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NASA NTRS1993

Solar flux forecasting using mutual information with an optimal delay

Solar flux F(sub 10.7) directly affects the atmospheric density, thereby changing the lifetime and prediction of satellite orbits. For this reason, accurate forecasting of F(sub 10.7) is crucial for orbit determination of spacecraft. Our attempts to model and forecast F(sub 10.7) uncovered highly entangled dynamics. We concluded that the general lack of predictability in solar activity arises from its nonlinear nature. Nonlinear dynamics allow us to predict F(sub 10.7) more accurately than is possible using stochastic methods for time scales shorter than a characteristic horizon, and with about the same accuracy as using stochastic techniques when the forecasted data exceed this horizon. The forecast horizon is a function of two dynamical invariants: the attractor dimension and the Lyapunov exponent. In recent years, estimation of the attractor dimension reconstructed from a time series has become an important tool in data analysis. In calculating the invariants of the system, the first necessary step is the reconstruction of the attractor for the system from the time-delayed values of the time series. The choice of the time delay is critical for this reconstruction. For an infinite amount of noise-free data, the time delay can, in principle, be chosen almost arbitrarily. However, the quality of the phase portraits produced using the time-delay technique is determined by the value chosen for the delay time. Fraser and Swinney have shown that a good choice for this time delay is the one suggested by Shaw, which uses the first local minimum of the mutual information rather than the autocorrelation function to determine the time delay. This paper presents a refinement of this criterion and applies the refined technique to solar flux data to produce a forecast of the solar activity.

Ashrafi, S.↗

NASA NTRS1994

Physical Models of Cognition

This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.

Zak, Michail↗

NASA NTRSDate not supplied

A Distributed Simulation-to-Flight Framework to Support Investigating Trust/Trustworthiness in Multi-Agent Systems

As autonomous systems continue to grow both in use and complexity, the necessity for robust and extensible simulation-to-flight methods is paramount for establishing an effective architecture for autonomous systems. A fundamental objective of the ATTRACTOR (Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability) project was to design and develop a distributed mixed-reality simulation environment to begin establishing a basis for certification of autonomous systems via research into trust and trustworthiness. In this paper, we present an autonomous systems architecture and development framework paired with a persistent distributed modeling and simulation environment for test and evaluation of autonomous systems. The Autonomous Entity Operations Network (AEON) framework enables autonomous system development with an easily extensible collection of libraries and plug-n-play nodes facilitated by the Data Distribution Service (DDS) communication protocol standard. The Baseline Environment for Autonomous Modeling (BEAM) simulation environment is a distributed mixed-reality Unity™-based environment built around the same DDS communication paradigm allowing for easy integration with AEON-based autonomous applications. They were designed under ATTRACTOR in order to measure and establish trustworthiness and trust in single- and multi-agent human-machine systems whether these machines are fixed-wing general aviation, rotary-wing Unmanned Aerial Vehicles (UAVs), ground rovers, or even spacecraft. Together AEON and BEAM enable sim-to-flight with minimal configuration changes. By using AEON and BEAM, source code that runs in simulation ports directly to hardware and has successfully flown in the lab and in the National Airspace System (NAS) at NASA LaRC many times over the lifetime of ATTRACTOR.

Benjamin N Kelley↗

NASA NTRSDate not supplied

Bootstrapping Multi-Agent Unmanned Aerial Vehicle (UAV) System Integration Using Ground-Based Assets: Lessons Learned

In support of the Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR) project, a fleet of unmanned ground vehicles (UGVs) was developed as a test and evaluation (T\&E) platform to reduce system integration gaps between simulation and live flight hardware. While simulation and hardware-in-the-loop bench testing provide adequate environments for preliminary validation, differences in system deployment architecture, software interfaces, and hardware infrastructure increase the risks to safety, property, and the project. Given ATTRACTOR’s goal of establishing a basis of certification of trust and trustworthiness in multi-agent autonomous systems, bridging these gaps was critical to successful project execution and feasibility assessment. In this paper we present the UGV fleet and its role in speeding up system integration, smoothing the transition from simulation to flight, and providing researchers an easy-to-use hardware test bed. An overview of the hardware and software on-board the vehicles is provided along with supporting infrastructure. The system integration process is documented including results in supporting both the overarching design reference mission (DRM) of ATTRACTOR and individual research efforts conducted since the creation of the fleet. Finally, we discuss the practical lessons learned regarding the testing, deployment, and operation of multi-agent autonomous systems.

Matthew P. Vaughan↗

NASA NTRSDate not supplied

A Distributed Simulation-to-Flight Framework to Support Investigating Trust/Trustworthiness in Multi-Agent Systems

Benjamin N Kelley↗

NASA NTRS2023

Compliant Behaviors for Supervised and Autonomous Robotic Operations

The demands of traditional industrial robotics differ significantly from those of remote, supervised operations in hostile environments, such as operations in space. While industry requires robots that can perform repetitive tasks with precision and speed, the space environment needs robots to cope with uncertainties, dynamics, and communication delays or interruptions, similar to human astronauts. These demands make a well-suited application for compliant robotics and behavior-based programming. Pose Target Wrench Limiting (PTWL) is a compliant behavior paradigm developed specifically to meet these demands. PTWL controls a robot by moving a virtual attractor to a target pose. The attractor applies virtual forces, based on stiffness and damping presets, to an underlying admittance controller. Guided by virtual forces, the robot will follow the attractor until safety conditions are violated or success criteria are met. PTWL was tested on a variety of quasi-static and dynamic tasks that may be useful for future space operations. Results demonstrate that PTWL is a powerful tool. It makes teleoperation easy and safe for a wide range of quasi-static tasks. It also facilitates the creation of semi-autonomous state machines that can reliably complete complex tasks with minimal human intervention.

Joseph D. Cressman↗

NASA NTRS2023

Compliant Robotic Behaviors for Satellite Servicing

The demands of traditional industrial robotics differ significantly from those of space robotics. While industry requires robots that can perform repetitive tasks with precision and speed, the space environment needs robots to cope with uncertainties, dynamics, and communication delays or interruptions, similar to human astronauts. These demands make a well-suited application for compliant robotics and behavior-based programming. Pose Target Wrench Limiting (PTWL) is a compliant behavior paradigm developed specifically to meet these demands. PTWL controls a robot by moving a virtual attractor to a target pose. The attractor applies virtual forces, based on stiffness and damping presets, to an underlying admittance controller. Guided by virtual forces, the robot will follow the attractor until safety conditions are violated or success criteria are met. We tested PTWL on a variety of quasi-static tasks that may be useful for future space operations. Our results demonstrate that PTWL is an extremely powerful tool. It makes teleoperation easy and safe for a wide range of quasi-static tasks. It also facilitates the creation of semi-autonomous state machines that can reliably complete complex tasks with minimal human intervention.

Compliance↗

NASA NTRS2018

Towards Informing an Intuitive Mission Planning Interface for Autonomous Multi-Asset Teams via Image Descriptions

Establishing a basis for certification of autonomous systems using trust and trustworthiness is the focus of Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR). The Human-Machine Interface (HMI) team is working to capture and utilize the multitude of ways in which humans are already comfortable communicating mission goals and translate that into an intuitive mission planning interface. Several input/output modalities (speech/audio, typing/text, touch, and gesture) are being considered and investigated in the context human-machine teaming for the ATTRACTOR design reference mission (DRM) of Search and Rescue or (more generally) intelligence, surveillance, and reconnaissance (ISR). The first of these investigations, the Human Informed Natural-language GANs Evaluation (HINGE) data collection effort, is aimed at building an image description database to train a Generative Adversarial Network (GAN). In addition to building an image description database, the HMI team was interested if, and how, modality (spoken vs. written) affects different aspects of the image description given. The results will be analyzed to better inform the designing of an interface for mission planning.

Generative Adversarial Network (GAN)↗

DOE OSTI2022

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗

DOE OSTI2025

X-Ray Microtomography Measurements of Coevolving Particle Size and Shape

This study measures simultaneous changes in particle size and shape during grain crushing and proposes quantitative metrics to track their coevolving statistical distribution. Idealized granular materials with widely different initial particle shapes (i.e., spheres, quasi-ellipsoids, plates, and rods) are compressed oedometrically at vertical stress levels sufficient to induce particle breakage. X-ray microtomography and digital image analysis are then used to track changes in particle-scale characteristics. The observations indicate that more irregular particles tend to exhibit a higher degree of breakage compared to more spherical grains subjected to an equivalent stress level. Despite these differences, the measurements also indicate that all the tested particle sets approach a common attractor (expressed in terms of aspect ratio, flatness, and elongation), regardless of their initial morphology. A new shape evolution index is proposed to quantify such trends. With this new metric, it is shown that in all the tested materials, the particle shape evolves faster than size, especially for the more regular morphologies, thus implying that the shape tends to reach its attractor point before the grading reaches its ultimate particle size distribution. Furthermore, this finding underpins an ultimate stage of crushing-driven compression that occurs with particle size reduction but minimal shape changes (i.e., self-replicating shapes due to fractures).

Oedometric compression↗

DOE OSTI2025

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↗

DOE OSTI2020

Far-from-equilibrium search for the QCD critical point

Initial conditions for relativistic heavy-ion collisions may be far from equilibrium (i.e., there are large initial contributions from the shear stress tensor and bulk pressure) but it is expected that on very short time scales the dynamics converge to a universal attractor that defines hydrodynamic behavior. Thus far, studies of this nature have only considered an idealized situation at LHC energies (high temperatures T and vanishing baryon chemical potential µ B = 0) but, in this work, we investigate for the first time how far-from-equilibrium effects may influence experimentally driven searches for the Quantum Chromodynamic critical point at RHIC. We find that the path to the critical point is heavily influenced by far from equilibrium initial conditions where viscous effects lead to dramatically different {T, µ B } trajectories through the QCD phase diagram. We compare hydrodynamic equations of motion with shear and bulk coupled together at finite µB for both DNMR and phenomenological Israel-Stewart equations of motion and discuss their influence on potential attractors at finite µ B and their corresponding {T, µ B } trajectories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Design of Hopfield Networks Based on Superconducting Coupled Oscillators

The global energy shortage has driven the development of many energy-efficient computational platforms beyond Moore's law, among which brain-inspired neuromorphic computing is one of the promising solutions. Associative memory and pattern recognition are important computations solved by brain-inspired Hopfield networks. Classical Hopfield networks store memories via fixed point attractors of their dynamics. In oscillatory Hopfield networks, these attractors are replaced by periodic orbits. Here, we design an oscillatory Hopfield network based on coupled superconducting oscillators. We first employ a mathematical phase reduction approach to map networks of coupled superconducting rapid single flux quantum (RSFQ) ring oscillators to coupled Kuramoto phase-oscillator networks. We use this theory to numerically optimize the hardware's mutual inductances in order to directly match the phase-reduced superconducting oscillators to a model of phase-oscillator-based Hopfield networks. The resulting network can store multiple oscillatory phase-locked memory patterns and recover the patterns based on the initial phase conditions. As different pattern recognition tasks, or learning, require tunable connectivity strengths between the oscillatory nodes, we further employ a coupler circuit that enables tuning the coupling strength between two oscillators by applying an external flux. We demonstrate the functionality of our design through numerical simulations of a small example network with oscillators operating at 86 GHz and recognizing patterns within 10 ns. Our approach enables the learning and retrieval of dynamical memory patterns with a wide range of applications where rhythmic dynamic output is beneficial.

Cheng, Ran↗

DOE OSTI2024

A Theory for the Balance between Warm Rain and Ice Crystal Processes of Precipitation in Mixed-Phase Clouds

Abstract Mixed-phase clouds contain both supercooled cloud liquid and ice crystals. In principle, precipitation may be initiated either by the liquid phase or by the ice phase. Ice crystals may grow by vapor diffusion to become snow (“ice crystal process”), forming “cold” precipitation. Equally, cloud droplets, when large enough, coalesce to form “warm” precipitation by the “warm rain process.” Warm rain could be supercooled and freeze as “warm” graupel. In the present paper, a new simplified theoretical analysis is provided to examine the microphysical system consisting of three species of hydrometeor, namely, cloud liquid, “cold ice” (crystals, snow), and “warm rain” (frozen or supercooled). This is obtained by nondimensionalizing and simplifying the evolution equations for the mass of each species. Analytical formulas are given for equilibria. Feedback analysis shows that the sign of the feedback is linked to the abundance of precipitation, with a neutral surface in the 3D phase space. The system’s precipitation amount explodes while in the initial unstable regime, crossing the neutral surface and approaching the equilibrium point that is a stable attractor. Positive and negative feedbacks are elucidated. In a standard case, the cold ice mass is about 1000 times larger than the warm rain mass. To illustrate the physical behavior of the theory, sensitivity tests are performed with respect to environmental conditions (e.g., aerosol, updraft speed) and microphysical parameters (e.g., riming and sedimentation rates for cold ice). Cold ice prevails, especially in fast ascent, due to its low bulk density, favoring slow sedimentation and a wide cross-sectional area for riming. Significance Statement The theory elucidates how the ice phase can prevail in the precipitation from any mixed-phase clouds with supercooled cloud liquid and crystals. The ice phase radically suppresses cloud liquid by riming when active and “wins” the competition against coalescence. This prevalence of ice is shown to arise from the low bulk density of snow. The cloud is viewed as a system of negative and positive feedbacks that prevail in realms of stability and instability in a 3D phase space.

Meteorology & Atmospheric Sciences↗

DOE OSTI2022

Computational Response Theory for Dynamics

Quantifying the sensitivity - how a quantity of interest (QoI) varies with respect to a parameter – and response – the representation of a QoI as a function of a parameter - of a computer model of a parametric dynamical system is an important and challenging problem. Traditional methods fail in this context since sensitive dependence on initial conditions implies that the sensitivity and response of a QoI may be ill-conditioned or not well-defined. If a chaotic model has an ergodic attractor, then ergodic averages of QoIs are well-defined quantities and their sensitivity can be used to characterize model sensitivity. The response theorem gives sufficient conditions such that the local forward sensitivity – the derivative with respect to a given parameter - of an ergodic average of a QoI is well-defined. We describe a method based on ergodic and response theory for computing the sensitivity and response of a given QoI with respect to a given parameter in a chaotic model with an ergodic and hyperbolic attractor. This method does not require computation of ensembles of the model with perturbed parameter values. The method is demonstrated and some of the computations are validated on the Lorenz 63 and Lorenz 96 models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Prefabricated Zero Ascend Omnispecies (ZAO) Modular Fish Passage Modules Using Advanced Manufacturing Techniques

The Zero Ascend Omnispecies (ZAO) fish passage attraction module “ZAO Attractor” is a novel system designed to facilitate upstream passage for a broad spectrum of fish species, with a particular focus on American shad and river herring (alewife and/or blueback herring). Combining the use of prefabricated, modular components with advanced manufacturing, the ZAO aims to provide a cost-effective and scalable solution for fish passage attractions across various hydropower sites. The system features a surface level entry, so fish do not need to climb. In addition, it is designed to be adjusted and repositioned to create the most effective attraction flows by managing the outflows from hydropower turbines. Budget Period 1 (BP1) focused on the design and modeling of the ZAO Attractor and demonstrated the engineering feasibility of a modular, prefabricated, hydrodynamically efficient structure with surface level entry and passage. It was discovered that there were limited published studies on the direct correlation between quantified flow patterns and fish attraction, emphasizing the need for controlled studies to observe and measure these effects. In Budget Period 2 (BP2), controlled studies with live fish were prioritized to address these complexities. In conclusion, the ZAO fish passage attraction module presents a promising approach to fish passage at hydropower stations, with the potential to balance environmental concerns with renewable energy development. However, further field validation and optimization are necessary to ensure its effectiveness and practicality in real-world applications.

13 HYDRO ENERGY↗

NASA NTRS1981

Chaotic /strange/ and periodic behavior in instability saturation by the oscillating two-stream instability

The nonlinear Schroedinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two-stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one-dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set-like structure (i.e., scale invariance) in the surface of section.

Russell, D. A.↗