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NASA NTRS1998

Markov Tracking for Agent Coordination

Partially observable Markov decision processes (POMDPs) axe an attractive representation for representing agent behavior, since they capture uncertainty in both the agent's state and its actions. However, finding an optimal policy for POMDPs in general is computationally difficult. In this paper we present Markov Tracking, a restricted problem of coordinating actions with an agent or process represented as a POMDP Because the actions coordinate with the agent rather than influence its behavior, the optimal solution to this problem can be computed locally and quickly. We also demonstrate the use of the technique on sequential POMDPs, which can be used to model a behavior that follows a linear, acyclic trajectory through a series of states. By imposing a "windowing" restriction that restricts the number of possible alternatives considered at any moment to a fixed size, a coordinating action can be calculated in constant time, making this amenable to coordination with complex agents.

Washington, Richard↗

NASA NTRS2013

Uncertainty Quantification of GEOS-5 L-band Radiative Transfer Model Parameters Using Bayesian Inference and SMOS Observations

Uncertainties in L-band (1.4 GHz) radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation opacity and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an uncertainty estimate. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at a range of incidence angles, at horizontal and vertical polarization, and for morning and evening overpasses. Tb simulations are generated with the Goddard Earth Observing System (GEOS-5) and confronted with Tb observations from the Soil Moisture Ocean Salinity (SMOS) mission. The MCMC algorithm suggests that the relative uncertainty of the RTM parameter estimates is typically less than 25 of the maximum a posteriori density (MAP) parameter value. Furthermore, the actual root-mean-square-differences in long-term Tb averages and standard deviations are found consistent with the respective estimated total simulation and observation error standard deviations of m3.1K and s2.4K. It is also shown that the MAP parameter values estimated through MCMC simulation are in close agreement with those obtained with Particle Swarm Optimization (PSO).

MCMC↗

DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗

NASA NTRS1993

System identification for Space Station Freedom using observer/Kalman filter Markov parameters

The Modal Identification Experiment (MIE) is a proposed experiment to define the dynamic characteristics of Space Station Freedom. Previous studies emphasized free-decay modal identification. The feasibility of using a forced response method (Observer/Kalman Filter Identification (OKID)) is addressed. The interest in using OKID is to determine the input mode shape matrix which can be used for controller design or control-structure interaction analysis, and investigate if forced response methods may aid in separating closely spaced modes. A model of the SC-7 configuration of Space Station Freedom was excited using simulated control system thrusters to obtain acceleration output. It is shown that an 'optimum' number of outputs exists for OKID. To recover global mode shapes, a modified method called Global-Local OKID was developed. This study shows that using data from a long forced response followed by free-decay leads to the 'best' modal identification. Twelve out of the thirteen target modes were identified for such an output.

Papadopoulos, Michael↗

DOE OSTI2022

Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis

Catalysis from single active sites is analyzed using methods developed from single molecule kinetics. Using a stochastic Markov state description, the observable properties of general catalytic networks of reactions are expressed using an eigenvalue decomposition of the transition matrix for the Markov process. By the use of a sensitivity analysis, the necessary eigenvalues and eigenvectors are related to the energies of controlling barriers and wells located along the reaction routes. A generalization of the energetic span theory allows the eigenvalues to be computed from several activation energies corresponding to distinct barrier-well pairings. The formalism is demonstrated accurately for model problems for a physically realistic mechanism for an alkene hydrogenation reaction on a single atom catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

pop-cosmos : redshifts and physical properties of KiDS-1000 galaxies

ABSTRACT Principled Bayesian inference of galaxy properties has not previously been performed for wide-area weak-lensing surveys with millions of sources. We address this gap by applying the pop-cosmos generative model to perform spectral energy distribution (SED) fitting for 4 million KiDS (Kilo-Degree Survey)-1000 galaxies. Calibrated on deep COSMOS2020 photometric data, pop-cosmos specifies a physically motivated prior over the galaxy population up to $z \simeq 6$ in stellar population synthesis (SPS) parameter space. Using the Speculator SPS emulator with GPU (graphics processing unit)-accelerated Markov Chain Monte Carlo sampling, we perform full posterior inference at 8.2 GPU seconds per galaxy, obtaining joint constraints on galaxy redshifts and physical properties. We validate photometric redshifts against $\sim \!185\,\!000$ KiDS galaxies cross-matched to Dark Energy Spectroscopic Instrument Data Release 1 spectroscopic samples, achieving low bias ($2\times 10^{-3}$), scatter ($\sigma _{\mathrm{MAD}}=0.03$), and outlier fraction (3.2 per cent) for the Bright Galaxy Survey, with comparable performance (bias $3\times 10^{-2}$, $\sigma _{\mathrm{MAD}}=0.05$, 1.0 per cent outliers) for luminous red galaxies (LRGs). Within the LRG sample, we identify massive, dusty, star-forming contaminants at $z \simeq 0.4$ satisfying standard colour selections for quenched populations. We infer trends in stellar mass, star formation, metallicity, and dust across five tomographic redshift bins consistent with established scaling relations. Using specific star formation rate constraints, we identify $\sim$7 per cent of KiDS-1000 galaxies as quenched, versus 37 per cent implied by conservative colour cuts. This enables the construction of weak-lensing samples defined by physical properties while mitigating intrinsic alignment systematics and preserving statistical power. Our analysis validates pop-cosmos out of sample, establishing it as a scalable approach for galaxy evolution and cosmological analyses with photometric surveys.

Halder, Anik [Institute of Astronomy and Kavli Ins↗

DOE OSTI2021

Gauge R & R studies for angular measurements

Angular measurements lie on the circumference of a circle and have different characteristics than standard scalar measurements. For applications involving angular data, treating the measured values as scalars can lead to misinterpretation of results if its wrap-around nature is not taken into account. In this article, we propose a variance components wrapped normal model for angular measurements that is analogous to the standard normal model for continuous measurements. This model allows decomposition of contributions to the overall variance to be separated and compared to understand the drivers of the spread of the data. In this work, we analyze gauge R & R study data using Bayesian methods and illustrate the use of this wrapped normal model with simulated and real data. We also performed a small simulation study in considering the design of gauge R & R studies with angular measurements.

42 ENGINEERING↗

DOE OSTI2021

PRIME

SAND2021-0565 O PRIME is a modeling framework designed for the real-time characterization and forecasting of partially observed epidemics. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The estimation problem is posed as one of Bayesian inference and solved using a Markov Chain Monte Carlo technique. The framework can accommodate multiple epidemic waves and can help identify different disease dynamics at the regional, state, and country levels. Examples are provided using publicly available COVID-19 data. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Safta, Cosmin↗

DOE OSTI2024

PRIME - A Software Toolkit for the Characterization of Partially Observed Epidemics in a Bayesian Framework

PRIME is a modeling framework designed for the “real-time’” characterization and forecasting of partially observed epidemics. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and solved using a Markov Chain Monte Carlo technique. The framework can accommodate multiple epidemic waves and can help identify different disease dynamics at the regional, state, and country levels. We include examples using publicly available COVID-19 data.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2005

Studies of Cosmic Ray Modulation and Energetic Particle Propagation in Time-Dependent 3-Dimensional Heliospheric Magnetic Fields

The primary goal of this project was to perform theoretical calculations of propagation of cosmic rays and energetic particles in 3-dimensional heliospheric magnetic fields. We used Markov stochastic process simulation to achieve to this goal. We developed computation software that can be used to study particle propagation in, as two examples of heliospheric magnetic fields that have to be treated in 3 dimensions, a heliospheric magnetic field suggested by Fisk (1996) and a global heliosphere including the region beyond the termination shock. The results from our model calculations were compared with particle measurements from Ulysses, Earth-based spacecraft such as IMP-8, WIND and ACE, Voyagers and Pioneers in outer heliosphere for tests of the magnetic field models. We particularly looked for features of particle variations that can allow us to significantly distinguish the Fisk magnetic field from the conventional Parker spiral field. The computer code will eventually lead to a new generation of integrated software for solving complicated problems of particle acceleration, propagation and modulation in realistic 3-dimensional heliosphere of realistic magnetic fields and the solar wind with a single computation approach.

Zhang, Ming↗

DOE OSTI2020

Electrokinetic Analysis of Poorly Conductive Electrocatalytic Materials

While many factors can influence the activity of the electrochemical interface at atomic and molecular levels, the electron and ion transport have a big impact on the overall electrochemical performance. Here, we investigate how electrical resistance (conductivity) of the electrode affects the measured electrocatalytic activity using the hydrogen evolution reaction as a model reaction. We clearly demonstrate the effect of the poor electronic conductivity of MoS 2 on the electrochemical performance, as both values of the exchange current density as well as the Tafel slope depend on the level of utilization of the active material and the ohmic losses. A quantitative analysis using the composite electrode model is provided, showing the importance of the experimental conditions and good control of electrode/electrolyte system for the proper evaluation and comparison of electrocatalysts’ kinetic parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantum magic and multipartite entanglement in the structure of nuclei

Motivated by the Gottesman-Knill theorem, we present a detailed study of the quantum complexity of p -shell and s d -shell nuclei. Valence-space nuclear shell-model wave functions generated by the code are mapped to qubit registers using the Jordan-Wigner mapping (12 qubits for the p shell and 24 qubits for the s d shell), from which measures of the many-body entanglement ( n -tangles) and magic (nonstabilizerness) are determined. While exact evaluations of these measures are possible for nuclei with a modest number of active nucleons, Monte Carlo simulations are required for the more complex nuclei. The broadly applicable Pauli-string I ̂ Z ̂ exact (PSIZe) Markov chain Monte Carlo (MCMC) technique is introduced to accelerate the evaluation of measures of magic in deformed nuclei (with hierarchical wave functions), by factors of ≈ 8 for some nuclei. Significant multinucleon entanglement is found in the s d shell, dominated by proton-neutron configurations, along with significant measures of magic. This is evident not only for the deformed states, but also for nuclei on the path to instability via regions of shape coexistence and level inversion. These results indicate that quantum-computing resources will accelerate precision simulations of such nuclei and beyond. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2000

Back to the Future: Consistency-Based Trajectory Tracking

Given a model of a physical process and a sequence of commands and observations received over time, the task of an autonomous controller is to determine the likely states of the process and the actions required to move the process to a desired configuration. We introduce a representation and algorithms for incrementally generating approximate belief states for a restricted but relevant class of partially observable Markov decision processes with very large state spaces. The algorithm presented incrementally generates, rather than revises, an approximate belief state at any point by abstracting and summarizing segments of the likely trajectories of the process. This enables applications to efficiently maintain a partial belief state when it remains consistent with observations and revisit past assumptions about the process' evolution when the belief state is ruled out. The system presented has been implemented and results on examples from the domain of spacecraft control are presented.

Kurien, James↗

NASA NTRS2008

Black Hole Mergers as Probes of Structure Formation

Observations of gravitational waves from massive black hole (MBH) mergers can provide us with important clues about the era of structure formation in the early universe. Previous research in this field has been limited to calculating merger rates of MBHs using different models where many assumptions are made about the specific values of physical parameters of the mergers, resulting in merger rate estimates that span 5 to 6 orders of magnitude. We develop a semi-analytical, phenomenological model that includes plausible combinations of several physical parameters involved in the mergers. which we then turn around to determine how well LISA observations will be able to enhance our understanding of the universe during the critical z approximately equal to 5-30 structure formation era. We do this by generating synthetic LISA observable data (masses, redshifts, merger rates), which are then analyzed using a Markov Chain Monte Carlo (MCMC) method. This allows us to constrain the physical parameters of the mergers.

Alicea-Munoz, Emily↗

NASA NTRS1980

Optimal regulation in systems with stochastic time sampling

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Montgomery, R. C.↗

NASA NTRS1982

GEM: Statistical weather forecasting procedure

The objective of the Generalized Exponential Markov (GEM) Program was to develop a weather forecast guidance system that would: predict between 0 to 6 hours all elements in the airways observations; respond instantly to the latest observed conditions of the surface weather; process these observations at local sites on minicomputing equipment; exceed the accuracy of current persistence predictions at the shortest prediction of one hour and beyond; exceed the accuracy of current forecast model output statistics inside eight hours; and be capable of making predictions at one location for all locations where weather information is available.

Robert G. Miller↗

DOE OSTI2020

Toroidal modeling of runaway electron loss due to 3-D fields in DIII-D and COMPASS

The 3-D field induced relativistic runaway electron (RE) loss has been simulated for DIII-D, COMPASS and ITER plasmas, utilizing the MARS-F code incorporated with the recently developed and updated RE orbit module (REORBIT). Modeling shows effectively 100% loss of a post-disruption, high-current runaway beam in DIII-D, due to the 1 kG level of magnetic field perturbation produced by a fast growing n = 1 resistive kink instability. The RE loss is shown to be independent of the particle energy or the initial location of particles in the configuration space. Applied resonant magnetic perturbation (RMP) fields from in-vessel coils are not effective for RE beam mitigation in DIII-D, but do produce finite (>10%) RE loss in COMPASS, consistent with experimental observations in above two devices. The major reasons for this difference in RE control by RMP between these two devices are (i) the coil proximity to the RE beam and (ii) the effective coil current scaling versus the machine size and the toroidal magnetic field. About 10% RE loss fraction is also predicted for an ITER 15 MA scenario with pre-disruption plasma, highlighting the role of the plasma response. Up to 30% loss is computed, however, by artificially scaling the equilibrium pressure to zero. This is due to the more resistive plasma response and stronger resulting field line stochasticity. Distributions of the lost REs to the limiting surface show poloidally peaked profile near the high-field-side in both DIII-D and COMPASS, covering about 100o poloidal angle. Higher perturbation field level and/or higher particle energy also result in REs being lost to the low-field-side of the limiting surface of these two devices, increasing the effective wetted area. Finally, for the modeled ITER plasmas, the applied RMP field, with optimal poloidal spectrum that maximizes the edge localized mode control, leads to REs being lost to the lower divertor region of the limiting surface within a narrow poloidal band.

3-D field↗

NASA NTRS1991

Supercomputer optimizations for stochastic optimal control applications

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

Chung, Siu-Leung↗