Chapter 5, Thresholds and Complex Dynamics of Interdependent Cascading Infrastructure Systems
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Carreras, Benjamin A↗
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Heterogeneous recurrence monitoring and control of nonlinear stochastic processes
Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Predicting Critical Transitions in Multiscale Data
Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.
97 MATHEMATICS AND COMPUTING↗
Fractional noise destroys or induces a stochastic bifurcation
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
FTL: Transfer Learning Nonlinear Plasma Dynamic Transitions in Low Dimensional Embeddings (FTL) v1.0
Fusion Transfer Learning (FTL) model provides a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. The knowledge transfer process leverages a pre-trained neural encoder-decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL's capacity to capture transitional behaviors and dynamical features in plasma dynamics -- a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics (MHD) modes.
Bai, Zhe↗
Building and using dynamic risk-informed diagnosis procedures for complex system accidents
Accidents pose unique challenges for operating crews in complex systems such as nuclear power plants, presenting limitations in plant status information and lack of detailed monitoring, diagnosis, and response planning support. Advances in severe accident simulation and dynamic probabilistic risk assessment provide an opportunity to garner detailed insight into accident scenarios. In this article, we demonstrate how to build and use a framework which leverages dynamic probabilistic risk assessment, simulation, and dynamic Bayesian networks to provide real-time monitoring and diagnostic support for severe accidents in a nuclear power plant. We use general purpose modeling technology, the dynamic Bayesian network, and adapt it for risk management of complex engineering systems. This article presents a prototype model for monitoring and diagnosing system states associated with loss of flow and transient overpower accidents in a generic sodium fast reactor. We discuss using this framework to create a risk-informed accident management framework called Safely Managing Accidental Reactor Transients procedures. This represents a new application of risk assessment, expanding probabilistic risk assessment techniques beyond static decision support into dynamic, real-time models which support accident diagnosis and management.
Groth, Katrina M.↗
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Electron and Electron-Nuclear Dynamics of Open Quantum Subsystems
Leveraging an open-subsystem formulation of Density Functional Theory (DFT) we aim at describing periodic and molecular systems alike, including their electronic and nuclear dynamics. Subsystem DFT enables first principles simulations to approach realistic time- and length-scales, and most importantly sheds light on the dynamical behavior of complex systems. Taking subsystem DFT to the time domain allows us to inspect the electron dynamics of condensed-phase systems in real time. In liquids and interfaces, we observe all the relevant regimes proper of non-Markovian open quantum system dynamics, such as electronic energy transfer, and screening. In addition, the ab-initio modeling of system-bath interactions brought us to observe and justify the holographic time-dependent electron density theorem. Contrary to interactions between molecular (finite) systems, when molecules interact with metal or semiconductor surfaces the electron dynamics is strongly non-Markovian with dramatic repercussions to the molecule’s response to external perturbations. Metals and semiconductors typically have large polarizabilities, and even in a regime of low coupling their effect on impinging molecular species is significant–line broadening, peak shift, and intensity borrowing are observed, characterized, and explained in terms of inter-subsystem dynamical interactions and a many-body decomposition of the system’s density-density response function in a way that transcends the canons of Fermi Golden Rule.
33 ADVANCED PROPULSION SYSTEMS↗
DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-Shot Transfer the Dynamic Response of Networked Systems
This article develops a deep graph operator network (DeepGraphONet) framework that learns to approximate the dynamics of a complex system (e.g., the power grid or traffic) with an underlying subgraph structure. Here, we build our DeepGraphONet by fusing the ability of graph neural networks to exploit spatially correlated graph information and deep operator networks to approximate the solution operator of dynamical systems. The resulting DeepGraphONet can then predict the dynamics within a given short/medium-term time horizon by observing a finite history of the graph state information. Furthermore, we design our DeepGraphONet to be resolution independent. That is, we do not require the finite history to be collected at the exact/same resolution. In addition, to disseminate the results from a trained DeepGraphONet, we design a zero-shot learning strategy that enables using it on a different subgraph. Finally, empirical results on the transient stability prediction problem of power grids and traffic flow forecasting problem of a vehicular system illustrate the effectiveness of the proposed DeepGraphONet.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Transfer learning nonlinear plasma dynamic transitions in low dimensional embeddings via deep neural networks
Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel, data-driven model reduction methods, coupled with detection of abnormal modes with plasma physics, opens a unique opportunity to identify plasma instabilities through automated construction of parsimonious models that can be tuned to balance accuracy and cost. Our fusion transfer learning (FTL) model demonstrates success in rapidly reconstructing nonlinear kink mode structures by learning from a limited amount of nonlinear simulation data. The knowledge transfer process leverages a pre-trained neural encoder–decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL’s capacity to capture transitional behaviors and dynamical features in plasma dynamics—a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics modes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Uncertainty-Aware, Structure-Preserving Machine Learning Approach for Domain Shift Detection From Nonlinear Dynamic Responses of Structural Systems
Complex structural systems deployed for aerospace, civil, or mechanical applications must operate reliably under varying operational conditions. Structural health monitoring (SHM) systems help ensure the reliability of these systems by providing continuous monitoring of the state of the structure. SHM relies on synthesizing measured data with a predictive model to make informed decisions about structural states. However, these models—which may be thought of as a form of a digital twin—need to be updated continuously as structural changes (e.g., due to damage) arise. We propose an uncertainty-aware machine learning model that enforces distance preservation of the original input state space and then encodes a distance-aware mechanism via a Gaussian process (GP) kernel. The proposed approach leverages the spectral-normalized neural GP algorithm to combine the flexibility of neural networks with the advantages of GP, subjected to structure-preserving constraints, to produce an uncertainty-aware model. This model is used to detect domain shift due to structural changes that cannot be observed directly because they may be spatially isolated (e.g., inside a joint or localized damage). This work leverages detection theory to detect domain shift systematically given statistical features of the prediction variance produced by the model. The proposed approach is demonstrated on a nonlinear structure being subjected to damage conditions. In conclusion, it is shown that the proposed approach is able to rely on distances of the transformed input state space to predict increased variance in shifted domains while being robust to normative changes.
Algorithms↗
Mixed quantum/classical theory (MQCT) approach to the dynamics of molecule–molecule collisions in complex systems
Correlation between state-to-state transition cross-sections and energy transfer in p-H 2 O + p-H 2 at collision energyU= 12 000 cm −1 .
Chemistry↗
Update on ORNL TRANSFORM Tool: Simulating Multi-Module Advanced Reactor with End-to-End I&C
The Small Modular Reactor (SMR) Dynamic System Modeling Tool project is in the fourth year of development. The project is designed to support collaborative modeling and study of various advanced SMR (non-light water cooled reactor) concepts, including the use of multiple coupled reactors at a single site. The focus of this report is the development of a steam generator and drum system model that includes the complex dynamics of typical steam drum systems, the development of instrumentation and controls for the steam generator with drum system model, and the development of multi-reactor module models that reflect the full power reactor innovative small module design concept. The objective of the project is to provide a common simulation environment and baseline modeling resources to facilitate rapid development of dynamic advanced reactor models; ensure consistency among research products within the Instrumentation, Controls, and Human-Machine Interface technical area; and leverage cross-cutting capabilities while minimizing duplication of effort. The combined simulation environment and suite of models are identified as the TRANSFORM tool. The critical elements of this effort include (1) defining a standardized, common simulation environment that can be applied throughout the Advanced Reactors Technology program; (2) developing a library of baseline component modules that can be assembled into full plant models using available geometry, design, and thermal-hydraulic data; (3) defining modeling conventions for interconnecting component models; and (4) establishing user interfaces and support tools to facilitate simulation development (i.e., configuration and parameterization), execution, and results display and capture.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Ice sculpting: An artificial spin ice Tutorial on controlling microstate and geometry for magnonics and neuromorphic computing
Artificial spin ice, arrays of strongly interacting nanomagnets, are complex magnetic systems with many emergent properties, rich microstate spaces, intrinsic physical memory, high-frequency dynamics in the GHz range, and compatibility with a broad range of measurement approaches. This Tutorial article aims to provide the foundational knowledge needed to understand, design, develop, and improve the dynamic properties of artificial spin ice. Special emphasis is placed on introducing the theory of micromagnetics, which describes the complex dynamics within these systems, along with their design, fabrication methods, and standard measurement and control techniques. The article begins with a review of the historical background, introducing the underlying physical phenomena and interactions that govern artificial spin ice. We then explore the standard experimental techniques used to prepare the microstate space of the nanomagnetic array and to characterize magnetization dynamics, both in artificial spin ice and more broadly in ferromagnetic materials. Finally, we introduce the basics of neuromorphic computing applied to the case of artificial spin ice systems with a goal to help researchers new to the field grasp these exciting new developments.
Sultana, Rawnak [Univ. of Delaware, Newark, DE (Un↗
Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics
The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. Here, in this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.
Hamiltonians↗
Dynamics of Thermally Driven Domain Transformation in Ferroelectric Thin Films
An important feature in ultrathin ferroelectric films is the spontaneous formation of nanoscale polarization domain patterns. Epitaxial strain can greatly increase the ferroelectric transition temperature such that films can be in the ferroelectric state during growth. On the other hand, depolarization fields compete with ferroelectricity in ultrathin films, and, consequently, the optimal domain configuration during growth is a moving target. Under these conditions it is readily possible for a grown film to be in a nonequilibrium domain configuration. As the energy landscape in the system is quite complex, the relaxation dynamics by which a system can evolve towards the true equilibrium configuration are also quite interesting. Here, to capture the details of this process we used Bragg-geometry x-ray photon correlation spectroscopy (XPCS), in which x-ray scattering speckle patterns contain the information from the domain arrangements inside the film. With modest heating (∼150 °C) domain relaxation from 𝑇 (tetragonal) to 𝑀 𝐶 (monoclinic) was observed in BaTiO 3 films grown on ultrathin ferroelectric PbTiO 3 layers. Two-time correlation analysis reveals fascinating details associated with sticking points and reversals in the process.
36 MATERIALS SCIENCE↗
WASP-12b AND HAT-P-8b are members of triple star systems
We present high spatial resolution images that demonstrate that WASP-12b and HAT-P-8b orbit the primary stars of hierarchical triple star systems. In each case, two distant companions with colors and brightnesses consistent with M dwarfs co-orbit the hot Jupiter planet host as well as one another. Our adaptive optics images spatially resolve the secondary around WASP-12, previously identified by Bergfors et al. and Crossfield et al. into two distinct sources separated by 84.3 ± 0.6 mas (21 ± 3 AU). We find that the secondary to HAT-P-8, also identified by Bergfors et al., is in fact composed of two stars separated by 65.3 ± 0.5 mas (15 ± 1 AU). Our follow-up observations demonstrate physical association through common proper motion. HAT-P-8 C has a particularly low mass, which we estimate to be 0.18 ± 0.02 M {sub ☉} using photometry. Due to their hierarchy, WASP-12 BC and HAT-P-8 BC will enable the first dynamical mass determination for hot Jupiter stellar companions. These previously well studied planet hosts now represent higher-order multi-star systems with potentially complex dynamics, underscoring the importance of diffraction-limited imaging and providing additional context for understanding the migrant population of transiting hot Jupiters.
79 ASTRONOMY AND ASTROPHYSICS↗
Measurement-based Power System Dynamic Model Reduction Using ARX Equivalents
The increasing complexity of power system has made it difficult to simulate large-scale power system in detail. Therefore, to improve computational efficiency, model reduction techniques has been applied to reduce the external area and focus on the dynamics of the internal area. This paper proposes a measurement-based model reduction method which reduces the external system by replacing external system with ARX equivalents. The modeled transfer function parameters are obtained using system identification approach. Case studies on the NPCC system and EI system are carried out. Results show that the proposed reduction method can effectively retain the dynamic behavior of the study area while mitigating computation burden.
Jiang, Zhihao↗