system including the correlation between the cells. Our method paves the way to the data-driven study of biological many-body systems.