New Horizons of Systems Science: Systems Dynamics Relationship to Systems Engineering Principles, Complex Systems, Category Theory
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Systems Engineering Principles↗
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Application of modern network theory to analysis of complex systems
Modern network theory applications to analysis of complex systems
Faken, J. C.↗
Predictive Complexity of Quantum Subsystems
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement.
Asplund, Curtis T. (ORCID:0000000305575850)↗
Information transfer in complex systems, with applications to regulation
Information theory of complex systems
Conant, R. C.↗
Microscopic Derivation of Transition-state Theory for Complex Quantum Systems
The decay of quantum complex systems through a potential barrier is often described with transition-state theory, also known as RRKM theory in chemistry. Here we derive the basic formula for transition-state theory based on a generic Hamiltonian as might be constructed in a configuration-interaction basis. Two reservoirs of random Hamiltonians from Gaussian orthogonal ensembles are coupled to intermediate states representing the transition states at a barrier. Under the condition that the decay of the reservoirs to open channels is large, an analytic formula for reaction rates is derived. Here, the transition states act as independent Breit–Wigner resonances which contribute additively to the total transition probability, as is well known for electronic conductance through resonant tunneling states. It is also found that the transition probability is independent of the decay properties of the states in the second reservoir over a wide range of decay widths.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Applicability of Complexity Theory to Martian Fluvial Systems: A Preliminary Analysis
In the last 15 years, terrestrial geomorphology has been revolutionized by the theories of chaotic systems, fractals, self-organization, and selforganized criticality. Except for the application of fractal theory to the analysis of lava flows and rampart craters on Mars, these theories have not yet been applied to problems of Martian landscape evolution. These complexity theories are elucidated below, along with the methods used to relate these theories to the realities of Martian fluvial systems.
Rosenshein, E. B.↗
Quantum Electrodynamics Coupled-Cluster at Scale: High-Performance Implementation for Complex Systems
Coupled-cluster theory (CC) is a highly accurate and versatile method for simulating complex interactions within quantum systems. The extension of CC theory to model mixed electron-photon processes with quantum electrodynamics (QED) has improved our capability to predict cavity-modified chemistry, a field where photons are used as cost-effective and eco-friendly alternatives to catalyze/inhibit chemical reactions. However, calculations with CC methods, even without incorporating QED effects, are often prohibitively expensive. Simulations of larger systems require scalable infrastructures that exist for traditional CC methods but not for QED-CC methods. As such, we present a GPU-enabled, high-performance, open-source implementation of the quantum electrodynamics coupled-cluster method with single and double excitations (QED-CCSD) within the ExaChem quantum chemistry software package. ExaChem relies on the Tensor Algebra for Many-body Methods (TAMM) infrastructure: a parallel heterogeneous tensor library designed to achieve scalable performance on modern heterogeneous supercomputing platforms. Furthermore, we discuss theoretical foundations, algorithmic details, and numerical benchmarks to showcase the larger systems that ExaChem can simulate and how the integration of photonic degrees-of-freedom alters their ground-state properties.
Basis sets↗
Layered complex networks as fluctuation amplifiers
Abstract In complex networked systems theory, an important question is how to evaluate the system robustness to external perturbations. With this task in mind, I investigate the propagation of noise in multi-layer networked systems. I find that, for a two layer network, noise originally injected in one layer can be strongly amplified in the other layer, depending on how well-connected are the complex networks in each layer and on how much the eigenmodes of their Laplacian matrices overlap. These results allow to predict potentially harmful conditions for the system and its sub-networks, where the level of fluctuations is important, and how to avoid them. The analytical results are illustrated numerically on various synthetic networks.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Achieving designed texture and flows in bulk active nematics using optimal control theory
Being intrinsically nonequilibrium, active materials can potentially perform functions that would be thermodynamically forbidden in passive materials. However, active systems have diverse local attractors that correspond to distinct dynamical states, many of which exhibit chaotic turbulent-like dynamics and thus cannot perform work or useful functions. Designing such a system to choose a specific dynamical state is a formidable challenge. Motivated by recent advances enabling optogenetic control of experimental active materials, we describe an optimal control theory framework that identifies a spatiotemporal sequence of light-generated activity that drives an active nematic system toward a prescribed dynamical steady state. Active nematics are unstable to spontaneous defect proliferation and chaotic streaming dynamics in the absence of control. We demonstrate that optimal control theory can compute activity fields that redirect the dynamics into a variety of alternative dynamical programs and functions. This includes dynamically reconfiguring between states, selecting and stabilizing emergent behaviors that do not correspond to attractors, and are hence unstable in the uncontrolled system. Furthermore, our results provide a roadmap to leverage optical control methods to rationally design structure, dynamics, and function in a wide variety of active materials.
Complex systems theory↗
An approximate inertial manifold (AIM) based closure for turbulent flows
A closure model for turbulent flows is developed based on a dynamical system theory. An appropriately discretized formulation of the governing equations is considered for this process. The key ingredient is an approximation of the system’s attractor, where all the trajectories in phase space are confined. This approximate inertial manifold based approach provides a path to track trajectories of the system in a lower-dimensional subspace. Unlike conventional coarse-graining approaches, the turbulent field is decomposed into resolved and unresolved dynamics using the properties of the governing equations. The novelty of the approach relies on the reconstruction of the unresolved field constrained by the governing equations. A posteriori tests for homogeneous isotropic turbulence and the Kuramoto–Sivashinsky equation show promising results for considerable dimension reduction with strong convergence properties. The proposed model outperforms the dynamic Smagorinsky model, and the computational overhead is competitive with similar approaches.
97 MATHEMATICS AND COMPUTING↗
Survey on stochastic distribution systems: A full probability density function control theory with potential applications
Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non-Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data-driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision-making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.
42 ENGINEERING↗
Constructing tensor network influence functionals for general quantum dynamics
Here, we describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of its bond dimension and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Discovering causal structure with reproducing-kernel Hilbert space ε -machines
We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Causal interaction in high frequency turbulence at the biosphere–atmosphere interface: Structure–function coupling
At the biosphere–atmosphere interface, nonlinear interdependencies among components of an ecohydrological complex system can be inferred using multivariate high frequency time series observations. Information flow among these interacting variables allows us to represent the causal dependencies in the form of a directed acyclic graph (DAG). Here, we use high frequency multivariate data at 10 Hz from an eddy covariance instrument located at 25 m above agricultural land in the Midwestern US to quantify the evolutionary dynamics of this complex system using a sequence of DAGs by examining the structural dependency of information flow and the associated functional response. We investigate whether functional differences correspond to structural differences or if there are no functional variations despite the structural differences. We base our analysis on the hypothesis that causal dependencies are instigated through information flow, and the resulting interactions sustain the dynamics and its functionality. To test our hypothesis, we build upon causal structure analysis in the companion paper to characterize the information flow in similarly clustered DAGs from 3-min non-overlapping contiguous windows in the observational data. We characterize functionality as the nature of interactions as discerned through redundant, unique, and synergistic components of information flow. Through this analysis, we find that in turbulence at the biosphere–atmosphere interface, the variables that control the dynamic character of the atmosphere as well as the thermodynamics are driven by non-local conditions, while the scalar transport associated with CO and H 2 O is mainly driven by short-term local conditions.
58 GEOSCIENCES↗
An experimental approach to validating a theory of human error in complex systems
The problem of 'human error' is pervasive in engineering systems in which the human is involved. In contrast to the common engineering approach of dealing with error probabilistically, the present research seeks to alleviate problems associated with error by gaining a greater understanding of causes and contributing factors from a human information processing perspective. The general approach involves identifying conditions which are hypothesized to contribute to errors, and experimentally creating the conditions in order to verify the hypotheses. The conceptual framework which serves as the basis for this research is discussed briefly, followed by a description of upcoming research. Finally, the potential relevance of this research to design, training, and aiding issues is discussed.
Morris, N. M.↗
Information transfer in complex systems, with applications to regulation Interim scientific report
Information theory and relevance to study of complex systems
Conant, R. C.↗
Self-dissimilarity as a High Dimensional Complexity Measure
For many systems characterized as "complex" the patterns exhibited on different scales differ markedly from one another. For example the biomass distribution in a human body "looks very different" depending on the scale at which one examines it. Conversely, the patterns at different scales in "simple" systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity "signature" of that system. Here we present a novel quantification of self-dissimilarity. This signature can, if desired, incorporate a novel information-theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self-dissimilarity can be measured for many kinds of real-world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain-forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used a s the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity we present several numerical experiments. In particular, we show that underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series produced by that map
Wolpert, David H.↗