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Title:Causal history analysis of complex system dynamics
Author(s):Jiang, Peishi
Director of Research:Kumar, Praveen
Doctoral Committee Chair(s):Kumar, Praveen
Doctoral Committee Member(s):Cai, Ximing; Dominguez, Francina; Gupta, Hoshin; Passalacqua, Paola
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):information theory
complex system dynamics
Abstract:Complex system arises as a result of inter-dependencies between multiple components. The nonlinear interactions occurring in the system usually lead to emergent behaviors. The emergence prevails in many natural systems, such as the fractal dynamics of stream chemistry, the chaotic behavior of atmospheric convection, the entropy production due to the dissipative structure of plants, and so forth. Multivariate interactions of the entire system definitely play a key role in sustaining these emergent behaviors, which will not happen solely based on the dynamics of univariate or the interactions within a specific set of variables. Therefore, improving the understanding on the whole system dynamics requires the consideration of how the entire evolutionary dynamics of a system, termed causal history, jointly shapes its present state. In this dissertation, the primary goal is to establish a framework for the study of whole system evolutionary dynamics from multivariate interactions. To achieve that, an information-theoretic formulation is developed to characterize the joint influence from the entire causal history to the present state of each variable using a directed acyclic graph representation. The proposed framework builds on the quantification and characterization of information flow from one source through a causal pathway and two sources through the interaction of separable pathways, which takes advantage of the idea of momentary information transfer and partial information decomposition. Momentary information transfer captures the amount of information flow between any two variables lagged at two specific points in time. Partial information decomposition characterizes the joint effect from two sources into redundant, synergistic and unique contributions. To evaluate the joint influence from the causal history, we partition it into immediate causal history, as a function of lag τ from the recent time, to capture the influence of recent dynamics, and the complementary distant causal history. Further, each of these influences are decomposed into self and cross feedbacks. Such a partition allows the characterization of the information flow from the self- and cross-dependencies with other variables in both histories. This causal history analysis approach is then implemented to investigate the dynamics of different types of systems. It successfully illustrates the memory dependencies of short- and long-memory processes. Further, we find the information characterization differs from system to system, illustrating their various dynamics. A long-memory process, for instance, is sustained by self-feedback-dominated recent dynamics and cross- dependency dominated earlier dynamics. In the analysis of observed stream chemistry data, this analysis indicates the key role of the flow rate in creating cross connectivities among stream solutes and also its influence on the dynamics of each solute. Meanwhile, the information from cross-dependence is non-negligible even after correcting for the dependency of flow rate in raw data. It suggests that besides its self-feedback interaction, the resulting 1/f signature of each solute is also maintained by the interactions with other variables in the stream. Last, we evaluate the structure of numerical models based on the idea of information flow between variables. Since we have the ability to intervene in numerical models, the evaluation analyzes how intervening or freezing one or multiple lagged source variables impacts the dynamics of each target variable. Such interventional-effect is different from the prior observational data based analysis anchored on statistical dependencies, and thus provides a complementary view on the component interaction. The analysis of the Lorenz model illustrates the potential contradictory conclusion drawn from the two perspectives, in terms of the extent of information transferred from source variables. It, therefore, reveals the importance of numerical modelling effort in providing insights on the dynamics of the simulated natural systems, in addition to the analysis of observational data. A better and deeper understanding of complex system dynamics is becoming a necessity due to a higher demand on multidisciplinary research nowadays. With increasing availability of observational data and complexity of numerical models, the information-theoretic metrics proposed and utilized here open new avenues for understanding complex system dynamics.
Issue Date:2019-04-16
Rights Information:Copyright 2019 Peishi Jiang
Date Available in IDEALS:2019-08-23
Date Deposited:2019-05

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