Results for “MARKOV PROCESS” — Page 14

NASA NTRS2011

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates.

Sundqvist, Jon O.↗

NASA NTRS2002

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and Its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates.

generalised↗

NASA NTRS1987

On the next generation of reliability analysis tools

The current generation of reliability analysis tools concentrates on improving the efficiency of the description and solution of the fault-handling processes and providing a solution algorithm for the full system model. The tools have improved user efficiency in these areas to the extent that the problem of constructing the fault-occurrence model is now the major analysis bottleneck. For the next generation of reliability tools, it is proposed that techniques be developed to improve the efficiency of the fault-occurrence model generation and input. Further, the goal is to provide an environment permitting a user to provide a top-down design description of the system from which a Markov reliability model is automatically constructed. Thus, the user is relieved of the tedious and error-prone process of model construction, permitting an efficient exploration of the design space, and an independent validation of the system's operation is obtained. An additional benefit of automating the model construction process is the opportunity to reduce the specialized knowledge required. Hence, the user need only be an expert in the system he is analyzing; the expertise in reliability analysis techniques is supplied.

Babcock, Philip S., IV↗

NASA NTRSDate not supplied

Adding GPU Support to the Markov Chain Monte Carlo Code Catmip

In geophysics, we are confronted with many under-determined inverse problems. For example, all of our observations of earthquakes are made at the Earth’s surface. So, when we try to infer how slip during an earthquake evolves in space and time, we find that there are many potential slip histories that are consistent with our limited observations and our understanding of earthquake physics. One way to approach these problems is with Bayesian analysis which allows us to infer the ensemble of all potential slip models that satisfy the observations and our prior knowledge of earthquake physics. In Bayesian analysis, our prior knowledge is known as the prior probability density function or prior PDF, the fit to the data is known as the data likelihood, and the target PDF that satisfies both the prior PDF and data likelihood is known as the posterior PDF. However, simulating the posterior PDF typically requires using Markov Chain Monte Carlo (MCMC) to draw tens of billions of random realizations of earthquake slip models, which may not be computationally feasible. To make this and similar geophysical inversions computationally tractable, we developed the Cascading Adaptive Transitional Metropolis In Parallel (CATMIP) algorithm. CATMIP is an efficient parallel Markov Chain Monte Carlo (MCMC) sampler that is used for model fitting and uncertainty quantification in geophysics. Example use cases are earthquake rupture modeling, determining mineral composition on Mars, reconstructing the history of ocean salinity, and historical earthquake relocation. CATMIP employs many parallel instances of the Metropolis algorithm for sampling in a transitioning framework. Transitioning is a process in which a set of random samples at equilibrium with a known probability density function (PDF) are used as seeds for the Markov chains to sample successive target PDFs that incrementally move the distribution from the starting seeds to the final desired PDF that describes the relative plausibility of potential values for the model parameters. The algorithm is implemented as a Master-Worker model employing MPI for communication. The worker processes are loosely coupled with global parameters periodically optimized by the master process. This provides a very high amount of parallelism with little communication between updates. During the presentation we will discuss the history of the algorithm and elaborate the earthquake rupture modeling use case for the CATMIP package. Our first step toward GPU optimization was to optimize the code for the CPU. CPU profiling revealed that most of the compute time is spent in calls to level 2 BLAS routines and calls to GSL random number generators. We revised the algorithm to employ level 3 BLAS routines instead. In our presentation we will describe how this was accomplished. Adding GPU support to CATMIP consisted mostly of replacing the calls to GSL with calls to GPU vendor-provided library routines. A small number of loops were directly implemented in CUDA. In the presentation will provide implementation details. Finally, we will discuss methods for profiling and opportunities for further optimizing GPU execution. By creating a code with the flexibility to run on either a CPU or GPU architecture, CATMIP can be used on systems ranging from large CPU-based HPC environments to single servers with GPU acceleration and everything in between.

HECC↗

NASA NTRS1979

An 'adding' algorithm for the Markov chain formalism for radiation transfer

An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.

Esposito, L. W.↗

NASA NTRS1986

An approximation formula for a class of fault-tolerant computers

An approximation formula is derived for the probability of failure for fault-tolerant process-control computers. These computers use redundancy and reconfiguration to achieve high reliability. Finite-state Markov models capture the dynamic behavior of component failure and system recovery, and the approximation formula permits an estimation of system reliability by an easy examination of the model.

White, A. L.↗

NASA NTRS1988

The inclusion of semi-Markov reconfiguration transitions into the computer-aided Markov evaluator (CAME) program

The modifications to the rule-based CAME program which allow it to more accurately model the fault-handling processes of fault-tolerant systems are described. This new capability is added to the CAME program by modeling the fault-handling processes of fault-tolerant systems. The integrated airframe/propulsion control system architecture (IAPSA II) reference configuration currently under development is detailed.

Rosch, Gene↗

NASA NTRS1985

An abstract specification language for Markov reliability models

Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

Butler, R. W.↗

NASA NTRS1986

An abstract language for specifying Markov reliability models

Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

Butler, Ricky W.↗

DOE OSTI2025

Pervaporative Dehydration of 2,3-Butanediol by Dense Poly(vinylidene fluoride) Hollow Fiber Membranes: Parameter Estimation, Process Design, and Technoeconomic Evaluation under Uncertainty

Pervaporation, combined with other separation processes, can effectively remove water from fermentation product streams, making it highly suitable for purifying alcohols like 2,3-butanediol (BDO). In this study, a dense poly(vinylidene fluoride) (PVDF) hollow fiber membrane module prototype was fabricated for BDO dehydration, achieving >0.2 LMH total flux and >95% BDO rejection. With a Markov chain Monte Carlo (MCMC) approach, Bayesian inference was used to quantify the uncertainty of the permeance parameters. A membrane cascade model was developed to scale up a process that purifies a preconcentrated BDO feed (70 wt %) to high purity (90 wt %). Through propagation of the uncertainty of the parameters and sensitivity analyses of the process variables, a cascade design was recommended. Despite data and model limitations, the framework enabled a reliable system analysis and economic evaluation, validated through tight confidence intervals in key process metrics, establishing the foundation for future applications of Bayesian methods in membrane-based processes.

Animal feed↗

NASA NTRS2018

Planetary Crater Detection and Registration Using Marked Point Processes, Multiple Birth and Death Algorithms, and Region-Based Analysis

Because of the large variety of sensors and spacecraft collecting data, planetary science needs to integrate various multi-sensor and multi-temporal images. These multiple data represent a precious asset, as they allow the study of targets spectral responses and of changes in the surface structure; because of their variety, they also require accurate and robust registration. A new crater detection algorithm, used to extract features that will be integrated in an image registration framework, is presented. A marked point process-based method has been developed to model the spatial distribution of elliptical objects (i.e. the craters) and a birth-death Markov chain Monte Carlo method, coupled with a region-based scheme aiming at computational efficiency, is used to find the optimal configuration fitting the image. The extracted features are exploited, together with a newly defined fitness function based on a modified Hausdorff distance, by an image registration algorithm whose architecture has been designed to minimize the computational time.

Image Processing:Pattern Recognition↗

NASA NTRS2017

Planetary Crater Detection and Registration Using Marked Point Processes, Multiple Birth and Death Algorithms, and Region-Based Analysis

Because of the large variety of sensors and spacecraft collecting data, planetary science needs to integrate various multi-sensor and multi-temporal images. These multiple data represent a precious asset, as they allow the study of targets spectral responses and of changes in the surface structure; because of their variety, they also require accurate and robust registration. A new crater detection algorithm, used to extract features that will be integrated in an image registration framework, is presented. A marked point process-based method has been developed to model the spatial distribution of elliptical objects (i.e. the craters) and a birth-death Markov chain Monte Carlo method, coupled with a region-based scheme aiming at computational efficiency, is used to find the optimal configuration fitting the image. The extracted features are exploited, together with a newly defined fitness function based on a modified Hausdorff distance, by an image registration algorithm whose architecture has been designed to minimize the computational time.

Image Processing; Pattern Recognition↗

NASA NTRS2000

Quantum Decision Maker Theory and Simulation

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics.

Quantum↗

NASA NTRS1991

An error bound for instantaneous coverage

An error bound is derived for a reliability model approximation method. The approximation method is appropriate for the semi-Markov models of reconfigurable systems that are designed to achieve extremely high reliability. The semi-Markov models of these system are complex, and a significant amount of their complexity arises from the detailed descriptions of the reconfiguration processes. The reliability model approximation method consists of replacing a detailed description of a reconfiguration process with the probabilities of the possible outcomes of the reconfiguration process. These probabilities are included in the model as instantaneous jumps from the fault-occurrence state. Since little time is spent in the reconfiguration states, instantaneous jumps are a close approximation to the original model. This approximation procedure is shown to produce an overestimation for the probability of system failure, and an error bound is derived for this overestimation.

White, Allan L.↗

DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Hyporheic-zone Processes and Stream Oxygen Dynamics: Insights from a Multiscale Reactive Transport Model: Modeling Archive

This archive contains the data and Python scripts required to reproduce the analyses and figures in the study: Gomez-Velez, J. D., Rathore, S. S., Cohen, M. J., & Painter, S. L. (2025). Hyporheic-zone Processes and Stream Oxygen Dynamics: Insights from a Multiscale Reactive Transport Model. Submitted to Water Resources Research. The analysis utilizes the subgrid model Advection Dispersion Equation with Lagrangian Subgrids (ADELS) implemented in the Advanced Terrestrial Simulator (ATS; https://amanzi.github.io/ats/stable/). In this case, the ATS and Amanzi versions are (1) ATS version 1.5.1_f5ba18f8 and (2) Amanzi version 1.6-dev_53444cca4. The repository includes a Jupyter Notebook and the necessary data (Pandas DataFrames stored as pickle files) to generate the figures for the manuscript. Additionally, it contains Python scripts to create ATS input files, run the ATS simulations, and post-process the results. Finally, it provides routines for parameter estimation using the Single-Station Metabolism (SSM) model with the Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm with ZS enhancements (DREAM-ZS).

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2015

Orbit Determination for the Lunar Reconnaissance Orbiter Using an Extended Kalman Filter

Orbit determination (OD) analysis results are presented for the Lunar Reconnaissance Orbiter (LRO) using a commercially available Extended Kalman Filter, Analytical Graphics' Orbit Determination Tool Kit (ODTK). Process noise models for lunar gravity and solar radiation pressure (SRP) are described and OD results employing the models are presented. Definitive accuracy using ODTK meets mission requirements and is better than that achieved using the operational LRO OD tool, the Goddard Trajectory Determination System (GTDS). Results demonstrate that a Vasicek stochastic model produces better estimates of the coefficient of solar radiation pressure than a Gauss-Markov model, and prediction accuracy using a Vasicek model meets mission requirements over the analysis span. Modeling the effect of antenna motion on range-rate tracking considerably improves residuals and filter-smoother consistency. Inclusion of off-axis SRP process noise and generalized process noise improves filter performance for both definitive and predicted accuracy. Definitive accuracy from the smoother is better than achieved using GTDS and is close to that achieved by precision OD methods used to generate definitive science orbits. Use of a multi-plate dynamic spacecraft area model with ODTK's force model plugin capability provides additional improvements in predicted accuracy.

Orbit Determination↗

NASA NTRS2017

Kepler Uniform Modeling of KOIs: MCMC Notes for Data Release 25

This document describes data products related to the reported planetary parameters and uncertainties for the Kepler Objects of Interest (KOIs) based on a Markov-Chain-Monte-Carlo (MCMC) analysis. Reported parameters, uncertainties and data products can be found at the NASA Exoplanet Archive . The codes used for this data analysis are available on the Github website (Rowe 2016). The relevant paper for details of the calculations is Rowe et al. (2015). The main differences between the model fits discussed here and those in the DR24 catalogue are that the DR25 light curves were used in the analysis, our processing of the MAST light curves took into account different data flags, the number of chains calculated was doubled to 200 000, and the parameters which are reported are based on a damped least-squares fit, instead of the median value from the Markov chain or the chain with the lowest 2 as reported in the past.

DR25↗