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DOE OSTI2021

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗

DOE OSTI2024

A Gaussian process based surrogate approach for the optimization of cylindrical targets

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular, surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this study, we apply surrogate modeling and optimization techniques that are well established in the existing literature to one-dimensional simulation data of a new cylindrical target design containing deuterium–tritium fuel. These models predict yields without the need for expensive simulations. We find that Bayesian optimization with Gaussian process surrogates enhances sampling efficiency in low-dimensional design spaces but becomes less efficient as dimensionality increases. Nonetheless, optimization routines within two-dimensional and five-dimensional design spaces can identify designs that maximize yield, while also aligning with established physical intuition. Optimization routines, which ignore constraints on hydrodynamic instability growth, are shown to lead to unstable designs in 2D, resulting in yield loss. However, routines that utilize 1D simulations and impose constraints on the in-flight aspect ratio converge on novel cylindrical target designs that are stable against hydrodynamic instability growth in 2D and achieve high yield.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Broadband Processing in a Noisy Shallow Ocean Environment: A Particle Filtering Approach

Here we report that when a broadband source propagates sound in a shallow ocean the received data can become quite complicated due to temperature-related sound-speed variations and therefore a highly dispersive environment. Noise and uncertainties disrupt this already chaotic environment even further because disturbances propagate through the same inherent acoustic channel. The broadband (signal) estimation/detection problem can be decomposed into a set of narrowband solutions that are processed separately and then combined to achieve more enhancement of signal levels than that available from a single frequency, thereby allowing more information to be extracted leading to a more reliable source detection. A Bayesian solution to the broadband modal function tracking, pressure-field enhancement, and source detection problem is developed that leads to nonparametric estimates of desired posterior distributions enabling the estimation of useful statistics and an improved processor/detector. In conclusion, to investigate the processor capabilities, we synthesize an ensemble of noisy, broadband, shallow-ocean measurements to evaluate its overall performance using an information theoretical metric for the preprocessor and the receiver operating characteristic curve for the detector.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Deconvolving distribution of relaxation times, resistances and inductance from electrochemical impedance spectroscopy via statistical model selection: Exploiting structural-sparsity regularization and data-driven parameter tuning

The distribution of relaxation times (DRT) has drawn increasing attention for interpreting electrochemical impedance spectroscopy (EIS). Deconvolution of DRT from EIS is a challenging ill-posed problem that requires regularization methods. In this work, we formulate DRT reconstruction task as a statistical model selection problem with structural-sparsity penalties. We utilize the Elastic net regularization that simultaneously benefits from Ridge and Lasso regularizations with optimal tuning parameter automatically determined by the information criteria. We benchmark our approach on four synthetic experiments (a ZARC element, ZARC mixtures, a RC circuit and a Fractal element) and two real EIS datasets of a Lithium ion battery and an organic-inorganic halide class of perovskites in oxygen environment at different gas pressures. We demonstrate the superiority of proposed model selection procedure, that is capable of eliminating pseudo peaks and representing asymmetries in DRT as well as precisely estimating resistances. Here, we highlight our approach is robust to reducing and subsampling EIS frequency range, making it a promising tool for timing-resolved, localized and large scale EIS data analysis. For the Lithium ion battery data analysis, we extend the classical DRT model to incorporate the inductive effect and illustrate DRT as a guidance for equivalent circuit modeling to refine impedance reconstruction at low risks of overfitting. Furthermore, the structural-sparsity regularization could be extended for multidimensional and Bayesian EIS data analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Implementing and evaluating a Gaussian mixture framework for identifying gene function from TnSeq data

The rapid acceleration of microbial genome sequencing increases opportunities to understand bacterial gene function. Unfortunately, only a small proportion of genes have been studied. Recently, TnSeq has been proposed as a cost-effective, highly reliable approach to predict gene functions as a response to changes in a cell’s fitness before-after genomic changes. However, major questions remain about how to best determine whether an observed quantitative change in fitness represents a meaningful change. To address the limitation, we develop a Gaussian mixture model framework for classifying gene function from TnSeq experiments. In order to implement the mixture model, we present the Expectation-Maximization algorithm and a hierarchical Bayesian model sampled using Stan’s Hamiltonian Monte-Carlo sampler. We compare these implementations against the frequentist method used in current TnSeq literature. From simulations and real data produced by E.coli TnSeq experiments, we show that the Bayesian implementation of the Gaussian mixture framework provides the most consistent classification results.

Li, Kevin↗

NASA NTRS2004

Discovering Planetary Nebula Geometries: Explorations with a Hierarchy of Models

Astronomical objects known as planetary nebulae (PNe) consist of a shell of gas expelled by an aging medium-sized star as it makes its transition from a red giant to a white dwarf. In many cases this gas shell can be approximately described as a prolate ellipsoid. Knowledge of the physics of ionization processes in this gaseous shell enables us to construct a model in three dimensions (3D) called the Ionization-Bounded Prolate Ellipsoidal Shell model (IBPES model). Using this model we can generate synthetic nebular images, which can be used in conjunction with Hubble Space Telescope (HST) images of actual PNe to perform Bayesian model estimation. Since the IBPES model is characterized by thirteen parameters, model estimation requires the search of a 13-dimensional parameter space. The 'curse of dimensionality,' compounded by a computationally intense forward problem, makes forward searches extremely time-consuming and frequently causes them to become trapped in local solutions. We find that both the speed and of the search can be improved by judiciously reducing the dimensionality of the search space. Our basic approach employs a hierarchy of models of increasing complexity that converges to the IBPES model. Earlier studies establish that a hierarchical sequence converges more quickly, and to a better solution, than a search relying only on the most complex model. Here we report results for a hierarchy of five models. The first three models treat the nebula as a 2D image, while the last two models explore its characteristics as a 3D object and enable us to characterize the physics of the nebula. This five-model hierarchy is applied to HST images of ellipsoidal PNe to estimate their geometric properties and gas density profiles.

Huyser, Karen A.↗

NASA NTRS2010

A Ground Flash Fraction Retrieval Algorithm for GLM

A Bayesian inversion method is introduced for retrieving the fraction of ground flashes in a set of N lightning observed by a satellite lightning imager (such as the Geostationary Lightning Mapper, GLM). An exponential model is applied as a physically reasonable constraint to describe the measured lightning optical parameter distributions. Population statistics (i.e., the mean and variance) are invoked to add additional constraints to the retrieval process. The Maximum A Posteriori (MAP) solution is employed. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The approach is feasible for N greater than 2000, and retrieval errors decrease as N is increased.

Koshak, William J.↗

DOE OSTI2026

A Bayesian desmearing algorithm for Bonse–Hart USANS with anisotropic scattering

Ultra-small-angle neutron scattering (USANS) using Bonse–Hart optics provides micrometer-scale structural insights but suffers from severe slit-geometry smearing. While well-established for isotropic systems, quantitative desmearing of anisotropic data remains a challenge because conventional corrections break down for non-radial scattering. In this work, we address this by developing a resolution-aware Bayesian framework that explicitly incorporates anisotropy via an affine deformation to the scattering pattern, guided by the principle of parsimony. This results in orientation-resolved point-spread functions that enable a self-consistent determination of both the resolution and deformation parameters. Using Gaussian process regression with uncertainty quantification and a probabilistic correction for multiple scattering, we demonstrate the framework’s effectiveness through numerical benchmarks and experimental studies of a stretched polymer melt. Our approach enables the seamless integration of SANS and USANS data, facilitating quantitative structural analysis of deformed materials at nanometer to micrometer scales.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Bayesian chain graph models to characterize microbe-environment dynamics

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is problematic given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence, thus agreeing with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via the Bayesian linear regression (LASSO). In addition, we propose an adaptive extension so that different shrinkages can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via an appropriate hierarchical structure. We test the performance of our model in a variety of simulated datasets, thereby showing superior performance to state-of-the-art approaches. We further apply our model to human gut and soil microbial compositional datasets, and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data.

compositional data↗

NASA NTRS2021

Upper Limits on the Isotropic Gravitational-Wave Background from Advanced LIGO and Advanced Virgo's Third Observing Run

We report results of a search for an isotropic gravitational-wave background (GWB) using data from Advanced LIGO's and Advanced Virgo's third observing run (O3) combined with upper limits from the earlier O1 and O2 runs. Unlike in previous observing runs in the advanced detector era, we include Virgo in the search for the GWB. The results of the search are consistent with uncorrelated noise, and therefore we place upper limits on the strength of the GWB. We find that the dimensionless energy density Ω(sub GW) ≤ 5.8 × 10(exp -9) at the 95% credible level for a at (frequency-independent) GWB, using a prior which is uniform in the log of the strength of the GWB, with 99% of the sensitivity coming from the band 20-76.6 Hz; Ω(sub GW)(f) ≤ 3.4 × 10(exp -9) at 25 Hz for a power-law GWB with a spectral index of 2/3 (consistent with expectations for compact binary coalescences), in the band 20-90.6 Hz; and Ω(sub GW)(f) ≤ 3.9 × 10(exp -10) at 25 Hz for a spectral index of 3, in the band 20-291.6 Hz. These upper limits improve over our previous results by a factor of 6.0 for a at GWB, 8.8 for a spectral index of 2/3, and 13.1 for a spectral index of 3. We also search for a GWB arising from scalar and vector modes, which are predicted by alternative theories of gravity; we do not find evidence of these, and place upper limits on the strength of GWBs with these polarizations. We demonstrate that there is no evidence of correlated noise of magnetic origin by performing a Bayesian analysis that allows for the presence of both a GWB and an effective magnetic background arising from geophysical Schumann resonances. We compare our upper limits to a fiducial model for the GWB from the merger of compact binaries, updating the model to use the most recent data-driven population inference from the systems detected during O3a. Finally, we combine our results with observations of individual mergers and show that, at design sensitivity, this joint approach may yield stronger constraints on the merger rate of binary black holes at z ≳ 2 than can be achieved with individually resolved mergers alone.

Ryan Abbott↗

DOE OSTI2019

Acoustic emission Bayesian source location: Onset time challenge

Robust identification of the most accurate observed input data among a pool of observations is key in modeling and decision making. A statistically biased observed measurement deteriorates the predictive power of a model and affects decision-making ability based on the prediction of the model. When two competing methods of measurement are available, such as methods which identify arrival times in acoustic emission (AE) signals, a principal question is whether one of the two obtained datasets, or a combination of the two, should be used later on, for example, to localize an AE source. This question becomes more important when collecting not repeatable data such as AE signals created by a propagating crack. Here this paper considers an inverse source location problem in a concrete block to address the mentioned issue, a proposed methodology which also has wider application in competitive data selection. Elastic energy released by an AE event, such as a propagating crack, is recorded by acoustic emission data acquisition system. The onset time of AE signals is often used to locate the source of the event, and its accuracy directly affects the precision of source identification. This research proposes an innovative approach to select the most probable onset time obtained from two automatic picker methods. The proposed method selects the most probable onset times, which are observed by each picker for each sensor, in a probabilistic fashion. To validate the proposed method, the most accurate onset time observed by each picker is identified by visual inspection and is compared with the one is selected by the proposed method. Finally, the dataset is used for source location identification. Results show that picked onset times determined by the proposed method generate more accurate source identification when compared with coordinates obtained using each dataset individually.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Machine learning based approach to predict ductile damage model parameters for polycrystalline metals

Damage models for ductile materials typically need to be parameterized, often with the appropriate parameters changing for a given material depending on the loading conditions. This can make parameterizing these models computationally expensive, since an inverse problem must be solved for each loading condition. Using standard inverse modeling techniques typically requires hundreds or thousands of high-fidelity computer simulations to estimate the optimal parameters. Additionally, the time of a human expert is required to set up the inverse model. Machine learning has recently emerged as an alternative approach to inverse modeling in these settings, where the machine learning model is trained in an offline manner and new parameters can be quickly generated on the fly, after training is complete. Here, this work utilizes such a workflow to enable the rapid parameterization of a ductile damage model called TEPLA with a machine learning inverse model. The machine learning model can efficiently estimate the model parameters much faster, as compared to previously employed methods, such as Bayesian calibration. The results demonstrate good accuracy on a synthetic test dataset and is validated against experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2013

AUTOMATIC CLASSIFICATION OF VARIABLE STARS IN CATALOGS WITH MISSING DATA

We present an automatic classification method for astronomical catalogs with missing data. We use Bayesian networks and a probabilistic graphical model that allows us to perform inference to predict missing values given observed data and dependency relationships between variables. To learn a Bayesian network from incomplete data, we use an iterative algorithm that utilizes sampling methods and expectation maximization to estimate the distributions and probabilistic dependencies of variables from data with missing values. To test our model, we use three catalogs with missing data (SAGE, Two Micron All Sky Survey, and UBVI) and one complete catalog (MACHO). We examine how classification accuracy changes when information from missing data catalogs is included, how our method compares to traditional missing data approaches, and at what computational cost. Integrating these catalogs with missing data, we find that classification of variable objects improves by a few percent and by 15% for quasar detection while keeping the computational cost the same.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Joint Planck and WMAP assessment of low CMB multipoles

The remarkable progress in cosmic microwave background (CMB) studies over past decade has led to the era of precision cosmology in striking agreement with the ΛCDM model. However, the lack of power in the CMB temperature anisotropies at large angular scales (low-ℓ), as has been confirmed by the recent Planck data also (up to 0ℓ=4), although statistically not very strong (less than 3σ), is still an open problem. One can avoid to seek an explanation for this problem by attributing the lack of power to cosmic variance or can look for explanations i.e., different inflationary potentials or initial conditions for inflation to begin with, non-trivial topology, ISW effect etc. Features in the primordial power spectrum (PPS) motivated by the early universe physics has been the most common solution to address this problem. In the present work we also follow this approach and consider a set of PPS which have features and constrain the parameters of those using WMAP 9 year and Planck data employing Markov-Chain Monte Carlo (MCMC) analysis. The prominent feature of all the models of PPS that we consider is an infra-red cut off which leads to suppression of power at large angular scales. We consider models of PPS with maximum three extra parameters and use Akaike information criterion (AIC) and Bayesian information criterion (BIC) of model selection to compare the models. For most models, we find good constraints for the cut off scale k{sub c}, however, for other parameters our constraints are not that good. We find that sharp cut off model gives best likelihood value for the WMAP 9 year data, but is as good as power law model according to AIC. For the joint WMAP 9 + Planck data set, Starobinsky model is slightly preferred by AIC which is also able to produce CMB power suppression up to 0ℓ≤3 to some extent. However, using BIC criteria, one finds model(s) with least number of parameters (power law model) are always preferred.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Development of Bayesian analysis program for extraction of polarisation observables at CLAS

At the mass scale of a proton, the strong force is not well understood. Various quark models exist, but it is important to determine which quark model(s) are most accurate. Experimentally, finding resonances predicted by some models and not others would give valuable insight into this fundamental interaction. Several labs around the world use photoproduction experiments to find these missing resonances. The aim of this work is to develop a robust Bayesian data analysis program for extracting polarisation observables from pseudoscalar meson photoproduction experiments using CLAS at Jefferson Lab. This method, known as nested sampling, has been compared to traditional methods and has incorporated data parallelisation and GPU programming. It involves an event-by-event likelihood function, which has no associated loss of information from histogram binning, and results can be easily constrained to the physical region. One of the most important advantages of the nested sampling approach is that data from different experiments can be combined and analysed simultaneously. Results on both simulated and previously analysed experimental data for the K{sup +}Λ channel will be discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Maximum-a-Posteriori Cosmic Ray Muon Trajectory Estimation with Energy Loss for Muon Tomography Applications

Recent cosmic ray muon tomography applications use detectors that measure position and direction of the individual muons before and after traversing the imaged object. However, muon reconstruction techniques are limited in resolution due to low muon flux and the effects of a single Coulomb scattering assumption. In the present work, the use of a Bayesian framework and a Gaussian approximation of multiple Coulomb scattering (MCS) is explored for maximum-a-posteriori estimation of the most likely path of a cosmic ray muon traversing a uniform and non uniform medium and undergoing MCS. Results were generated using a validated Geant4 workspace. The algorithm is expected to be able to predict muon tracks with improved accuracy and to increase the useful muon flux by 30% over a traditional point-of-closest-approach (PoCA) method. The effect of energy loss due to ionization is investigated, and an energy loss relation is derived and validated.

Chatzidakis, Stylianos↗

DOE OSTI2019

Support for Reactor Operators in Case of Cyber-Security Threats (NEUP Final Report)

Increasing use of digital technology in nuclear power plants (NPPs) poses cyber-security as a crucial threat to public safety and to continuous energy production. Cyber-security risks are comprised of complex known and unknown interactions between various entities, system vulnerabilities, network protocols, human users and malicious attacks. There is little understanding or research geared towards plant operators’ response under cyber-security threats and operational procedures to cope with such threats. This is particularly critical when a cyber-security event masquerades as a safety incident or an evolving accident. Instead of leading operators to the remediation of the accident, the masked cyber event may lead them to circumvent the safety mechanisms of the plant. Given these challenges, the objective of this project is to develop a tool to characterize abnormal NPP events as “cyber” or “safety” incidents, and to further develop this tool as a real-time operator aid to assist in response to the incident. This NEUP Final Report summarizes the research efforts towards the above goals and the results in the following three aspects. First, a methodology for classifying abnormal NPP events as cyber-attacks or safety incidents was developed. This provides the basis for responding to potential cyber-attacks. In this methodology, the causal relationships between various variables (i.e., physical variables, network variables, and control variables) for a nuclear system under consideration are modeled using dynamic Bayesian networks. Based on observations of certain variables (i.e., the evidence), inference is performed to identify the state of hidden variables, which helps indicate the occurrence of cyber-attacks or safety incidents. The proposed methodology was applied to the full scope NPP simulator system at The Ohio State University as a case study. The result shows that the proposed methodology is capable of distinguishing between cyber-attacks and safety incidents. Second, a game-theoretic approach for responding to cyber-attacks on nuclear power plants was developed. This is the second major goal of the project, and the method is used to recommend optimal responses to reactor operators in the case of cyber-attacks. We consider two cases in this research. In the first case, the interaction between the defender (i.e., the reactor operator) and the attacker is modeled as a two-player, nonzero-sum, Markov game with an infinite time horizon. In the second case, we consider a semi-Markov game between the defender and the attacker within a finite time horizon. The model in the second case enables us to consider the time sensitive response of the defender. In each case, the method for deriving the Nash equilibrium is developed. The Nash Equilibrium of the game provides the valid prediction of both players’ actions because no single player can benefit from unilaterally deviating from the equilibrium policy if the other player adheres to his/hers, hence it provides the best response of the defender to cyber-attacks. The proposed method in each case is demonstrated through a simplified benchmark digital feedwater control system. Third, a prototype display is developed to integrate the above information. The prototype display depicts the communication information to the operator and incorporates the cyber-security tool developed by the team into the interface. It consists of the regular display in current control rooms, as well as a panel used to indicate the occurrence of cyber-attacks or safety events and a panel used to guide the operator’s response to detected cyber-attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗