Model predictive complex system control from observational and interventional data.

Complex systems, characterized by intricate interactions among numerous entities, give rise to emergent behaviors whose data-driven modeling and control are of utmost significance, especially when there is abundant observational data but the intervention cost is high. Traditional methods rely on precise dynamical models or require extensive intervention data, often falling short in real-world applications. To bridge this gap, we consider a specific setting of the complex systems control problem: how to control complex systems through a few online interactions on some intervenable nodes when abundant observational data from natural evolution is available. We introduce a two-stage model predictive complex system control framework, comprising an offline pre-training phase that leverages rich observational data to capture spontaneous evolutionary dynamics and an online fine-tuning phase that uses a variant of model predictive control to implement intervention actions. To address the high-dimensional nature of the state-action space in complex systems, we propose a novel approach employing action-extended graph neural networks to model the Markov decision process of complex systems and design a hierarchical action space for learning intervention actions. This approach performs well in three complex system control environments: Boids, Kuramoto, and Susceptible-Infectious-Susceptible (SIS) metapopulation. It offers accelerated convergence, robust generalization, and reduced intervention costs compared to the baseline algorithm. This work provides valuable insights into controlling complex systems with high-dimensional state-action spaces and limited intervention data, presenting promising applications for real-world challenges.

Emergence and Causality in Complex Systems: A Survey of Causal Emergence and Related Quantitative Studies.

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of individual properties. On the other hand, causality can exhibit emergence, meaning that new causal laws may arise as we increase the level of abstraction. Causal emergence (CE) theory aims to bridge these two concepts and even employs measures of causality to quantify emergence. This paper provides a comprehensive review of recent advancements in quantitative theories and applications of CE. It focuses on two primary challenges: quantifying CE and identifying it from data. The latter task requires the integration of machine learning and neural network techniques, establishing a significant link between causal emergence and machine learning. We highlight two problem categories: CE with machine learning and CE for machine learning, both of which emphasize the crucial role of effective information (EI) as a measure of causal emergence. The final section of this review explores potential applications and provides insights into future perspectives.