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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Studies in astronomical time series analysis: Modeling random processes in the time domain

Random process models phased in the time domain are used to analyze astrophysical time series data produced by random processes. A moving average (MA) model represents the data as a sequence of pulses occurring randomly in time, with random amplitudes. An autoregressive (AR) model represents the correlations in the process in terms of a linear function of past values. The best AR model is determined from sampled data and transformed to an MA for interpretation. The randomness of the pulse amplitudes is maximized by a FORTRAN algorithm which is relatively stable numerically. Results of test cases are given to study the effects of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the optical light curve of the quasar 3C 273 is given.

Scargle, J. D.↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
NASA NTRS2003

Estimating Uncertainty in GPCP and TRMM Multi-Satellite Precipitation Estimates

One of the high-priority problems in satellite precipitation estimation is developing algorithms for estimating the errors in precipitation retrievals by individual sensors and subsequent multi-satellite combinations. Classically, we distinguish between "random" and "bias" errors, which do and do not, respectively average to zero over a "big enough" time/space sample. The current operational GPCP and TRMM multi-satellite algorithms are nearly unique in estimating random error for the monthly precipitation estimates from individual sensor systems (including gauge), following Huffman, and then making multi-sensor combinations. No routinely operational global precipitation produces estimates of bias error. Subsequently, a similar scheme has been followed to provide random error estimates for the Multi-satellite Precipitation Analysis (MPA) being computed in real time and after real time for TRMM. The Huffman algorithm for random error is briefly reviewed, including a discussion of the limitations imposed on the algorithm by standard monthly precipitation data sets. Starting from a very simple theoretical treatment of the histogram of precipitation samples in a month, an equation is developed that depends on the estimated average precipitation rate for the month, the number of samples in the month, and two constants. The constants are set separately for each source of precipitation estimate (such as "raingauge") by calibration at selected ground sites. We discuss recent work validating the random error estimates to highlight the successes and limitations of this first-generation approach. We then consider what information is needed from the individual sensor algorithms to facilitate additional accuracy in the estimation of random errors across the time/space span of climate regimes which a global estimation system must handle. In addition, the thorny issue of estimating bias is raised. Finally, the role of error estimates (and the qualitative errors!) in creating combinations of precipitation estimates from different individual sensors is discussed. This issue is particularly important when fine scales in space and time are being considered, say the 0.25 x 0.25-deg 3-hourly estimates in the MPA.

Huffman, G. J.↗
NASA NTRS1981

Information efficiency of line-scan imaging mechanisms

Information theory is used to formulate a single figure of merit for assessing the performance of line-scan imaging systems as a function of their spatial response (PSF or MTF), sensitivity, and sampling and quantization intervals and of the statistical properties of a random radiance field. Information density and efficiency (i.e., the ratio of information density to data density) tend to be optimum when the MTF and sampling passband of the imaging system are matched to the Wiener spectrum of the radiance field. Computational results for the statistical properties of natural radiance fields and the responses of common line-scan imaging mechanisms indicate that information density and efficiency are not strongly sensitive to variations in typical statistical properties of the radiance field and that the best practically realizable performance is approached when the sampling intervals are approximately 0.5-0.7 times the equivalent diameter of the PSF.

Huck, F. O.↗
NASA NTRS2022

Grand Canyon Ecological Forecasting: Using NASA Earth Observations to Monitor and Model Juniper Woodland Mortality in Grand Canyon National Park

Significant die-offs of the drought tolerant species Utah juniper (Juniperus osteosperma) and one-seeded juniper (Juniperus monosperma) have been observed throughout central and northern Arizona, including Grand Canyon National Park (GCNP). As climate models project rising temperatures and continuous drought, land managers are concerned for the future of juniper in and around GCNP. This project incorporated data from Landsat 8 Operational Land Imager (OLI), the Shuttle Radar Topography Mission (SRTM), and ocular samples of the National Agriculture Imagery Program (NAIP) in a random forest model to identify patterns between characteristics of the landscape and locations of juniper woodland mortality and to model areas subject to vulnerability. This study found no significant correlation between ocularly sampled juniper tree mortality and remotely sensed environmental variables used thus, accurately modeling mortality vulnerability in the future was not feasible. The ocular sampling, however, allows the partners at the GCNP’s Science & Resource Management Division to better understand areas of juniper tree woodland mortality and the relative amount of mortality in the park. Additionally, the areas of juniper tree mortality found in this project provide the partners with guidance for future field sampling.

Scarlet Jackson↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

2022 Central California Travel Study

# 2022 Central California Travel Study The 2022 Central California Travel Study collected demographic and travel pattern information to better understand household travel behavior in the state’s San Joaquin Valley region. ## Data Collection Agency The Fresno Council of Governments conducted the household travel study in collaboration with metropolitan planning organizations in Fresno, Kern, Kings, Madera, Merced, San Joaquin, Stanislaus, and Tulare counties in California. ## Survey Methodology The two-part study consisted of a survey and a travel diary. The survey gathered data on household demographic composition and typical travel behaviors. The travel diary gathered individual travel data during a specified travel period for all members of a given household. ## Travel Diary Methods Households with smartphones were encouraged to complete their travel diaries using the rMove smartphone app for up to seven consecutive days. Households without smartphones or those unwilling to participate via smartphone completed their travel diaries online (using the web-version of rMove) or by calling the survey call center. These households reported travel for one day (Tuesday, Wednesday, or Thursday). ## Recruitment Sampling Methods The majority of the recruitment was conducted via address-based sampling, a type of probability sampling, with a focus on reaching county-level targets in collaboration with metropolitan planning organizations in the region. Supplemental sampling methods, primarily non-probability, were employed during all waves of data collection to improve survey representation. The supplemental sample included targeted outreach to hard-to-survey populations via transit rider email lists; local housing authorities; Nichols Research, a California-based market research firm; and the Ipsos™ KnowledgePanel, an online random probability panel. See the documentation for more information about sampling and weighting. ## Survey Records, Data, and Documentation In total, 7,406 households completed 19,084 surveys representing 150,012 trips across 42,567 person-days.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2006

Thermal Conductivity of Polymer/Nano-filler Blends

To improve the thermal conductivity of an ethylene vinyl acetate copolymer, Elvax 260 was compounded with three carbon based nano-fillers. Multiwalled carbon nanotubes (MWCNT), vapor grown carbon nanofibers (CNF) and expanded graphite (EG) were investigated. In an attempt to improve compatibility between the Elvax and nanofillers, MWCNTs and EGs were modified through non covalent and covalent attachment of alkyl groups. Ribbons were extruded to form samples in which the nanofillers were aligned, and samples were also fabricated by compression molding in which the nano-fillers were randomly oriented. The thermal properties were evaluated by DSC and TGA, and mechanical properties of the aligned samples were determined by tensile testing. The degree of dispersion and alignment of the nanoparticles were investigated using high-resolution scanning electron microscopy. Thermal conductivity measurements were performed using a Nanoflash technique. The thermal conductivity of the samples was measured in both the direction of alignment as well as perpendicular to that direction. The results of this study will be presented.

Ghose, Sayata↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
DOE OSTI2023

Efficient Subset Simulation using Hamiltonian Neural Network enhanced Markov Chain Monte Carlo Methods

The Monte Carlo method delivers an unbiased estimate of the probability of failure. However, the variance of the estimate depends on the number of evaluated samples. This number must be very large for estimations of a low probability of failure. If the evaluation of each sample is computationally expensive, the crude Monte Carlo simulation strategy is impracticable. Therefore, subset simulations are used to reduce the required number of evaluations. Subset simulations require a Markov Chain Monte Carlo sampler, such as the random walk Metropolis-Hastings algorithm. The algorithm, however, struggles with sampling in low-probability regions, especially if they are narrow. As a consequence, advanced Markov Chain Monte Carlo simulations have been developed. In particular, the Hamiltonian Monte Carlo method explores the target distribution rapidly. Driven by the idea of Hamiltonian dynamics, this sampler provides a non-random walk through the target distribution. The incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results for reliability analysis. One downside of the Hamiltonian Monte Carlo method is that gradient evaluations are computationally expensive, especially when dealing with high-dimensional problems and evaluating long trajectories. We show that integrating Hamiltonian neural networks in Hamiltonian Monte Carlo simulations significantly speeds up the sampling task. Furthermore, the enhancement of adaptive trajectory length within the Hamiltonian Monte Carlo results in the efficient proposal of the following states. Based on this recent enhancement, we provide a fast sampling strategy for subset simulations using Hamiltonian neural networks to replace the evaluation of the gradient and significantly speed up the Hamiltonian Monte Carlo simulation.

97 MATHEMATICS AND COMPUTING↗