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Results for “Markov chain model”

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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
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↗
NASA NTRS1990

Space system operations and support cost analysis using Markov chains

This paper evaluates the use of Markov chain process in probabilistic life cycle cost analysis and suggests further uses of the process as a design aid tool. A methodology is developed for estimating operations and support cost and expected life for reusable space transportation systems. Application of the methodology is demonstrated for the case of a hypothetical space transportation vehicle. A sensitivity analysis is carried out to explore the effects of uncertainty in key model inputs.

Unal, Resit↗
DOE OSTI2021

Quantum Algorithm for High Energy Physics Simulations

Simulating quantum field theories is a flagship application of quantum computing. However, calculating experimentally relevant high energy scattering amplitudes entirely on a quantum computer is prohibitively difficult. It is well known that such high energy scattering processes can be factored into pieces that can be computed using well established perturbative techniques, and pieces which currently have to be simulated using classical Markov chain algorithms. These classical Markov chain simulation approaches work well to capture many of the salient features, but cannot capture all quantum effects. To exploit quantum resources in the most efficient way, we introduce a new paradigm for quantum algorithms in field theories. This approach uses quantum computers only for those parts of the problem which are not computable using existing techniques. In particular, we develop a polynomial time quantum final state shower that accurately models the effects of intermediate spin states similar to those present in high energy electroweak showers with a global evolution variable. The algorithm is explicitly demonstrated for a simplified quantum field theory on a quantum computer.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Trustworthy Physics-Informed Deep Learning for Predictive Scientific Computing

This project has developed powerful trustworthy physics-informed deep learning (TPiDL) models and methods to fundamentally enhance the scale and power of computational modeling in the scientific and engineering domains. Deep learning (DL) has radically advanced the state-of-the-art in machine learning, computer vision, natural language processing, and also scientific computing. Nevertheless, progress has been driven almost entirely by empirical observations, hacks, and tricks. Under the support of this project, the graph operator learning tools and advanced trustworthy physical informed neural networks have been developed. In addition, stochastic gradient replica-exchange Markov Chain Monte Carlo (MCMC) sampling algorithms have been designed to quantify the uncertainties and speed up the training of large-scale neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗
NASA NTRS1996

On the Use of Kronecker Operators for the Solution of Generalized Stochastic Petri Nets

We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of marking-dependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulse-based reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the state-space explosion. In the conclusion, we point out ideas to parallelize our approach.

Ciardo, Gianfranco↗
NASA NTRS1990

A numerical model of the Uranian dust rings

The present numerical simulations of the Uranian rings discovered by Voyager 2 indicate that they may be the visible component of low optical depth moonlet belts made up of 10 to 100,000 cm objects; these objects would serve as the sources of dust, via both micrometeoroid bombardment and the collisional release of ejecta. It is proposed that the dust bands are generated by continuous ejection and reabsorption of micron-scale regolith material within the hypothesized moolet belts, and it is noted that numerical simulations of such a system in a Markov-chain formalism can reproduce Uranian dust ring characteristics.

Colwell, Joshua E.↗
NASA NTRS1979

Extensions to the classical calculation of the effect of mutual shadowing in diffuse reflection

The classical method for accounting for the mutual shadowing among closely packed particles in multiple scattering calculations is extended in the following ways. (1) By modeling the particle distribution by a Poisson process with a varying density parameter, a 'Van der Waals' type approximation allows extension to a greater fractional volume density, D. In this case it is only required that D squared be much less than 1 instead of D being much less than 1. (2) In the case that the particle distribution is not uniform the classical calculation may be weighted by the pair correlation function of the distribution. (3) The use of the Markov chain formalism for radiative transfer allows inclusion of the effect of shadowing for two orders of scattering. For conditions such as might apply in Saturn's rings, the inclusion of this effect makes less than a 0.1% difference in the calculated phase curves, compared to previous calculations which have included shadowing only in the first scattering. The latter are thus shown to be quite accurate.

Esposito, L. W.↗
NASA NTRS2019

Cellular Statistical Models of Broken Cloud Fields. Part IV: Effects of Pixel Size on Idealized Satellite Observations

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF) which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud/clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master-matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

Mikhail D. Alexandrov↗
DOE OSTI2022

Estimating Cosmological Constraints from Galaxy Cluster Abundance using Simulation-Based Inference

Inferring the values and uncertainties of cosmological parameters in a cosmology model is of paramount importance for modern cosmic observations. In this paper, we use the simulation-based inference (SBI) approach to estimate cosmological constraints from a simplified galaxy cluster observation analysis. Using data generated from the Quijote simulation suite and analytical models, we train a machine learning algorithm to learn the probability function between cosmological parameters and the possible galaxy cluster observables. The posterior distribution of the cosmological parameters at a given observation is then obtained by sampling the predictions from the trained algorithm. Our results show that the SBI method can successfully recover the truth values of the cosmological parameters within the 2σ limit for this simplified galaxy cluster analysis, and acquires similar posterior constraints obtained with a likelihood-based Markov Chain Monte Carlo method, the current state-of the-art method used in similar cosmological studies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Photoproduction of the Σ + hyperon using linearly polarized photons with CLAS

Measurements of the polarization observables Σ, P, T, O x , O z for the reaction $\vec{γ}$ p → $K^0_S$Σ + using a linearly polarized photon beam of energy 1.1 to 2.1 GeV are reported. The measured data provide information on a channel that has not been studied extensively, but is required for a full coupled-channel analysis in the nucleon resonance region. Observables have been simultaneously extracted using likelihood sampling with a Markov-Chain Monte Carlo process. Angular distributions in bins of photon energy E γ are produced for each polarization observable. T, O x , and O z are first time measurements of these observables in this reaction. The extraction of Σ extends the energy range beyond a previous measurement. The measurement of P, the recoil polarization, is consistent with previous measurements. The measured data are shown to be significant enough to affect the estimation of the nucleon resonance parameters when fitted within a coupled-channels model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2016

Exocometary Gas in the HD 181327 Debris Ring

An increasing number of observations have shown that gaseous debris discs are not an exception. However, until now, we only knew of cases around A stars. Here we present the first detection of 12CO (2-1) disc emission around an F star, HD 181327, obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) observations at 1.3 mm. The continuum and CO emission are resolved into an axisymmetric disc with ring-like morphology. Using a Markov chain Monte Carlo method coupled with radiative transfer calculations, we study the dust and CO mass distribution. We find the dust is distributed in a ring with a radius of 86.0 +/- 0.4 au and a radial width of 23.2 +/- 1.0 au. At this frequency, the ring radius is smaller than in the optical, revealing grain size segregation expected due to radiation pressure. We also report on the detection of low-level continuum emission beyond the main ring out to approximately 200 au. We model the CO emission in the non-local thermodynamic equilibrium regime and we find that the CO is co-located with the dust, with a total CO gas mass ranging between 1.2 x 10(exp -6) solar mass and 2.9 x 10(exp -6) solar mass, depending on the gas kinetic temperature and collisional partners densities. The CO densities and location suggest a secondary origin, i.e. released from icy planetesimals in the ring. We derive a CO+CO2 cometary composition that is consistent with Solar system comets. Due to the low gas densities, it is unlikely that the gas is shaping the dust distribution.

exocometary gas↗
DOE OSTI2024

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Transport coefficient approach for characterizing nonequilibrium dynamics in soft matter

Nonequilibrium states in soft condensed matter require a systematic approach to characterize and model materials, enhancing predictability and applications. Among the tools, X-ray photon correlation spectroscopy (XPCS) provides exceptional temporal and spatial resolution to extract dynamic insight into the properties of the material. However, existing models might overlook intricate details. We introduce an approach for extracting the transport coefficient, denoted as $J(t)$, from the XPCS studies. This coefficient is a fundamental parameter in nonequilibrium statistical mechanics and is crucial for characterizing transport processes within a system. Our method unifies the Green–Kubo formulas associated with various transport coefficients, including gradient flows, particle–particle interactions, friction matrices, and continuous noise. We achieve this by integrating the collective influence of random and systematic forces acting on the particles within the framework of a Markov chain. We initially validated this method using molecular dynamics simulations of a system subjected to changes in temperatures over time. Subsequently, we conducted further verification using experimental systems reported in the literature and known for their complex nonequilibrium characteristics. The results, including the derived $J(t)$ and other relevant physical parameters, align with the previous observations and reveal detailed dynamical information in nonequilibrium states. This approach represents an advancement in XPCS analysis, addressing the growing demand to extract intricate nonequilibrium dynamics. Further, the methods presented are agnostic to the nature of the material system and can be potentially expanded to hard condensed matter systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1997

Parametric State Space Structuring

Structured approaches based on Kronecker operators for the description and solution of the infinitesimal generator of a continuous-time Markov chains are receiving increasing interest. However, their main advantage, a substantial reduction in the memory requirements during the numerical solution, comes at a price. Methods based on the "potential state space" allocate a probability vector that might be much larger than actually needed. Methods based on the "actual state space", instead, have an additional logarithmic overhead. We present an approach that realizes the advantages of both methods with none of their disadvantages, by partitioning the local state spaces of each submodel. We apply our results to a model of software rendezvous, and show how they reduce memory requirements while, at the same time, improving the efficiency of the computation.

Ciardo, Gianfranco↗
DOE OSTI2025

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Probing Physics beyond the Standard Model through Combined Analyses of Next-generation Type Ia Supernova, Cosmic Microwave Background, and Baryon Acoustic Oscillation Surveys

Observations of Type Ia supernovae (SNe Ia), which probe the late Universe, together with baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB), which probe the intermediate and early epochs, provide complementary constraints on the expansion history of the Universe. In this work, we forecast constraints on dark energy and other extensions to the standard cosmological model by combining the SN Ia sample expected from the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), data from current and forthcoming CMB surveys, and BAO measurements from the Dark Energy Spectroscopic Instrument (DESI). For the CMB, we use temperature, polarization, and lensing power spectra (TT/EE/TE/ϕϕ) from the South Pole Telescope, the planned Advanced Simons Observatory, and a CMB-S4–like experiment. We derive constraints on ΛCDM and its extensions involving the dark energy equation-of-state parameters (w 0 , w a ) and the sum of neutrino masses ∑m ν using a Markov Chain Monte Carlo (MCMC) sampling framework. We find that the LSST Year 3 SN Ia sample can improve upon the DES Year 5 dark energy constraints by a factor of 2−2.5×, with the gains driven primarily by the significantly higher SN Ia density in the LSST sample. Similarly, DESI-DR3 shows up to a 1.8× improvement on dark energy parameters over DR2, driven largely by the substantial increase in the low-redshift sample. Combining CMB with LSST-Y3-SN Ia and DESI-DR3-BAO yields σ(w 0 ) = 0.028 and σ(w a ) = 0.11 for w 0 w a CDM cosmology with the results being largely independent of the CMB dataset. The constraints weaken by 10%–30% when freeing ∑m ν and spatial curvature. Moreover, the joint analysis of the three datasets can enable a 2σ–3σ detection of ∑m ν .

Raghunathan, Srinivasan [University of California;↗