Introduction to Focus Issue: Causation inference and information flow in dynamical systems: Theory and applications

Abstract

Questions of causation are foundational across science and often relate further to problems of control, policy decisions, and forecasts. In nonlinear dynamics and complex systems science, causation inference and information flow are closely related concepts, whereby "information" or knowledge of certain states can be thought of as coupling influence onto the future states of other processes in a complex system. While causation inference and information flow are by now classical topics, incorporating methods from statistics and time series analysis, information theory, dynamical systems, and statistical mechanics, to name a few, there remain important advancements in continuing to strengthen the theory, and pushing the context of applications, especially with the ever-increasing abundance of data collected across many fields and systems. This Focus Issue considers different aspects of these questions, both in terms of founding theory and several topical applications. Published by AIP Publishing. https://doi

Debates—Does Information Theory Provide a New Paradigm for Earth Science? Causality, Interaction, and Feedback

“…Eichler () discusses various concepts regarding causality and spurious detections of causal interactions, and introduced a general algorithm to detect causality. A recent focus issue in the journal Chaos presents a series of theories and applications in the domain of causal inference using information flow (Bollt et al, ). For instance, Liang () develops a formalized version of information flow in a known physical model from an interventional perpective, while Bolt (, ) delineates the information flow in numerical models by using a transfer operator.…”

On Geometry of Information Flow for Causal Inference

“…In particular, contrasting forecasts is the defining concept underlying Granger Causality (G-causality), and it is closely related to the concept of information flow as defined by transfer entropy [7,8], which can be proved as a nonlinear version of Granger's otherwise linear (ARMA) test [9]. In this spirit, we find methods such as Convergent Cross-Mapping method (CCM) [10], and causation entropy (CSE) [11] to disambiguate direct versus indirect influences [11][12][13][14][15][16][17][18]. On the other hand, closely related to information flow are concepts of counter factuals: "what would happen if ..." [19] that are foundational questions for another school leading to the highly successful Pearl "Do-Calculus" built on a specialized variation of Bayesian analysis [20].…”

Using Information Flow for Whole System Understanding From Component Dynamics

“…In a watershed, or dynamical systems in general, information flow captures the attenuation or amplification of fluctuations among variables, thereby revealing the dynamic connectivity between them (Goodwell et al, 2018). Analysis of such information flow can provide a unique vantage point for understanding watershed functions: that of quantifying multivariate causal interactions (Balasis et al, 2013;Bollt et al, 2018) that link across space and time scales of the watershed dynamics (Jiang & Kumar, 2019).…”

“…On the flip side, can we also understand how system level constraints govern component level dynamics? In this paper we present a framework to address such questions by quantifying information flow among variables to characterize causal dependencies in complex systems (Balasis et al, 2013;Bollt et al, 2018). This draws upon the well-known idea that the whole is greater than the union of the parts.…”