Detecting chaos in lineage-trees: A deep learning approach

TL;DR

This paper introduces a deep learning method to detect chaos in low-dimensional dynamical systems, especially in biological lineage trees, by accurately estimating the largest Lyapunov exponent even in noisy conditions.

Contribution

The study presents a novel deep learning approach for estimating the Lyapunov exponent from tree-structured data, extending chaos detection to biological lineage systems.

Findings

Accurately estimates Lyapunov exponent from short, noisy data

Effective on various dynamical systems

Unique analysis of tree-shaped biological data

Abstract

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.