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A Massively Parallel Bayesian Approach to Planetary Protection Trajectory Analysis and Design

The NASA Planetary Protection Office has levied a requirement that the upper stage of future planetary launches have a less than 10(exp -4) chance of impacting Mars within 50 years after launch. A brute-force approach requires a decade of computer time to demonstrate compliance. By using a Bayesian approach and taking advantage of the demonstrated reliability of the upper stage, the required number of fifty-year propagations can be massively reduced. By spreading the remaining embarrassingly parallel Monte Carlo simulations across multiple computers, compliance can be demonstrated in a reasonable time frame. The method used is described here.

parallel computing↗

Effective Field Theory Analysis and Active Neutron Veto Design for the Cryogenic Dark Matter Search

Astrophysical measurements and cosmological predictions suggest the exists of a large amount of matter in the universe that does not interact via electromagnetic forces. This non-luminescent matter, known dark matter, exists in halos that encompass and are within galaxies, including the Milky Way. Therefore, dark matter particles should should be directly detectable by experiments on Earth, such as the Super Cryogenic Dark Matter Search (SuperCDMS). Dark matter is assumed to be low mass (< 100 GeV/c2) and interact via the weak force using either a spin-independent or spin-dependent coupling. However, making incorrect assumptions about dark matter interactions can lead to misleading results. Because interactions with dark matter particles are rare, direct detection experiments must be able to shield for or reject backgrounds to very low levels. Low energy neutron backgrounds that make it to the detectors are especially dangerous, because they cannot be easily distinguished from the expected dark matter signal. Scintillator doped with a high neutron-capture cross-section material can be used to detect neutrons via their resulting gamma rays. Examples of such detectors using liquid scintillator have been successfully used in past high-energy physics (HEP) experiments. However, a liquid scintillator can leak and is not as amenable to modular or complex shapes as a solid scintillator. The light outputs and efficiencies of gadolinium-loaded polystyrene-based scintillators have been explored using a wide variety of gadolinium compounds with varying concentrations. Collection strategies using a wavelength shift- ing (WLS) fiber and silicon photomultipliers (SiPMs) were also evaluated as a possible neutron veto for an upgrade to SuperCDMS SNOLAB. The scattering of dark matter particles off nuclei in direct detection experiments can be described in terms of a multidimensional effective field theory (EFT). A new systematic analysis technique is developed using the EFT approach and Bayesian inference methods to exploit, when possible, the energy-dependent information of the detected events, experimental efficiencies, and backgrounds. Highly dimensional likelihoods are calculated over the mass of the weakly interacting massive particle (WIMP) and multiple EFT coupling coefficients, which can then be used to set limits on these parameters and choose models (EFT operators) that best fit the direct detection data. Expanding the parameter space beyond the standard spin-independent isoscalar cross section and WIMP mass reduces tensions between previously published experiments. Combining these experiments to form a single joint likelihood leads to stronger limits than when each experiment is considered on its own. Simulations using two nonstandard operators (O3 and O8) are used to test the proposed analysis technique in up to five dimensions and demonstrate the importance of using multiple likelihood projections when determining constraints on WIMP mass and EFT coupling coefficients. In particular, this shows that an explicit momentum dependence in dark matter scattering can be identified. CDMSlite Run 2 was a search for Weakly Interacting Massive Particles (WIMPs) with a cryogenic 600 g Germanium detector operated deep underground. It was operated in a mode optimizing sensitivity to WIMPs of relatively low mass, 2 - 20 GeV, while sacrificing background rejection. An EFT analysis of CDMSlite Run 2 data from SuperCDMS Soudan is presented here. A binned likelihood Bayesian analysis was performed on the data, optimizing over the parameters of EFT interactions and the recoil energy spectra due to the dominant Compton scattering and tritium backgrounds. Recoil energy regions within 5σ of known activation peaks were removed from the analysis. The Bayesian evidences of the resulting likelihoods show that CDMSlite Run 2 data is entirely consistent with the background models with no EFT interaction necessary. Upper limits on the WIMP mass and coupling coefficients amplitudes and phases are presented for each EFT operator.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Traffic safety analysis and model updating for freeways using Bayesian method

Freeway crash prediction models are the basic of traffic safety research, yet crash occurrence and the influencing factors change over time. In order to make sure the implemented safety models fit the current traffic environment, this study conducts a comparative analysis of 2017 and 2020 datasets collected from freeways in Suzhou, China. Herein, considering the spatial correlation among analysis units and the hierarchical data structure, a Bayesian conditional autoregressive negative binomial (CAR-NB) model and a Bayesian hierarchical CAR-NB (HCAR-NB) model were used to explore the safety influencing factors, and a traditional NB model was developed for further comparison. To update the HCAR-NB model from 2017 to 2020, Bayesian inference with informative priors was used to improve its goodness of fit and efficiency. Preliminary results showed that 1) the HCAR-NB model outperformed the NB model and CAR-NB model in prediction accuracy, and 2) the number of crashes was significantly correlated with average speed, speed variance, road segment length, number of lanes, and presence of ramps. The potential for safety improvement (PSI) method was applied to the modeling results to identify hotspots for the two years. The results confirmed that the hotspots spatiotemporally shifted among the freeways. The proposed crash prediction model and updating method are expected to assist implementation of informed countermeasures for freeway safety improvement.

97 MATHEMATICS AND COMPUTING↗

EFIT‐AI: Machine Learning and Artificial Intelligence Assisted Equilibrium Reconstruction for Tokamak Experiments and Burning Plasmas (Final Report)

The EFIT-AI project is creating a modern advanced equilibrium reconstruction code suitable for tokamak experiments of burning plasmas. EFIT [1,2] was the first and is the most extensively used equilibrium reconstruction code in the world. This project builds on the production-level experience and adds key elements as follows. 1. A Model Order Reduction (MOR) version of the two-dimensional (2D) Grad-Shafranov equation solver (EFIT-MORNN) using physics-informed neural networks. 2. Improved optimization and data analysis capabilities using a Bayesian framework enhanced with machine learning. 3. A MOR version of the three-dimensional (3D) perturbed equilibrium reconstruction tool.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Explainable Bayesian Neural Network for Probabilistic Transient Stability Analysis Considering Wind Energy

While several data-driven models have been developed for transient stability assessment, how to consider the uncertainties from load and renewable generations and provide interpretation of data-driven assessment results are still open. This paper proposes an explainable Bayesian Neural Network (BNN) for probabilistic transient stability assessment (TSA). By extracting the uncertainties from loads and wind farms, the BNN model can make a reliable prediction and quantify the prediction uncertainties. We also develop the Gradient Shap algorithm to make the global and local explanations for the probabilistic TSA model, a significant advantage over existing black-box data-driven methods. Numerical results on the modified IEEE 39-bus system show that the proposed method outperforms the existing methods in terms of prediction accuracy and uncertainty quantification capabilities. The explainability of the proposed method allows system operators to design preventive controls for enhancing system stability.

Bayesian Neural Network↗

A Bayesian and HRA-Aided Method for the Novel Reliability Analysis of Software

Technological advancements and nuclear power plant modernization has inspired considerable research in the areas of safety and reliability, yet there remains a lack of consensus for the reliability assessment of digital instrumentation and control (I&C) systems. Motivated by the lack of consensus for reliability analysis methods, this work employs a novel framework that incorporates Bayesian, human reliability, and common-cause failure (CCF) modeling techniques. The novel framework allows the use of state-of-the-art or classical modeling techniques when accounting for human and CCF effects on system reliability. The Bayesian and HRA-Aided Method for the Reliability Analysis of Software (BAHAMAS) is demonstrated by a case study for the quantification of software hazards found in a previous analysis of a digital reactor trip system. The results demonstrate the ability of BAHAMAS to account for human activities during the software development life cycle and their influence on software reliability. BAHAMAS is a flexible tool for extending the coverage of conventional probabilistic risk assessments to include modernized digital I&C systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Searches for New Physics With Muon Conversion at Fermilab and Triboson Production at the LHC

We report on several efforts to search for physics beyond the standard model of particle physics at broad energy scales. The Mu2e experiment at Fermilab will search for charged lepton flavor violation via the muon to electron conversion process, which is suppressed in the Standard Model. Mu2e will be operated at a low energy, yet can probe New Physics at very high mass scales (O(1e3 - 1e4 ) TeV). At high energies, the CMS experiment at the CERN LHC continues to deliver an impressive suite of Standard Model measurements and limits on a variety of New Physics signatures. Mu2e is under construction and slated to collect its first physics data in the coming years. This thesis describes work done during the construction phase of Mu2e and focuses on two critical areas: magnetic field modeling and statistical analysis. We describe a novel method for field modeling which we validate using a simulated dataset representing the expected magnetic field in the Detector Solenoid. This method blends a standard least-squares fitting technique that utilizes physically motivated analytical model functions with a novel physics informed network that is constructed to obey Maxwell’s equations. We show the technique can model the field with an accuracy of 10−7 despite the presence of injected noise in the pseudo-measurements at the 10−5 level. We then present preliminary results of the calibration of 3D Hall probes at the sub-10−4 level. These probes will be used to directly measure the Mu2e Detector Solenoid magnetic field on a sparse grid; these measurements serve as the input to the field model fitting. Finally, we describe the first implementation of both an unbinned shape analysis and a Bayesian interpretation applied to Mu2e pseudo-data. Up to 20% tighter limits can be set by the shape analysis compared to a standard cut & count analysis. The AlCap experiment collected data at PSI in 2015 to measure several important quantities related to nuclear muon capture on an aluminum target, which is a significant background process for Mu2e. The neutron emission from muon capture can introduce background hits in the Mu2e detectors and can increase radiation damage in various elements of the apparatus. We present measurements of the neutron group fluence and mean neutron multiplicity for muon capture on aluminum nuclei. Finally, we discuss an analysis of triboson production at CMS using an Effective Field Theory framework. Standard Model triboson production, which was first observed at CMS in 2020, has a relatively small cross section and provides direct access to both anomalous triple gauge couplings and quartic gauge couplings. These couplings, interpreted in the Standard Model Effective Field Theory, are studied in the present work. We target the boosted regime where the background rate is low and yields are enhanced when dimension-6 and dimension-8 Wilson coefficients are non-zero. We do not observe an excess in the data and therefore set bounds on the Wilson coefficients. For dimension-6 coefficients the tightest observed (expected) bounds are set on cW /Λ2 where Λ is the mass scale of new physics; the bounds are [−0.13, 0.12] TeV−2 ([−0.12, 0.12] TeV−2 ) at 95% CL. The tightest bounds in dimension-8 are set on fT,0 / Λ4 ; the observed (expected) bounds at 95% CL are [−0.63, 0.69] TeV−4 ([−0.54, 0.62] TeV−4 ). Additional results are presented which include scenarios where multiple Wilson coefficients are non-zero, the application of signal model clipping to address unitarity violation in Effective Field Theories, and a novel template fit developed for easier reinterpretation of our results.

Kampa, Cole Erik [Northwestern U. (main)] (ORCID:0↗

Bayesian Framework for Predicting and Controlling Metabolic Phenotypes in Microbial System

To improve titers, rates and yields for sucrose production in an engineered strain of Synechococcus elongatus PCC7942, we employed Bayesian metabolic control analysis to transcriptomics and external metabolomics data generated for various phases during the circadian clock. Top overexpression candidates included sodium-dependent bicarbonate transporter (H2cO3_Nat_syn), and UTP—glucose-1-phosphate uridylyltransferase (GALUi). Top repression candidates included Glycogen/starch synthetases, ADP-glucose type (GLCS3), Glutamate racemase (GLUR), and ribonucleoside diphosphate reductase (RNDR1).

60 APPLIED LIFE SCIENCES↗

Sensitivity Analysis and Emulation for Functional Data using Bayesian Adaptive Splines

When a computer code is used to simulate a complex system, one of the fundamental tasks is to assess the sensitivity of the simulator to the different input parameters. In the case of computationally expensive simulators, this is often accomplished via a surrogate statistical model, a statistical output emulator. An effective emulator is one that provides good approximations to the computer code output for wide ranges of input values. In addition, an emulator should be able to handle large dimensional simulation output for a relevant number of inputs; it should flexibly capture heterogeneities in the variability of the response surface; it should be fast to evaluate for arbitrary combinations of input parameters, and it should provide an accurate quantification of the emulation uncertainty. In this paper we discuss the Bayesian approach to multivariate adaptive regression splines (BMARS) as an emulator for a computer model that outputs curves. We introduce modifications to traditional BMARS approaches that allow for fitting large amounts of data and allow for more efficient MCMC sampling. We emphasize the ease with which sensitivity analysis can be performed in this situation. We present a sensitivity analysis of a computer model of the deformation of a protective plate used in pressure-driven experiments. Our example serves as an illustration of the ability of BMARS emulators to fulfill all the necessities of computability, flexibility and reliable calculation on relevant measures of sensitivity.

97 MATHEMATICS AND COMPUTING↗

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. II. Bayesian model calibration

Dynamic shockless compression experiments provide the ability to explore material behavior at extreme pressures but relatively low temperatures. Typically, the data from these types of experiments are interpreted through an analytic method called Lagrangian analysis. Here, in this work, alternative analysis methods are explored using modern statistical methods. Specifically, Bayesian model calibration is applied to a new set of platinum data shocklessly compressed to 570 GPa. Several platinum equation-of-state models are evaluated, including traditional parametric forms as well as a novel non-parametric model concept. The results are compared to those in Paper I obtained by inverse Lagrangian analysis. The comparisons suggest that Bayesian calibration is not only a viable framework for precise quantification of the compression path, but also reveals insights pertaining to trade-offs surrounding model form selection, sensitivities of the relevant experimental uncertainties, and assumptions and limitations within Lagrangian analysis. The non-parametric model method, in particular, is found to give precise unbiased results and is expected to be useful over a wide range of applications. The calibration results in estimates of the platinum principal isentrope over the full range of experimental pressures to a standard error of 1.6%, which extends the results from Paper I while maintaining the high precision required for the platinum pressure standard.

Brown, Justin Lee↗

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗

Neural network approximation of Bayesian models for the inference of ion and electron temperature profiles at W7-X

Here, we describe a method for training a neural network (NN) to approximate the full model Bayesian inference of plasma profiles from x-ray imaging diagnostic measurements. The modeling is carried out within the Minerva Bayesian modeling framework where models are defined as a set of assumptions, prior beliefs on parameter values and physics knowledge. The goal is to use NNs for fast ion and electron temperature profile inversion from measured image data. The NN is trained solely on artificial data generated by sampling from the joint distribution of the free parameters and model predictions. The training is carried out in such a way that the mapping learned by the network constitutes an approximation of the full model Bayesian inference. The analysis is carried out on images constituted of 20 × 195 pixels corresponding to binned lines of sight and spectral channels, respectively. Through the full model inference, it is possible to infer electron and ion temperature profiles as well as impurity density profiles. When the network is utilized for the inference of the temperature profiles, the analysis time can be reduced down to a few tens of microseconds for a single time point, which is a drastic improvement if compared to the ≈4 h long Bayesian inference. The procedure developed for the generation of the training set does not rely on diagnostic-specific features, and therefore it is in principle applicable to any other model developed within the Minerva framework. The trained NN has been tested on data collected during the first operational campaign at W7-X, and compared to the full model Bayesian inference results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. Here, we present a spectral decomposition method that allows for corrections to line positions and bound–bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

47 OTHER INSTRUMENTATION↗

A model-independent analysis of the Fermi Large Area Telescope gamma-ray data from the Milky Way dwarf galaxies and halo to constrain dark matter scenarios

Here, we implemented a novel technique to perform the collective spectral analysis of sets of multiple gamma-ray point sources using the data collected by the Large Area Telescope onboard the Fermi satellite. The energy spectra of the sources are reconstructed starting from the photon counts and without assuming any spectral model for both the sources and the background. In case of faint sources, upper limits on their fluxes are evaluated with a Bayesian approach. Our analysis technique is very useful when several sources with similar spectral features are studied, such as sources of gamma rays from annihilation of dark matter particles. We also present the results obtained by applying this analysis to a sample of dwarf spheroidal galaxies and to the Milky Way dark matter halo. The analysis of dwarf spheroidal galaxies yields upper limits on the product of the dark matter pair annihilation cross section and the relative velocity of annihilating particles that are well below those predicted by the canonical thermal relic scenario in a mass range from a few GeV to a few tens of GeV for some annihilation channels.

79 ASTRONOMY AND ASTROPHYSICS↗