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Results for “Complex dynamical systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Decision-Making in Complex Dynamical Systems of Systems With One Opposing Subsystem

Many complex dynamical systems consist of a large number of interacting subsystems that operate harmoniously and make decisions that are designed for the benefit of the entire enterprise. If, in an attempt to disrupt the operation of the entire system, one subsystem gets attacked and is made to operate in a manner that is adversarial with the others, then the entire system suffers, resulting in an adversarial decision-making environment among its subsystems. Such an environment may affect not only the decision-making process of the attacked subsystem but also possibly the other remaining subsystems as well. The disruption caused by the attacked subsystem may cause the remaining subsystems to either coalesce as a unified team making team-based decisions, or disintegrate and act as independent decision-making entities. The decision-making process in these types of complex systems of systems is best analyzed within the general framework of cooperative and non-cooperative game theory. In this paper, we will develop an analysis that provides a theoretical basis for modeling the decision-making process in such complex systems. We show how cooperation among the subsystems can produce Noninferior Nash Strategies (NNS) that are fair and acceptable to all subsystems within the team while at the same time provide the subsystems in the team with the security of the Nash equilibrium against the opposing attacked subsystem. We contrast these strategies with the all Nash Strategies (NS) that would result if the operation of the entire system disintegrated and became adversarial among all subsystems as a result of the attack. An example of a system consisting of three subsystems with one opposing subsystem as a result of an attack is included to illustrate the results.

Talebi, Shahriar↗
DOE OSTI2023

Decentralized digital twins of complex dynamical systems

Abstract In this article, we introduce a decentralized digital twin (DDT) modeling framework and its potential applications in computational science and engineering. The DDT methodology is based on the idea of federated learning, a subfield of machine learning that promotes knowledge exchange without disclosing actual data. Clients can learn an aggregated model cooperatively using this method while maintaining complete client-specific training data. We use a variety of dynamical systems, which are frequently used as prototypes for simulating complex transport processes in spatiotemporal systems, to show the viability of the DDT framework. Our findings suggest that constructing highly accurate decentralized digital twins in complex nonlinear spatiotemporal systems may be made possible by federated machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Transforming a Simple Structure Model to Represent a Complex Dynamic System with Unknown Boundary Restraints

Imposing a boundary condition on a structure can significantly alter its dynamic properties. However, sometimes the specifics of the new boundary conditions are not known. When the effects of a boundary condition are uncertain or there is not enough information, engineers need to excite the complex structure to obtain these modified properties. In order to experimentally obtain the new properties, engineers need multiple experiments and many outputs for interpolation in order to sufficiently represent the entire structure. In this study, the researchers attached a stinger to a cantilever beam, acting as a new transverse restraint of unknown properties. This paper presents a conversion expression that predicts the dynamic behavior of any point in the system with the new boundary condition. This expression relies only on one impact hammer experiment with one output and the model of the stinger-free cantilever beam, referred to as the simple structure. Researchers estimated the Transfer Function (TRF) of the beam and compared it with an experimentally measured TRF to validate the method. The mean absolute error of the estimated TRF compared to the experimental TRF is 1.99 dB. This demonstrates the use of the proposed method for estimating unmeasured TRFs in a system with an uncertain boundary condition using a single input, single output (SISO) test and a model of the simple structure.

42 ENGINEERING↗
DOE OSTI2021

Learning Implicit Models of Complex Dynamical Systems From Partial Observations [Slides]

Conclusions: certain data-driven models do implicitly what physics simulations do explicitly; theoretical underpinnings in Koopman theory, delay-coordinate embeddings, and Mori-Zwanzig formalism; best approach for given system with finite data an open question; physics-informed machine learning (PIML) emerging framework for combining explicit and implicit modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Optimal system size for complex dynamics in random neural networks near criticality

In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259–262 (1988)] in the context of random neural networks. When system size is infinite, it is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the sub-critical regime for finite size systems: the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Optimization Method to Branch and Bound Large SBO State Spaces Under Dynamic Probabilistic Risk Assessment via use of LENDIT Scales and S2R2 Sets

Traditional Probabilistic Risk Assessment (PRA) methods have been developed and are quite effective in evaluating risk associated with complex systems, but lack the capability to evaluate complex dynamic systems. These time and energy scales associated with the transient may vary as a function of transition time to a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems, while complete, results in issues associated with combinatorial explosion. In order to address the combinatorial complexity arising from the number of possible state configurations and discretization of transition times, a characteristic scaling metric (LENDIT – length, energy, number, distribution, information and time) is proposed as a means to describe systems uniformly and thus provide means to describe relational constraints expected in the dynamics of a complex (coupled) systems. Thus when LENDIT is used to characterize four sets – ‘state, system, resource and response’ (S2R2) – describing reactor operations (normal and off-normal), LENDIT and S2R2 in combination have the potential to ‘branch and bound’ the state space investigated by DPRA. In this paper we introduce the concept of LENDIT scales and S2R2 sets applied to a branch-and-bound algorithm and apply the methods to a station black out transient (SBO).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems

Abstract Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗
DOE OSTI2016

Environmental Systems Microbiology of Contaminated Environments

Environmental Systems Microbiology is well positioned to move forward in dynamic complex system analysis probing new questions and developing new insight into the function, robustness and resilience in response to anthropogenic perturbations. Recent studies have demonstrated that natural bacterial communities can be used as quantitative biosensors in both groundwater and deep ocean water, predicting oil concentration from the Gulf of Mexico Deep Water Horizon spill and from groundwater at nuclear production waste sites (16, 17, 25). Since the first demonstration of catabolic gene expression in soil remediation (34) it has been clear that extension beyond organismal abundance to process and function of microbial communities as a whole using the whole suite of omic tools available to the post genomic era. Metatranscriptomics have been highlighted as a prime vehicle for understanding responses to environmental drivers (35) in complex systems and with rapidly developing metabolomics, full functional understanding of complex community biogeochemical cycling is an achievable goal. Perhaps more exciting is the dynamic nature of these systems and their complex adaptive strategies that may lead to new control paradigms and emergence of new states and function in the course of a changing environment.

Sayler, Gary↗
DOE OSTI2021

Application of Machine Learning Techniques to an Agent-Based Model of Pantoea

Agent-based modeling (ABM) is a powerful simulation technique which describes a complex dynamic system based on its interacting constituent entities. While the flexibility of ABM enables broad application, the complexity of real-world models demands intensive computing resources and computational time; however, a metamodel may be constructed to gain insight at less computational expense. Here, we developed a model in NetLogo to describe the growth of a microbial population consisting of Pantoea . We applied 13 parameters that defined the model and actively changed seven of the parameters to modulate the evolution of the population curve in response to these changes. We efficiently performed more than 3,000 simulations using a Python wrapper, NL4Py . Upon evaluation of the correlation between the active parameters and outputs by random forest regression, we found that the parameters which define the depth of medium and glucose concentration affect the population curves significantly. Subsequently, we constructed a metamodel, a dense neural network, to predict the simulation outputs from the active parameters and found that it achieves high prediction accuracy, reaching an R 2 coefficient of determination value up to 0.92. Our approach of using a combination of ABM with random forest regression and neural network reduces the number of required ABM simulations. The simplified and refined metamodels may provide insights into the complex dynamic system before their transition to more sophisticated models that run on high-performance computing systems. The ultimate goal is to build a bridge between simulation and experiment, allowing model validation by comparing the simulated data to experimental data in microbiology.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Optimized Uncertainty Quantification Algorithm Within a Dynamic Event Tree Framework

Methods for developing Phenomenological Identification and Ranking Tables (PIRT) for nuclear power plants have been a useful tool in providing insight into modelling aspects that are important to safety. These methods have involved expert knowledge with regards to reactor plant transients and thermal-hydraulic codes to identify are of highest importance. Quantified PIRT provides for rigorous method for quantifying the phenomena that can have the greatest impact. The transients that are evaluated and the timing of those events are typically developed in collaboration with the Probabilistic Risk Analysis. Though quite effective in evaluating risk, traditional PRA methods lack the capability to evaluate complex dynamic systems where end states may vary as a function of transition time from physical state to physical state . Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. A limitation of DPRA is its potential for state or combinatorial explosion that grows as a function of the number of components; as well as, the sampling of transition times from state-to-state of the entire system. This paper presents a method for performing QPIRT within a dynamic event tree framework such that timing events which result in the highest probabilities of failure are captured and a QPIRT is performed simultaneously while performing a discrete dynamic event tree evaluation. The resulting simulation results in a formal QPIRT for each end state. The use of dynamic event trees results in state explosion as the number of possible component states increases. This paper utilizes a branch and bound algorithm to optimize the solution of the dynamic event trees. The paper summarizes the methods used to implement the branch-and-bound algorithm in solving the discrete dynamic event trees.

42 ENGINEERING↗
DOE OSTI2015

Branch-and-Bound algorithm applied to uncertainty quantification of a Boiling Water Reactor Station Blackout

Evaluation of the impacts of uncertainty and sensitivity in modeling presents a significant set of challenges in particular to high fidelity modeling. Computational costs and validation of models creates a need for cost effective decision making with regards to experiment design. Experiments designed to validate computation models can be used to reduce uncertainty in the physical model. In some cases, large uncertainty in a particular aspect of the model may or may not have a large impact on the final results. For example, modeling of a relief valve may result in large uncertainty, however, the actual effects on final peak clad temperature in a reactor transient may be small and the large uncertainty with respect to valve modeling may be considered acceptable. Additionally, the ability to determine the adequacy of a model and the validation supporting it should be considered within a risk informed framework. Low fidelity modeling with large uncertainty may be considered adequate if the uncertainty is considered acceptable with respect to risk. In other words, models that are used to evaluate the probability of failure should be evaluated more rigorously with the intent of increasing safety margin. Probabilistic risk assessment (PRA) techniques have traditionally been used to identify accident conditions and transients. Traditional classical event tree methods utilize analysts’ knowledge and experience to identify the important timing of events in coordination with thermal-hydraulic modeling. These methods lack the capability to evaluate complex dynamic systems. In these systems, time and energy scales associated with transient events may vary as a function of transition times and energies to arrive at a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. Unfortunately DPRA methods introduce issues associated with combinatorial explosion of states. This study presents a methodology to address combinatorial explosion using a Branch-and-Bound algorithm applied to Dynamic Event Trees (DET), which utilize LENDIT (L – Length, E – Energy, N – Number, D – Distribution, I – Information, and T – Time) as well as a set theory to describe system, state, resource, and response (S2R2) sets to create bounding functions for the DET. The optimization of the DET in identifying high probability failure branches is extended to create a Phenomenological Identification and Ranking Table (PIRT) methodology to evaluate modeling parameters important to safety of those failure branches that have a high probability of failure. The PIRT can then be used as a tool to identify and evaluate the need for experimental validation of models that have the potential to reduce risk. Finally, in order to demonstrate this methodology, a Boiling Water Reactor (BWR) Station Blackout (SBO) case study is presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Safe Physics-Informed Machine Learning for Dynamics and Control

This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems.

Drgona, Jan↗
DOE OSTI2023

Online data-driven changepoint detection for high-dimensional dynamical systems

In this study, the detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally different characteristic—which may be due to a change in the model parameters or due to intermittent phenomena arising from the same model. We propose two complementary approaches to achieve this, with the first devised using arguments from probabilistic unsupervised learning and the latter devised using supervised deep learning. To accelerate the deployment of transition detection algorithms in high-dimensional dynamical systems, we introduce dimensionality reduction techniques. Our experiments demonstrate that transitions can be detected efficiently, in real-time, for the two-dimensional forced Kolmogorov flow and the Rössler dynamical system, which are characterized by anomalous regimes in phase space where dynamics are perturbed off the attractor at potentially uneven intervals. Finally, we also demonstrate how variations in the frequency of detected changepoints may be utilized to detect a significant modification to the underlying model parameters by utilizing the Lorenz-63 dynamical system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Modelling new particle formation events in the South African savannah

Africa is one of the less studied continents with respect to atmospheric aerosols. Savannahs are complex dynamic systems sensitive to climate and land-use changes, but the interaction of these systems with the atmosphere is not well understood. Atmospheric particles, called aerosols, affect the climate on regional and global scales, and are an important factor in air quality. In this study, measurements from a relatively clean savannah environment in South Africa were used to model new particle formation and growth. There already are some combined long-term measurements of trace gas concentrations together with aerosol and meteorological variables available, but to our knowledge this is the first detailed simulation that includes all the main processes relevant to particle formation. The results show that both of the particle formation mechanisms investigated overestimated the dependency of the formation rates on sulphuric acid. From the two particle formation mechanisms tested in this work, the approach that included low volatile organic compounds to the particle formation process was more accurate in describing the nucleation events than the approach that did not. To obtain a reliable estimate of aerosol concentration in simulations for larger scales, nucleation mechanisms would need to include organic compounds, at least in southern Africa. This work is the first step in developing a more comprehensive new particle formation model applicable to the unique environment in southern Africa. Such a model will assist in better understanding and predicting new particle formation – knowledge which could ultimately be used to mitigate impacts of climate change and air quality.

Gierens, Rosa↗
DOE OSTI2020

Spatiotemporal Characteristics and Propagation of Summer Extreme Precipitation Events over United States: A Complex Network Analysis

Complex Network (CN) is a graph-theory based depiction of relation shared by various elements of a complex-dynamical system such as the atmosphere. Here we applied the concept of CN to understand the directionality and topological structure of summer extreme precipitation events (SEPEs) over the conterminous United States (CONUS). The SEPEs are calculated based on the 95th percentile daily rainfall at 0.5ox0.5o spatial resolution for CONUS to investigate the multi-dimensional characteristics of precipitation extremes. The derived CN coefficients (e.g., betweenness centrality, clustering coefficient, orientation, and network divergence) reveal important structural and dynamical information about the topology of the SEPEs and improve understanding of the dominant meteorological patterns. The initiation and propagation of SEPEs from the source-zones to the sink-zones are identified. The SEPEs are influenced by topography, dominant wind patterns, and moisture sources in terms of their topological structure and spatial dynamics.

Mondal, Somnath↗