Model-based Investigation of Cascade Dynamics on Multi-layer Networks

Abstract

This dissertation examines the spread of an activity among a network of heterogeneous agents with multiple communication modalities, the spread of a continuous activity level and the learning of rigid body dynamics from data.

Motivated by the remarkable ability of animal groups in responding to a real threat while not responding to a spurious one, we investigate how information propagates in a network of agents using the linear threshold model (LTM). We found that the key to the group's sensitivity to a threat and robustness to noise is the existence of multiple communication modalities. To distinguish different communication modalities, we extend the LTM to multiplex networks. We propose protocols for an agent to synthesize information from different communication modalities and study groups with heterogeneous protocols. We propose a provably accurate algorithm and an efficient approximate algorithm to compute the size of spread given a set of early adopters.

We generalize the discrete LTM into a continuous threshold model (CTM) and analyze cascade dynamics. We rigorously show the existence of a pitchfork bifurcation in the dynamics. Abrupt change of all agents' activity levels happens when the pitchfork is subcritical. We show how high disparity in the thresholds and network structure lead to a cascade.

Both the LTM and CTM assume the state of agents can be directly observed, which is often the case in biological systems. To incorporate these insights into designing coordinated engineering systems, e.g., a robot team, an agent need to infer the activity of neighboring agents from sensor data. We study the scenario where the activity is indicated by the configuration or the dynamics of a rigid body system. We propose a neural network model to learn rigid body dynamics assuming the sensor data are raw images. We design a coordinate-aware variational auto-encoder (VAE) to infer coordinates from image data and learn Lagrangian/Hamiltonian dynamics on the inferred coordinates. We show that the prior of Lagrangian/Hamiltonian dynamics improves accuracy and generalization. We show the coordinate-aware VAE is crucial in learning interpretable coordinates. This interpretability benefits long term prediction and allows for synthesis of energy-based controllers.