Modeling Global Dynamics from Local Snapshots with Deep Generative Neural Networks

TL;DR

This paper introduces DyMoN, a deep generative neural network framework that models complex stochastic dynamics from snapshot data without requiring longitudinal measurements, outperforming traditional models in biological system analysis.

Contribution

The paper presents DyMoN, a novel deep neural network approach that captures system dynamics from local snapshots, enabling trajectory generation and analysis without longitudinal data.

Findings

DyMoN effectively models biological system dynamics.

Outperforms Kalman filters and HMMs in capturing complex stochastic processes.

Enables extraction of dynamic features through neural network perturbation.

Abstract

Complex high dimensional stochastic dynamic systems arise in many applications in the natural sciences and especially biology. However, while these systems are difficult to describe analytically, "snapshot" measurements that sample the output of the system are often available. In order to model the dynamics of such systems given snapshot data, or local transitions, we present a deep neural network framework we call Dynamics Modeling Network or DyMoN. DyMoN is a neural network framework trained as a deep generative Markov model whose next state is a probability distribution based on the current state. DyMoN is trained using samples of current and next-state pairs, and thus does not require longitudinal measurements. We show the advantage of DyMoN over shallow models such as Kalman filters and hidden Markov models, and other deep models such as recurrent neural networks in its ability to embody the dynamics (which can be studied via perturbation of the neural network) and generate longitudinal hypothetical trajectories. We perform three case studies in which we apply DyMoN to different types of biological systems and extract features of the dynamics in each case by examining the learned model.