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NASA NTRS1981

A stochastic-dynamical approach to the study of the natural variability of the climate

A method, suggested by Leith (1975), which employed stochastic-dynamic forecasts obtained from a general circulation model in such a way as to satisfy the definition of climatic noise, was used to validate assumptions accounting for the effects of external influences in estimating the climatic noise. Two assumptions were investigated: (1) that the weather fluctuations can be represented as a Markov process, and (2) that changing external conditions do not influence the atmosphere's statistical properties on short time scales. The general circulation model's simulation of the daily weather fluctuations was generated by performing integrations with prescribed climatological boundary conditions for random initial atmospheric states, with resulting dynamical forecasts providing an ensemble of simulated data for the autoregressive modeling of weather fluctuations. To estimate the climatic noise from the observational data (consisting of hourly values of sea level pressure and surface temperature at 54 U.S. stations for the month of January for the years 1949-1975) use of the short time-scale assumption is made. The simulated and observed data were found not to be consistent with either white noise or a Markov process of weather fluctuations. Good agreement was found between the results of the hypothetical testing of the simulated and the observed surface temperatures; and only partial support was found for the short time-scale assumption, i.e., for sea level pressure.

Straus, D. M.↗

DOE OSTI2021

A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity

We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis . The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis . The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2015

Demonstration of emulator-based Bayesian calibration of safety analysis codes: Theory and formulation

System codes for simulation of safety performance of nuclear plants may contain parameters whose values are not known very accurately. New information from tests or operating experience is incorporated into safety codes by a process known as calibration, which reduces uncertainty in the output of the code and thereby improves its support for decision-making. The work reported here implements several improvements on classic calibration techniques afforded by modern analysis techniques. The key innovation has come from development of code surrogate model (or code emulator) construction and prediction algorithms. Use of a fast emulator makes the calibration processes used here with Markov Chain Monte Carlo (MCMC) sampling feasible. This study uses Gaussian Process (GP) based emulators, which have been used previously to emulate computer codes in the nuclear field. The present work describes the formulation of an emulator that incorporates GPs into a factor analysis-type or pattern recognition-type model. This “function factorization” Gaussian Process (FFGP) model allows overcoming limitations present in standard GP emulators, thereby improving both accuracy and speed of the emulator-based calibration process. Calibration of a friction-factor example using a Method of Manufactured Solution is performed to illustrate key properties of the FFGP based process.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2014

Design of Experiments, Model Calibration and Data Assimilation

This presentation provides an overview of emulation, calibration and experiment design for computer experiments. Emulation refers to building a statistical surrogate from a carefully selected and limited set of model runs to predict unsampled outputs. The standard kriging approach to emulation of complex computer models is presented. Calibration refers to the process of probabilistically constraining uncertain physics/engineering model inputs to be consistent with observed experimental data. An initial probability distribution for these parameters is updated using the experimental information. Markov chain Monte Carlo (MCMC) algorithms are often used to sample the calibrated parameter distribution. Several MCMC algorithms commonly employed in practice are presented, along with a popular diagnostic for evaluating chain behavior. Space-filling approaches to experiment design for selecting model runs to build effective emulators are discussed, including Latin Hypercube Design and extensions based on orthogonal array skeleton designs and imposed symmetry requirements. Optimization criteria that further enforce space-filling, possibly in projections of the input space, are mentioned. Designs to screen for important input variations are summarized and used for variable selection in a nuclear fuels performance application. This is followed by illustration of sequential experiment design strategies for optimization, global prediction, and rare event inference.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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↗

DOE OSTI2019

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗

DOE OSTI2015

Adaptive Bayesian Inference for Prediction

Performing rigorous predictive simulation necessitates that all available data be incorporated into the modeling process in order to accurately quantify uncertainties in predictions of the model. Statistical Bayesian inference is the most commonly used approach for incorporating data into uncertainty estimates. Statistical Bayesian inference uses data and an assumed error model to inform posterior distributions of model input variables and model discrepancies. An explicit characterization of the posterior distribution is not formed, but rather methods such as Markov chain Monte-Carlo (MCMC) are used to draw samples from the posterior. These samples are then used to evaluate statistics, such as integrals, of predicted quantities of interest (QoI). Recently the authors have developed an alternative reformulation of Bayesian inference based upon a measure-theoretic inversion technique. Unlike traditional statistical Bayesian inference, this reformulation allows us to directly interrogate the posterior distribution and, consequently, to generate samples from the posterior without MCMC. In this work we use forward propagation uncertainty quantification techniques to reduce the cost of approximating the posterior distribution. Specifically we investigate goal-oriented adaptive sparse grid approximation methods. These adaptive methods concentrate high-fidelity model evaluations in regions of the parameter space that both significantly contribute to the uncertainty in specified QoI and are informed by the available data. Numerical results are presented to compare our approach with the standard statistical Bayesian approach and to demonstrate the effectiveness of the goal-oriented adaptivity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

The exit-time problem for a Markov jump process

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Additionally, such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. Finally, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Deriving Physical Properties from Broadband Photometry with Prospector: Description of the Model and a Demonstration of its Accuracy Using 129 Galaxies in the Local Universe

Broadband photometry of galaxies measures an unresolved mix of complex stellar populations, gas, and dust. Interpreting these data is a challenge for models: many studies have shown that properties derived from modeling galaxy photometry are uncertain by a factor of two or more, and yet answering key questions in the field now requires higher accuracy than this. Here, we present a new model framework specifically designed for these complexities. Our model, Prospector- α , includes dust attenuation and re-radiation, a flexible attenuation curve, nebular emission, stellar metallicity, and a six-component nonparametric star formation history. The flexibility and range of the parameter space, coupled with Monte Carlo Markov chain sampling within the Prospector inference framework, is designed to provide unbiased parameters and realistic error bars. We assess the accuracy of the model with aperture-matched optical spectroscopy, which was excluded from the fits. We compare spectral features predicted solely from fits to the broadband photometry to the observed spectral features. Our model predicts H α luminosities with a scatter of ∼0.18 dex and an offset of ∼0.1 dex across a wide range of morphological types and stellar masses. This agreement is remarkable, as the H α luminosity is dependent on accurate star formation rates, dust attenuation, and stellar metallicities. The model also accurately predicts dust-sensitive Balmer decrements, spectroscopic stellar metallicities, polycyclic aromatic hydrocarbon mass fractions, and the age- and metallicity-sensitive features D{sub n}4000 and H δ . Although the model passes all these tests, we caution that we have not yet assessed its performance at higher redshift or the accuracy of recovered stellar masses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Stochastic simulation of occupant-driven energy use in a bottom-up residential building stock model

The residential buildings sector is one of the largest electricity consumers worldwide and contributes disproportionally to peak electricity demand in many regions. Strongly driven by occupant activities, household energy consumption is stochastic and heterogeneous in nature. However, most residential energy models applied by industry use homogeneous, deterministic activity schedules, which work well for predictions of annual energy consumption, but can result in unrealistic hourly or sub-hourly electric load profiles, with exaggerated or muted peaks. The increasing proportion of variable renewable energy generators means that representing the heterogeneity and stochasticity of occupant behavior is now crucial for reliable planning at both bulk-power and distribution-system scales. This work presents a novel and open-source occupancy simulation approach that can simulate a diverse set of individual occupant and household event schedules for all major electricity, fuel, and hot water end uses. To accomplish this, we evaluated three alternative occupant activity simulation approaches before selecting a hybrid combining time-inhomogeneous Markov chains and probability-sampling of event durations and magnitudes. Further, we integrated the stochastic occupancy simulation with an open-source bottom-up physics-simulation building stock model and published a set of 550,000 diverse household end-use activity schedules representing a national housing stock. The simulator was verified against time-use survey data, and simulation results were validated against measured end-use electricity data for accuracy and reliability. While we use data for the United States, our application demonstrates how similar approaches could be applied using the time-use survey data collected in many countries around the world.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

First study of reionization in the Planck 2015 normalized closed ΛCDM inflation model

We study reionization in two non-flat ΛCDM inflation models that best fit the Planck 2015 cosmic microwave background (CMB) anisotropy observations, ignoring or in conjunction with baryon acoustic oscillation distance measurements. We implement a principal component analysis (PCA) to estimate the uncertainties in the reionization history from a joint quasar–CMB data set. A thorough Markov Chain Monte Carlo analysis is done over the parameter space of the PCA modes for both non-flat ΛCDM inflation models as well as the original Planck 2016 tilted, spatially flat ΛCDM inflation model. Although both flat and non-flat models can closely match the low-redshift ( z ≲ 6) observations, we notice a possible tension between high-redshift ( z ~ 8) Lyman α emitter data and the non-flat models. This is solely due to the fact that the closed models have a relatively higher reionization optical depth compared to the flat one, which in turn demands more high-redshift ionizing sources and favours an extended reionization starting as early as z ≈ 14. We conclude that as opposed to flat cosmology, for the non-flat cosmology models (i) the escape fraction needs steep redshift evolution and even unrealistically high values at some redshifts and (ii) most of the physical parameters require to have non-monotonic redshift evolution, especially apparent when Lyman α emitter data are included in the analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

AN EMBEDDED ACTIVE NUCLEUS IN THE OH MEGAMASER GALAXY IRAS16399–0937

We present a multiwavelength study of the OH megamaser galaxy IRAS16399–0937, based on new Hubble Space Telescope (HST)/Advanced Camera for Surveys F814W and Hα+[N II] images and archive data from HST, Two Micron All Sky Survey, Spitzer, Herschel and the Very Large Array. This system has a double nucleus, whose northern (IRAS16399N) and southern (IRAS16399S) components have a projected separation of ∼6'' (3.4 kpc) and have previously been identified based on optical spectra as a low ionization nuclear emission line region (LINER) and starburst nucleus, respectively. The nuclei are embedded in a tidally distorted common envelope, in which star formation is mostly heavily obscured. The infrared spectrum is dominated by strong polycyclic aromatic hydrocarbon, but deep silicate and molecular absorption features are also present, and are strongest in the IRAS16399N nucleus. The 0.435-500 μm spectral energy distribution was fitted with a model including stellar, interstellar medium and active galactic nucleus (AGN) torus components using our new Markov Chain Monte Carlo code, CLUMPYDREAM. The results indicate that the IRAS16399N contains an AGN (L {sub bol} ∼ 10{sup 44} erg s{sup –1}) deeply embedded in a quasi-spherical distribution of optically thick clumps with a covering fraction ≈1. We suggest that these clumps are the source of the OHM emission in IRAS16399–0937. The high torus covering fraction precludes AGN photoionization as the origin of the LINER spectrum, however, the spectrum is consistent with shocks (v ∼ 100-200 km s{sup –1}). We infer that the ∼10{sup 8} M {sub ☉} black hole in IRAS16399N is accreting at a small fraction (∼1%) of its Eddington rate. The low accretion rate and modest nuclear star formation rates suggest that while the gas-rich major merger forming the IRAS16399–0937 system has triggered widespread star formation, the massive gas inflows expected from merger simulations have not yet fully developed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Fracton Hydrodynamics without Time-Reversal Symmetry

Here, we present an effective field theory for the nonlinear fluctuating hydrodynamics of a single conserved charge with or without time-reversal symmetry, based on the Martin-Siggia-Rose formalism. Applying this formalism to fluids with only charge and multipole conservation, and with broken time-reversal symmetry, we predict infinitely many new dynamical universality classes, including some with arbitrarily large upper critical dimensions. Using large scale simulations of classical Markov chains, we find numerical evidence for a breakdown of hydrodynamics in quadrupole-conserving models with broken time-reversal symmetry in one spatial dimension. Our framework can be applied to the hydrodynamics around stationary states of open systems, broadening the applicability of previously developed ideas and methods to a wide range of systems in driven and active matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

DOE OSTI2024

Bayesian inference of structured latent spaces from neural population activity with the orthogonal stochastic linear mixing model

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μ ECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2010

Probabilistic Motion Planning of Balloons in Strong, Uncertain Wind Fields

This paper introduces a new algorithm for probabilistic motion planning in arbitrary, uncertain vector fields, with emphasis on high-level planning for Montgolfiere balloons in the atmosphere of Titan. The goal of the algorithm is to determine what altitude--and what horizontal actuation, if any is available on the vehicle--to use to reach a goal location in the fastest expected time. The winds can vary greatly at different altitudes and are strong relative to any feasible horizontal actuation, so the incorporation of the winds is critical for guidance plans. This paper focuses on how to integrate the uncertainty of the wind field into the wind model and how to reach a goal location through the uncertain wind field, using a Markov decision process (MDP). The resulting probabilistic solutions enable more robust guidance plans and more thorough analysis of potential paths than existing methods.

Wolf, Michael T.↗

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 NTRS2018

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

Image Processing:Pattern Recognition↗