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Results for “Approximate Bayesian computation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Systematic study of the validity of the eikonal model including uncertainties

Nuclear reactions at intermediate beam energies are often interpreted using the eikonal model. In the analysis of complex reaction probes, where few-body reaction methods are needed, the eikonal method may be used as an efficient way for describing the fragment-target reaction process. In this work, we perform a systematic study to test the validity of the eikonal approximation for nucleon-nucleus reactions. We also quantify uncertainties due to the nucleon optical potential on reaction observables. We inspect the validity of the eikonal model and its semiclassical correction by comparing it to exact solutions (obtained from solving the optical-model equation with a finite-differences method) for a wide range of reactions. We also study the effect of relativistic corrections, both kinematic and dynamic, by effectively incorporating the relativistic effects at intermediate energies. The uncertainties from a Bayesian global optical potential (KDUQ) are propagated to the observables of interest. Our study includes neutron and proton reactions on 27 Al , 40 Ca , 90 Zr , and 208 Pb , for a wide range of energies 𝐸 lab = 0–400 MeV. We calculate neutron-total cross sections (elastic and reactions) as well as proton-absorption cross sections as a function of beam energy, using the eikonal model, the eikonal model with a semiclassical correction, and the exact solution. Here, we also compute angular distributions for the methods above. Our results show that for the proton-absorption cross section, the eikonal model can be used down to around 60 MeV and the semiclassical correction extends its use to 30 MeV. However, the validity of the eikonal model for the neutron-total cross section only goes down to ≈120 MeV, a range extended to ≈ 50 MeV when using the semiclassical correction. We find the semiclassical correction to the eikonal model to be less effective in describing the angular distributions. The 1⁢𝜎 uncertainty intervals on the observables we studied is less than 5% for most of the energies considered, but increases rapidly for higher energies, namely energies outside the range of KDUQ (𝐸 lab > 200MeV).

Cluster models↗
DOE OSTI2021

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A comparison of Gaussian processes and neural networks for computer model emulation and calibration

The Department of Energy relies on complex physics simulations for prediction in domains like cosmology, nuclear theory, and materials science. These simulations are often extremely computationally intensive, with some requiring days or weeks for a single simulation. In order to assure their accuracy, these models are calibrated against observational data in order to estimate inputs and systematic biases. Because of their great computational complexity, this process typically requires the construction of an emulator, a fast approximation to the simulation. In this paper, two emulator approaches are compared: Gaussian process regression and neural networks. Their emulation accuracy and calibration performance on three real problems of Department of Energy interest is considered. On these problems, the Gaussian process emulator tends to be more accurate with narrower, but still well-calibrated uncertainty estimates. The neural network emulator is accurate, but tends to have large uncertainty on its predictions. Finally, as a result, calibration with the Gaussian process emulator produces more constrained posteriors that still perform well in prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Bayesian analysis of the flutter margin method in aeroelasticity

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2022

A Framework for Deep Learning Emulation of Numerical Models With a Case Study in Satellite Remote Sensing

Numerical models based on physics represent the state of the art in Earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest generation computers, reducing the ability of modelers to generate simulations for understanding parameter sensitivities and characterizing variability and uncertainty. Thus, surrogate models are often developed to capture the essential attributes of the full-blown numerical models. Recent successes of machine learning methods, especially deep learning (DL), across many disciplines offer the possibility that complex nonlinear connectionist representations may be able to capture the underlying complex structures and nonlinear processes in Earth systems. A difficult test for DL-based emulation, which refers to function approximation of numerical models, is to understand whether they can be comparable to traditional forms of surrogate models in terms of computational efficiency while simultaneously reproducing model results in a credible manner. A DL emulation that passes this test may be expected to perform even better than simple models with respect to capturing complex processes and spatiotemporal dependencies. Here, we examine, with a case study in satellite-based remote sensing, the hypothesis that DL approaches can credibly represent the simulations from a surrogate model with comparable computational efficiency. Our results are encouraging in that the DL emulation reproduces the results with acceptable accuracy and often even faster performance. We discuss the broader implications of our results in light of the pace of improvements in high-performance implementations of DL and the growing desire for higher resolution simulations in the Earth sciences.

Bayesian Deep Learning↗
DOE OSTI2023

Adaptive learning-driven high-throughput synthesis of oxygen reduction reaction Fe–N–C electrocatalysts

Reducing human reliance on inefficient energy systems and fossil fuels has become more urgent due to the consequences of global climate change. However, traditional trial-and-error approaches have hampered our ability to accelerate the discovery and implementation of functional materials for efficient energy conversion devices, such as polymer electrolyte fuel cells (PEFCs). To address this, we develop an adaptive learning framework that integrates machine learning and state-of-the-art capabilities in high-throughput synthesis to achieve expedited optimization of iron-nitrogen-carbon PEFC oxygen reduction reaction (ORR) electrocatalysts. We use statistical inference, uncertainty quantification, and global optimization to build a computational design-of-experiment tool that identifies the optimum compositions to be investigated next to reduce the demands placed on experimental materials discovery. We benchmark the ability of the proposed strategy to discover optimum catalyst synthesis conditions in a six-dimensional search space when starting with a thirty-six-sample database. By following the adaptive learning strategy, we synthesize fourteen new catalysts from approximately ten billion unique compositions and discover four catalysts that outperform all original samples. The best machine learning-optimized catalyst is 33% more active than the highest-performing one in the initial database, showing an ORR activity seven times larger than those typically reported for the same class of materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Cosmic Inference: Constraining Parameters with Observations and a Highly Limited Number of Simulations

We look at cosmological probes that pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters that characterize the underlying physical system-our universe, from these observations and theoretical forward-modeling. The only way to accurately forward-model physical behavior on small scales is via expensive numerical simulations, which are further “emulated” due to their high cost. Emulators are commonly built with a set of simulations covering the parameter space with Latin hypercube sampling and an interpolation procedure; the aim is to establish an approximately constant prediction error across the hypercube. In this paper, we provide a description of a novel statistical framework for obtaining accurate parameter constraints. The proposed framework uses multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods with the goal of maintaining a low emulation error in the region of the hypercube preferred by the observational data. In this paper, we compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using a Lyα forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer-by a factor of a few in the Lyα P(k) case considered here-simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Scalable and efficient learning from crowds with Gaussian processes

Over the last few years, multiply-annotated data has become a very popular source of information. Online platforms such as Amazon Mechanical Turk have revolutionized the labelling process needed for any classification task, sharing the effort between a number of annotators (instead of the classical single expert). This crowdsourcing approach has introduced new challenging problems, such as handling disagreements on the annotated samples or combining the unknown expertise of the annotators. Probabilistic methods, such as Gaussian Processes (GP), have proven successful to model this new crowdsourcing scenario. However, GPs do not scale up well with the training set size, which makes them prohibitive for medium-to-large datasets (beyond 10K training instances). This constitutes a serious limitation for current real-world applications. In this work, we introduce two scalable and efficient GP-based crowdsourcing methods that allow for processing previously-prohibitive datasets. The first one is an efficient and fast approximation to GP with squared exponential (SE) kernel. The second allows for learning a more flexible kernel at the expense of a heavier training (but still scalable to large datasets). Since the latter is not a GP-SE approximation, it can be also considered as a whole new scalable and efficient crowdsourcing method, useful for any dataset size. Both methods use Fourier features and variational inference, can predict the class of new samples, and estimate the expertise of the involved annotators. A complete experimentation compares them with state-of-the-art probabilistic approaches in synthetic and real crowdsourcing datasets of different sizes. Finally, they stand out as the best performing approach for large scale problems. Moreover, the second method is competitive with the current state-of-the-art for small datasets.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

Coexistent Quantum Channel Characterization Using Spectrally Resolved Bayesian Quantum Process Tomography

The coexistence of quantum and classical signals over the same optical fiber with minimal degradation of the transmitted quantum information is critical for operating large-scale quantum networks over the existing communications infrastructure. In this work, we systematically characterize the quantum channel that results from simultaneously distributing approximate single-photon polarization-encoded qubits and classical light of varying intensities through fiber-optic channels of up to 15 km. Using spectrally resolved quantum process tomography with a Bayesian reconstruction method that we develop, we estimate the full quantum channel from experimental photon counting data, both with and without classical background. Furthermore, although we find the exact channel description to be a weak function of the pump polarization, we nevertheless show that the coexistent fiber-based quantum channel has high process fidelity with an ideal depolarizing channel when the noise is dominated by Raman scattering. These results provide a basis for the future development of quantum repeater designs and quantum error-correcting codes for real-world channels and inform models used in the analysis and simulation of quantum networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A generalized muon trajectory estimation algorithm with energy loss for application to muon tomography

Here, this work presents a generalized muon trajectory estimation (GMTE) algorithm to estimate the path of a muon in either uniform or nonuniform media. The use of cosmic ray muons in nuclear nonproliferation and safeguards verification applications has recently gained attention due to the non-intrusive and passive nature of the inspection, penetrating capabilities, as well as recent advances in detectors that measure position and direction of the individual muons before and after traversing the imaged object. However, muon image reconstruction techniques are limited in resolution due to low muon flux and the effects of multiple Coulomb scattering (MCS). Current reconstruction algorithms, e.g., point of closest approach (PoCA) or straight-line path (SLP), rely on overly simple assumptions for muon path estimation through the imaged object. For robust muon tomography, efficient and flexible physics-based algorithms are needed to model the MCS process and accurately estimate the most probable trajectory of a muon as it traverses an object. In the present work, the use of a Bayesian framework and a Gaussian approximation of MCS are explored for estimation of the most likely path of a cosmic ray muon traversing uniform or nonuniform media and undergoing MCS. The algorithm’s precision is compared to Monte Carlo simulated muon trajectories. It was found that the algorithm is expected to be able to predict muon tracks to less than 1.5 mm RMS for 0.5 GeV muons and 0.25 mm RMS for 3 GeV muons, a 50% improvement compared to SLP and 15% improvement when compared to PoCA. Further, a 30% increase in useful muon flux was observed relative to PoCA. Muon track prediction improved for higher muon energies or smaller penetration depth where energy loss is not significant. Finally, the effect of energy loss due to ionization is investigated, and a linear energy loss relation that is easy to use is proposed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Integration of Condition-Based, Diagnostic, Prognostic, And Anomaly Detection Data into Reliability Models to Support a Predictive Maintenance Context

Reliability data employed in plant reliability models are an approximated integral representation of the past industrywide operational experience, and they neglect the present asset health status (available, for example, from online monitoring data and diagnostic assessments) and forecasted health projection (when available from prognostic models). Ideally, in a predictive maintenance context, system reliability models should support decision making by propagating actual health information from the asset to the system level in order to provide a quantitative snapshot of system health and identify the most critical assets. Asset health should be informed solely by that specific asset’s current and historical performance data and should not be an approximated integral representation of the past industrywide operational experience (as currently performed by system reliability models through Bayesian updating processes). This paper proposes a reliability modeling approach that relies on asset diagnostic and prognostic assessments, along with monitoring data to measure asset health. We show how state-of-the art condition-based, diagnostic, prognostic, and anomaly detection models can be linked to system reliability models not in probability terms, but in terms of margin where margin is defined as the “distance” between the present status and an undesired event (e.g., failure or unacceptable performance). Then, we show how the propagation of margin data from the asset to the system level is performed through classical reliability models such as fault trees or reliability block diagrams. The described method is in fact able to propagate heterogenous health data from the asset to the system level in order to analytically assess system health.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian projection pursuit regression

In projection pursuit regression (PPR), a univariate response variable is approximated by the sum of $M$ “ridge functions,” which are flexible functions of one-dimensional projections of a multivariate input variable. Traditionally, optimization routines are used to choose the projection directions and ridge functions via a sequential algorithm, and $M$ is typically chosen via cross-validation. Here, we introduce a novel Bayesian version of PPR, which has the benefit of accurate uncertainty quantification. To infer appropriate projection directions and ridge functions, we apply novel adaptations of methods used for the single ridge function case ($M$=1), called the Bayesian Single Index Model; and use a Reversible Jump Markov chain Monte Carlo algorithm to infer the number of ridge functions $M$. We evaluate the predictive ability of our model in 20 simulated scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Finally, we generalize this methodology and demonstrate the ability to accurately model multivariate response variables. Its effective performance indicates that Bayesian Projection Pursuit Regression is a valuable addition to the existing regression toolbox.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Performance evaluation of cosmic ray muon trajectory estimation algorithms

Muons, being elementary particles with minimal interaction with nuclear materials and abundant at sea level, have sparked interest in utilizing them for imaging various applications, such as mining [Borselli et al., Sci. Rep. 12, 22329 (2022)], volcano imaging [Nagamine et al., Nucl. Instrum. Meth. A, 356, 585(1995)], and underground tunnel detection [Guardincerri et al., Pure Appl. Geophys. 174, 2133 (2017)]. Recently, their use in nuclear nonproliferation and safeguard verification has gained attention, particularly in cargo screening for nuclear waste smuggling [Baesso et al., J. Instrum. 9, C10041 (2014)], source localization [L. J. Schultz et al., Nucl. Instrum. Meth. A 519, 687 (2004)], and locating nuclear fuel debris in reactors [Borozdin et al., Phys. Rev. Let. 109, 152501 (2012)]. However, the resolution of muon image reconstruction techniques is limited due to multiple Coulomb scattering (MCS) within the target object. To achieve robust muon tomography, it is crucial to develop efficient and flexible physics-based algorithms that can model the MCS process accurately and estimate the most probable trajectory of muons as they pass through the target object. To address this limitation, in this study, a novel algorithmic approach utilizing the Bayesian probability theory and Gaussian approximation of MCS is chosen. Different energy levels, materials, and target sizes were considered in the evaluations. The results demonstrate that the Generalized Muon Trajectory Estimation (GMTE) algorithm offers significant improvements over currently used algorithms. Across all test scenarios, the GMTE algorithm demonstrated ~50% and 38% increase in precision compared to Straight Line Path (SLP) and Point of Closest Approach (PoCA) algorithms, respectively. Furthermore, it exhibited 10%–35% and 10%–15% increases in muon flux utilization for high and medium Z materials, respectively, compared to the PoCA algorithm. In conclusion, the extensive simulations confirm the enhanced performance and efficiency of the GMTE algorithm, offering improved resolution and reduced measurement time for cosmic ray muon imaging compared to the current SLP and PoCA algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Mechanistic within-host mathematical model of inhalational anthrax

We present a mathematical model of the dynamics of Bacillus anthracis bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using in vivo data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time t, assuming that the number of inhaled spores has a Poisson distribution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Shock Hugoniot calculations using on-the-fly machine learned force fields with ab initio accuracy

We present a framework for computing the shock Hugoniot using on-the-fly machine learned force field (MLFF) molecular dynamics simulations. In particular, we employ an MLFF model based on the kernel method and Bayesian linear regression to compute the free energy, atomic forces, and pressure, in conjunction with a linear regression model between the internal and free energies to compute the internal energy, with all training data generated from Kohn–Sham density functional theory (DFT). We verify the accuracy of the formalism by comparing the Hugoniot for carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that Kohn–Sham calculations for the Hugoniot can be accelerated by up to two orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9 single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We find good agreement with first principles results in the literature while providing tighter error bars. In addition, we confirm that the inter-element interaction in compounds decreases with temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗