Detecting chaos in lineage-trees: A deep learning approach

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such may behave chaotically under certain conditions, and so the ability detect chaos based on empirical measurement is an important step in understanding these processes. Classifying a system chaotic entails estimating its largest Lyapunov exponent (LLE), which quantifies average rate of convergence or divergence initially close trajectories state space. Estimating observations process especially challenging affected by small amount noise, used model many real-world processes, particular biological We describe method for accurately noisy data, training deep learning models synthetically generated trajectories. Once trained, they can be LLE data without any assumption underlying dynamics. Our naturally extends different input topologies, allowing us analyze tree-shaped characteristic inheritance dynamics, where near-identical replication offers unique hitherto unstudied avenue chaos. also characterize information extracted our their predictions, deeper into ways analyzed topologies.