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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Quantum formalism for classical statistics

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

A Bayesian nonrigid registration method to enhance intraoperative target definition in image-guided prostate procedures through uncertainty characterization

Purpose: This study introduces a probabilistic nonrigid registration method for use in image-guided prostate brachytherapy. Intraoperative imaging for prostate procedures, usually transrectal ultrasound (TRUS), is typically inferior to diagnostic-quality imaging of the pelvis such as endorectal magnetic resonance imaging (MRI). MR images contain superior detail of the prostate boundaries and provide substructure features not otherwise visible. Previous efforts to register diagnostic prostate images with the intraoperative coordinate system have been deterministic and did not offer a measure of the registration uncertainty. The authors developed a Bayesian registration method to estimate the posterior distribution on deformations and provide a case-specific measure of the associated registration uncertainty. Methods: The authors adapted a biomechanical-based probabilistic nonrigid method to register diagnostic to intraoperative images by aligning a physician's segmentations of the prostate in the two images. The posterior distribution was characterized with a Markov Chain Monte Carlo method; the maximum a posteriori deformation and the associated uncertainty were estimated from the collection of deformation samples drawn from the posterior distribution. The authors validated the registration method using a dataset created from ten patients with MRI-guided prostate biopsies who had both diagnostic and intraprocedural 3 Tesla MRI scans. The accuracy and precision of the estimated posterior distribution on deformations were evaluated from two predictive distance distributions: between the deformed central zone-peripheral zone (CZ-PZ) interface and the physician-labeled interface, and based on physician-defined landmarks. Geometric margins on the registration of the prostate's peripheral zone were determined from the posterior predictive distance to the CZ-PZ interface separately for the base, mid-gland, and apical regions of the prostate. Results: The authors observed variation in the shape and volume of the segmented prostate in diagnostic and intraprocedural images. The probabilistic method allowed us to convey registration results in terms of posterior distributions, with the dispersion providing a patient-specific estimate of the registration uncertainty. The median of the predictive distance distribution between the deformed prostate boundary and the segmented boundary was Less-Than-Or-Slanted-Equal-To 3 mm (95th percentiles within {+-}4 mm) for all ten patients. The accuracy and precision of the internal deformation was evaluated by comparing the posterior predictive distance distribution for the CZ-PZ interface for each patient, with the median distance ranging from -0.6 to 2.4 mm. Posterior predictive distances between naturally occurring landmarks showed registration errors of Less-Than-Or-Slanted-Equal-To 5 mm in any direction. The uncertainty was not a global measure, but instead was local and varied throughout the registration region. Registration uncertainties were largest in the apical region of the prostate. Conclusions: Using a Bayesian nonrigid registration method, the authors determined the posterior distribution on deformations between diagnostic and intraprocedural MR images and quantified the uncertainty in the registration results. The feasibility of this approach was tested and results were positive. The probabilistic framework allows us to evaluate both patient-specific and location-specific estimates of the uncertainty in the registration result. Although the framework was tested on MR-guided procedures, the preliminary results suggest that it may be applied to TRUS-guided procedures as well, where the addition of diagnostic MR information may have a larger impact on target definition and clinical guidance.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-T-51: Bayesian Network Models for Radiotherapy Error Detection

Purpose: To develop a probabilistic model of radiotherapy plans using Bayesian networks that will detect potential errors in radiation delivery. Methods: Semi-structured interviews with medical physicists and other domain experts were employed to generate a set of layered nodes and arcs forming a Bayesian Network (BN) which encapsulates relevant radiotherapy concepts and their associated interdependencies. Concepts in the final network were limited to those whose parameters are represented in the institutional database at a level significant enough to develop mathematical distributions. The concept-relation knowledge base was constructed using the Web Ontology Language (OWL) and translated into Hugin Expert Bayes Network files via the the RHugin package in the R statistical programming language. A subset of de-identified data derived from a Mosaiq relational database representing 1937 unique prescription cases was processed and pre-screened for errors and then used by the Hugin implementation of the Estimation-Maximization (EM) algorithm for machine learning all parameter distributions. Individual networks were generated for each of several commonly treated anatomic regions identified by ICD-9 neoplasm categories including lung, brain, lymphoma, and female breast. Results: The resulting Bayesian networks represent a large part of the probabilistic knowledge inherent in treatment planning. By populating the networks entirely with data captured from a clinical oncology information management system over the course of several years of normal practice, we were able to create accurate probability tables with no additional time spent by experts or clinicians. These probabilistic descriptions of the treatment planning allow one to check if a treatment plan is within the normal scope of practice, given some initial set of clinical evidence and thereby detect for potential outliers to be flagged for further investigation. Conclusion: The networks developed here support the use of probabilistic models into clinical chart checking for improved detection of potential errors in RT plans.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2023

Wildfire-fighting Use Case Requirements to Monitor

In this technical report, we provide requirements for a wildfire-fighting use-case, towards the Safety Demonstrator 1. The use case will incorporate ground and airborne assets operating in a coordinated fashion, and will comprise five activities, from detection to the execution of the initial attack. Depending on the activity and the data involved, the requirements identified may be non-probabilistic or probabilistic. In both cases, we first identify some of the requirements we wish to monitor, and then present a formalization using the language of requirements of the NASA requirements elicitation tool FRET. To formalize probabilistic requirements, we use a novel extension to FRET’s requirements language that incorporates notions of probability, and discuss how requirements can be translated into existing probabilistic temporal logics like PCTL. We exemplify how some of the requirements presented can be monitored using the existing tools Ogma and Copilot. We close with a summary and future directions.

Requirements↗
DOE OSTI2016

Bayesian estimation of Karhunen–Loève expansions; A random subspace approach

One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition) on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

Abstract Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Yang, Hyung Jun↗
DOE OSTI2023

gpde

The R package gpde is an R implementation of a probabilistic differential equation solver. The package has a basic implementation of the Chkrebtii (2013) probabilistic ODE solver and an extension using the connection between Kalman Filtering for SDEs and Gaussian Processes from work by Simo Sarkka. The package also implements the Integrated Wiener covariance function from Schober 2014 to obtain probabilistic ODE solutions with the Runge-Kutta solution as the mean result. This collection of tools has been built into an R package for easy use at LANL and in the probabilistic numerics community.

Grosskopf, Michael↗
DOE OSTI2023

Logical Activation Functions v.1.1

SAND2024-01501O Logical Activation Functions software is a PyTorch implementation from the paper, "Logical Activation Functions for Training Arbitrary Probabilistic Boolean Logic." The activation functions approximate logit-space marginalization of probabilistic truth tables from probabilistic interpretations of inputs. They also provide a general methodology to approximate logical relationships between abstract antecedents and consequents for machine learning architectures. They do not target any specific application or use-case. By training probabilistic truth tables, these activation functions can capture more expressive relationships in a neural network than typical elementwise activation functions. This code is only designed for a single compute node with a GPU and is limited to machine learning architectures than can fit within the memory of a single GPU. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Duersch, Jed↗
DOE OSTI2026

py-boomer v0.1.0

Py-BOOMER (Python Bayesian OWL Ontology MErgER in Python) is a probabilistic reasoning system for knowledge representation and ontological reasoning with uncertainty. Itnables reasoning over probabilistic facts and taxonomic relationships, finding the most likely consistent interpretation of potentially conflicting assertions. It uses a combination of graph-based reasoning and Bayesian probabilistic inference. Key features: Represent probabilistic ontological statements Reason over class subsumption hierarchies Evaluate class equivalence relationships Detect and resolve logical inconsistencies Calculate posterior probabilities for each assertion

Mungall, Chris [Lawrence Berkeley National Laborat↗
DOE OSTI2012

Peak Dose Assessment for Proposed DOE-PPPO Authorized Limits

The Oak Ridge Institute for Science and Education (ORISE), a U.S. Department of Energy (DOE) prime contractor, was contracted by the DOE Portsmouth/Paducah Project Office (DOE-PPPO) to conduct a peak dose assessment in support of the Authorized Limits Request for Solid Waste Disposal at Landfill C-746-U at the Paducah Gaseous Diffusion Plant (DOE-PPPO 2011a). The peak doses were calculated based on the DOE-PPPO Proposed Single Radionuclides Soil Guidelines and the DOE-PPPO Proposed Authorized Limits (AL) Volumetric Concentrations available in DOE-PPPO 2011a. This work is provided as an appendix to the Dose Modeling Evaluations and Technical Support Document for the Authorized Limits Request for the C-746-U Landfill at the Paducah Gaseous Diffusion Plant, Paducah, Kentucky (ORISE 2012). The receptors evaluated in ORISE 2012 were selected by the DOE-PPPO for the additional peak dose evaluations. These receptors included a Landfill Worker, Trespasser, Resident Farmer (onsite), Resident Gardener, Recreational User, Outdoor Worker and an Offsite Resident Farmer. The RESRAD (Version 6.5) and RESRAD-OFFSITE (Version 2.5) computer codes were used for the peak dose assessments. Deterministic peak dose assessments were performed for all the receptors and a probabilistic dose assessment was performed only for the Offsite Resident Farmer at the request of the DOE-PPPO. In a deterministic analysis, a single input value results in a single output value. In other words, a deterministic analysis uses single parameter values for every variable in the code. By contrast, a probabilistic approach assigns parameter ranges to certain variables, and the code randomly selects the values for each variable from the parameter range each time it calculates the dose (NRC 2006). The receptor scenarios, computer codes and parameter input files were previously used in ORISE 2012. A few modifications were made to the parameter input files as appropriate for this effort. Some of these changes included increasing the time horizon beyond 1,050 years (yr), and using the radionuclide concentrations provided by the DOE-PPPO as inputs into the codes. The deterministic peak doses were evaluated within time horizons of 70 yr (for the Landfill Worker and Trespasser), 1,050 yr, 10,000 yr and 100,000 yr (for the Resident Farmer [onsite], Resident Gardener, Recreational User, Outdoor Worker and Offsite Resident Farmer) at the request of the DOE-PPPO. The time horizons of 10,000 yr and 100,000 yr were used at the request of the DOE-PPPO for informational purposes only. The probabilistic peak of the mean dose assessment was performed for the Offsite Resident Farmer using Technetium-99 (Tc-99) and a time horizon of 1,050 yr. The results of the deterministic analyses indicate that among all receptors and time horizons evaluated, the highest projected dose, 2,700 mrem/yr, occurred for the Resident Farmer (onsite) at 12,773 yr. The exposure pathways contributing to the peak dose are ingestion of plants, external gamma, and ingestion of milk, meat and soil. However, this receptor is considered an implausible receptor. The only receptors considered plausible are the Landfill Worker, Recreational User, Outdoor Worker and the Offsite Resident Farmer. The maximum projected dose among the plausible receptors is 220 mrem/yr for the Outdoor Worker and it occurs at 19,045 yr. The exposure pathways contributing to the dose for this receptor are external gamma and soil ingestion. The results of the probabilistic peak of the mean dose analysis for the Offsite Resident Farmer indicate that the average (arithmetic mean) of the peak of the mean doses for this receptor is 0.98 mrem/yr and it occurs at 1,050 yr. This dose corresponds to Tc-99 within the time horizon of 1,050 yr.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2014

Application of the Combined Judgmental and Randomly Placed Sampling Method

In the wake of the 2001 anthrax incidents in the United States, there has been considerable discussion about the role of judgmental and probabilistic sampling strategies, particularly in the context of clearance sampling. The Combined Judgmental and Random (CJR) methodology provides a statistical methodology that allows practitioners to leverage information from both judgmental and randomly selected sample locations and then quantify the confidence in negative results. The objective of the CJR sampling design is to demonstrate, with high probability, that a high percentage of the decision area (or population) is acceptable, given that none of the samples are unacceptable. The purpose of this document is to assist practitioners to appropriately use the CJR methodology and to implement this sampling design in Visual Sample Plan (VSP). We begin by defining some fundamental terms. A decision area is the geographical or spatial area (indoor or outdoor) about which practitioners wish to draw a conclusion on the basis of sampling and other relevant information. Decision areas typically include all or part of a building, but they may be any contaminated (or potentially contaminated) area for which characterization or clearance is required. In this report, a statistical sampling approach refers to any sampling approach based on a mathematical or statistical model that provides confidence or probability statements about the decision area. Statistical sampling approaches typically involve taking samples at random locations, or at the nodes of a randomly located grid or lattice that is superimposed on the decision area. The term probabilistic sampling is often used to describe statistical sampling designs that exclusively use randomly located samples. This terminology implies that probabilistic statements can only be made based upon the results of randomly placed samples. However, the CJR method utilizes a Bayesian model that gives rise to a formal probabilistic statement regarding the acceptability of the decision area based upon the information obtained from both judgmental and random samples. Judgmental samples play a vital role in the characterization and clearance process because they include the informed prior belief and expert knowledge of personnel involved in the sampling process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Computational materials reliability assessment of hydrogen fueled gas turbine power generation engines

The use of blended fuel sources in land based gas turbine engines drives variations in the resulting operational profile (temperatures and pressures) which can impact engine reliability. Furthermore, variability in the manufacture of components affects the resulting microstructure which directly impacts material performance and reliability. Currently, data-driven models are typically used for maintaining and inspecting fleets of engines. Without explicitly capturing material and operational sources of variability conservatism must be used in developing component-level reliability models. Therefore, there exists an opportunity to use information from materials-scale physics models to better inform reliability modeling and reduce conservatism; the impact is more cost-efficient operation and maintenance of current and future fleets. Specifically, this work establishes a computational framework for evaluating the probabilistic high temperature creep performance of hot-section Ni-based superalloys where uncertainty comes from both microstructural and operational variability. A novel high-fidelity physics model which phenomenologically captures grain-boundary sensitive phenomena has been established. A probabilistic calibration procedure was used to calibrate the model and capture uncertainty in the parameterized model coefficients. A design of experiments methodology was established for identifying informative microstructural digital representations for suitable for forward model evaluation. Results show that training a machine-learning surrogate using this design criteria outperforms random selection of microstructural representations. Finally, two surrogate models were developed: (1) a deterministic surrogate model which predicts the local field response given microstructure, constitutive model parameters, and operating conditions (stress, temperature) and (2) a probabilistic model, where uncertainty comes from constitutive law uncertainty, built using denoising diffusion probabilistic models which samples responses given (1) microstructure and (2) operating conditions. These surrogate models enable partner Siemens Energy to rapidly perform UQ analysis specific to creep deformation across a range of microstructures and operating conditions. The impact is that these ML and physics codes can be used to establish more advanced reliability models for the inspection, servicing, and maintenance of land based gas turbine engines.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Wind Turbine Rotor Design Optimization Using Importance Sampling: Preprint

Probabilistic methods are commonly adopted to estimate both ultimate and fatigue loads in wind turbines, and multiple papers have presented a variety of approaches. In contrast, system-level, integrated design optimization methods for wind turbines have so far relied on deterministic methods to estimate loads and deflections. This work aims at addressing this gap by adopting importance sampling to estimate ultimate blade deflection for use within a rotor design optimization. A comparison between the results of this approach against traditional approaches using deterministic load evaluations show that the probabilistic approach is more conservative and that the solutions found with deterministic approaches violate the probabilistic constraint on tip deflection between 13% and 17%. This highlights the importance of accurate load and deflection estimates and demonstrates that probabilistic approaches can be successfully integrated within a wind turbine design process despite the higher computational costs.

17 WIND ENERGY↗
DOE OSTI2021

Sensitivity of a Subject-specific Ankle Sprain Simulation to Extrinsic Versus Intrinsic Biomechanical Factors

Ankle sprains are the most common musculoskeletal injury in sport and military activity, despite existing prophylactic strategies. The purpose of this report was to develop a probabilistic simulation of lateral ankle sprains during single-limb drop landing, towards accelerating innovation in ankle sprain prevention. A deterministic, subject-specific musculoskeletal model was extended with automation and probabilistic distributions on sprain-related biomechanical factors. Probabilistic simulations were generated using traditional Monte Carlo techniques and the advanced mean value method, a more computationally-efficient approach. Predicted distributions of peak ankle joint rotations, velocities, and moments borne by supporting passive structures agreed favorably with the deterministic model and with reports of real sprain biomechanics. Parameter sensitivities identified that predictions were most strongly influenced by drop height, subtalar joint posture at contact, invertor/evertor co-activation, and passive ankle stiffness. The advanced mean value method predicted confidence bounds comparable to a 1000-trial Monte Carlo simulation, and required only 14 model evaluations and 4-min processing time. The extended probabilistic simulation may be useful to virtually test new prophylactic strategies for ankle sprains, and is made available for open-source use (https://simtk.org/projects/sprain-sim).

60 APPLIED LIFE SCIENCES↗
NASA NTRS1990

The composite load spectra project

Probabilistic methods and generic load models capable of simulating the load spectra that are induced in space propulsion system components are being developed. Four engine component types (the transfer ducts, the turbine blades, the liquid oxygen posts and the turbopump oxidizer discharge duct) were selected as representative hardware examples. The composite load spectra that simulate the probabilistic loads for these components are typically used as the input loads for a probabilistic structural analysis. The knowledge-based system approach used for the composite load spectra project provides an ideal environment for incremental development. The intelligent database paradigm employed in developing the expert system provides a smooth coupling between the numerical processing and the symbolic (information) processing. Large volumes of engine load information and engineering data are stored in database format and managed by a database management system. Numerical procedures for probabilistic load simulation and database management functions are controlled by rule modules. Rules were hard-wired as decision trees into rule modules to perform process control tasks. There are modules to retrieve load information and models. There are modules to select loads and models to carry out quick load calculations or make an input file for full duty-cycle time dependent load simulation. The composite load spectra load expert system implemented today is capable of performing intelligent rocket engine load spectra simulation. Further development of the expert system will provide tutorial capability for users to learn from it.

Newell, J. F.↗
NASA NTRS1992

A new response surface approach for structural reliability analysis

This paper describes a new approach for computing structural reliability by post-processing previously computed probabilistic results for stress and strength. The objective is to provide an accurate method whereby independent probabilistic analyses for stress and strength functions can be performed independently and combined at a later time to compute probability of failure. The method provides a capability for testing different strength measures without the need for re-computing the probabilistic stress response. The proposed approach takes full account of the basic random variables effecting both stress and strength, and the failure region in the variable space identified during separate stress/strength probabilistic analyses. A simple closed-form example and a more complex analysis of a turbine blade subject to creep rupture is used to illustrate the method.

Thacker, B. H.↗
NASA NTRS1991

Structural reliability methods: Code development status

The Probabilistic Structures Analysis Method (PSAM) program integrates state of the art probabilistic algorithms with structural analysis methods in order to quantify the behavior of Space Shuttle Main Engine structures subject to uncertain loadings, boundary conditions, material parameters, and geometric conditions. An advanced, efficient probabilistic structural analysis software program, NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a deliverable. NESSUS contains a number of integrated software components to perform probabilistic analysis of complex structures. A nonlinear finite element module NESSUS/FEM is used to model the structure and obtain structural sensitivities. Some of the capabilities of NESSUS/FEM are shown. A Fast Probability Integration module NESSUS/FPI estimates the probability given the structural sensitivities. A driver module, PFEM, couples the FEM and FPI. NESSUS, version 5.0, addresses component reliability, resistance, and risk.

Millwater, Harry R.↗
NASA NTRS1991

Commercialization of NESSUS: Status

A plan was initiated in 1988 to commercialize the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) probabilistic structural analysis software. The goal of the on-going commercialization effort is to begin the transfer of Probabilistic Structural Analysis Method (PSAM) developed technology into industry and to develop additional funding resources in the general area of structural reliability. The commercialization effort is summarized. The SwRI NESSUS Software System is a general purpose probabilistic finite element computer program using state of the art methods for predicting stochastic structural response due to random loads, material properties, part geometry, and boundary conditions. NESSUS can be used to assess structural reliability, to compute probability of failure, to rank the input random variables by importance, and to provide a more cost effective design than traditional methods. The goal is to develop a general probabilistic structural analysis methodology to assist in the certification of critical components in the next generation Space Shuttle Main Engine.

Thacker, Ben H.↗