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DOE OSTI2025

Towards Improving luminosity using optics tuning and data-driven methods

The results of Run 24 experiments at Relativistic Heavy Ion Collider (RHIC) for improving luminosity using optics tuning are presented in this study. In the first experiment, MADx matching was used to output magnet strengths corresponding to specific s star movements around Interaction Region 8 (IR8). The corresponding Zero Degree Calorimeter (ZDC) signal was measured in place of luminosity, and Bayesian Optimization aids search of optimal movements. It was found that values retrieved from matching were inaccurate, resulting in negative feedback loops. The second experiment focused on calculating accurate s star movements. The matching method was replaced with a linear sensitivity matrix, directly relating optics to power supply, and its null space was used to fit constraints such as hysteresis effects. At the experiment, beam losses were observed at collimators around boundary of IR8, which were fixed for the third experiment. Dynamic mode decomposition was also introduced to improve quality of turn-by-turn (TBT) data as well as accuracy and consistency of optics measurements at IR8. These improvements will be tested in the experiment of next RHIC run for luminosity optimization.

Accelerator Physics↗

DOE OSTI2020

Efficient compressive and Bayesian characterization of biphoton frequency spectra

Frequency-bin qudits constitute a promising tool for quantum information processing, but their high dimensionality can make for tedious characterization measurements. Here we introduce and compare compressive sensing and Bayesian mean estimation for recovering the spectral correlations of entangled photon pairs. Using a conventional compressive sensing algorithm, we reconstruct joint spectra with up to a 26-fold reduction in measurement time compared to the equivalent raster scan. Applying a custom Bayesian model to the same data, we then additionally realize reliable and consistent quantification of uncertainty. Finally, these efficient methods of biphoton characterization should advance our ability to use the high degree of parallelism and complexity afforded by frequency-bin encoding.

42 ENGINEERING↗

DOE OSTI2023

Improving and Assessing the Quality of Uncertainty Quantification in Deep Learning

Deep learning (DL) models have enjoyed increased attention in recent years because of their powerful predictive capabilities. While many successes have been achieved, standard deep learning methods suffer from a lack of uncertainty quantification (UQ). While the development of methods for producing UQ from DL models is an active area of current research, little attention has been given to the quality of the UQ produced by such methods. In order to deploy DL models to high-consequence applications, high-quality UQ is necessary. This report details the research and development conducted as part of a Laboratory Directed Research and Development (LDRD) project at Sandia National Laboratories. The focus of this project is to develop a framework of methods and metrics for the principled assessment of UQ quality in DL models. This report presents an overview of UQ quality assessment in traditional statistical modeling and describes why this approach is difficult to apply in DL contexts. An assessment on relatively simple simulated data is presented to demonstrate that UQ quality can differ greatly between DL models trained on the same data. A method for simulating image data that can then be used for UQ quality assessment is described. A general method for simulating realistic data for the purpose of assessing a model’s UQ quality is also presented. A Bayesian uncertainty framework for understanding uncertainty and existing metrics is described. Research that came out of collaborations with two university partners are discussed along with a software toolkit that is currently being developed to implement the UQ quality assessment framework as well as serve as a general guide to incorporating UQ into DL applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Retrieving Temperatures and Abundances of Exoplanet Atmospheres with High-resolution Cross-correlation Spectroscopy

High-resolution spectroscopy (R ≥ 25,000) has recently emerged as one of the leading methods for detecting atomic and molecular species in the atmospheres of exoplanets. However, it has so far been lacking a robust method for extracting quantitative constraints on the temperature structure and molecular/atomic abundances. In this work, we present a novel Bayesian atmospheric retrieval framework applicable to high-resolution cross-correlation spectroscopy (HRCCS) that relies on the cross-correlation between data and models to extract the planetary spectral signal. We successfully test the framework on simulated data and show that it can correctly determine Bayesian credibility intervals on atmospheric temperatures and abundances, allowing for a quantitative exploration of the inherent degeneracies. Furthermore, our new framework permits us to trivially combine and explore the synergies between HRCCS and low-resolution spectroscopy to maximally leverage the information contained within each. This framework also allows us to quantitatively assess the impact of molecular line opacities at high resolution. We apply the framework to VLT CRIRES K-band spectra of HD 209458 b and HD 189733 b and retrieve abundant carbon monoxide but subsolar abundances for water, which are largely invariant under different model assumptions. This confirms previous analysis of these data sets, but is possibly at odds with detections of H{sub 2}O at different wavelengths and spectral resolutions. The framework presented here is the first step toward a true synergy between space observatories and ground-based high-resolution observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global fit of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalising flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

A systematic strategy for estimating hERG block potency and its implications in a new cardiac safety paradigm

Introduction: hERG block potency is widely used to calculate a drug's safety margin against its torsadogenic potential. Previous studies are confounded by use of different patch clamp electrophysiology protocols and a lack of statistical quantification of experimental variability. Since the new cardiac safety paradigm being discussed by the International Council for Harmonisation promotes a tighter integration of nonclinical and clinical data for torsadogenic risk assessment, a more systematic approach to estimate the hERG block potency and safety margin is needed. Methods: A cross-industry study was performed to collect hERG data on 28 drugs with known torsadogenic risk using a standardized experimental protocol. A Bayesian hierarchical modeling (BHM) approach was used to assess the hERG block potency of these drugs by quantifying both the inter-site and intra-site variability. A modeling and simulation study was also done to evaluate protocol-dependent changes in hERG potency estimates. Results: A systematic approach to estimate hERG block potency is established. The impact of choosing a safety margin threshold on torsadogenic risk evaluation is explored based on the posterior distributions of hERG potency estimated by this method. The modeling and simulation results suggest any potency estimate is specific to the protocol used. Discussion: This methodology can estimate hERG block potency specific to a given voltage protocol. The relationship between safety margin thresholds and torsadogenic risk predictivity suggests the threshold should be tailored to each specific context of use, and safety margin evaluation may need to be integrated with other information to form a more comprehensive risk assessment.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments

The measurement of fluorescence lifetimes, especially in small sample volumes, presents the dual challenge of probing a small number of fluorophores and fitting the concomitant sparse data set to the appropriate excited-state decay function. A common method of analysis, such as the maximum likelihood (ML) technique, assumes a uniform probability distribution of the parameters describing the fluorescence decay function. An improvement is thus suggested by implementing a suitable nonuniform distribution, as is provided by a Bayesian framework, where the distribution of parameters is obtained from both their prior knowledge and the evidence-based likelihood of an event for a given set of parameters. We have also considered the Dirichlet prior distribution, whose mathematical form enables analytical solutions of the fitting parameters to be rapidly obtained. If Gaussian and exponential prior distributions are judiciously chosen, they reproduce the experimental target lifetime to within 20% with as few as 20 total photon counts for the data set, as does the Dirichlet prior distribution. But because of the analytical solutions afforded by the Dirichlet prior distribution, it is proposed to employ a Dirichlet prior to search parameter space rapidly to provide, if necessary, appropriate parameters for subsequent employment of a Gaussian or exponential prior distribution

97 MATHEMATICS AND COMPUTING↗

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 OSTI2024

Assessing and benchmarking the fidelity of posterior inference methods for astrophysics data analysis

In this era of large and complex astronomical survey data, interpreting, validating, and comparing inference techniques becomes increasingly difficult. This is particularly critical for emerging inference methods like Simulation-Based Inference (SBI), which offer significant speedup potential and posterior modeling flexibility, especially when deep learning is incorporated. We present a study to assess and compare the performance and uncertainty prediction capability of Bayesian inference algorithms – from traditional MCMC sampling of analytic functions to deep learning-enabled SBI. We focus on testing the capacity of hierarchical inference modeling in those scenarios. Before we extend this study to cosmology, we first use astrophysical simulation data to ensure interpretability. We demonstrate a probabilistic programming implementation of hierarchical and non-hierarchical Bayesian inference using simulations derived from the DeepBench software library, a benchmarking tool developed by our group that generates simple and controllable astrophysical objects from first principles. This study will enable astronomers and physicists to harness the inference potential of these methods with confidence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Mass Detection for Heavy-Duty Vehicles using Gaussian Belief Propagation

Predicting vehicle mass is critical to accurately estimate energy use and emissions of commercial trucks. However, data from vehicle telematics is often not at sufficient temporal resolution or accuracy for use in model-based detection methods. In this work, a new statistical mass prediction technique is described for heavy-duty vehicles that incorporates the use Gaussian Belief Propagation (GBP) for probabilistic inference. Similar to Bayesian inference models, the GBP model typically requires less labeled training data than other contemporary machine learning techniques. First, a factor graph is constructed, and a set of Gaussian belief nodes with associated means and variances are fitted to the training data. To better handle noisy input data, the GBP mass prediction model utilizes a k-nearest factors (kNF) algorithm for probabilistic inference on unseen testing data. The proposed method is compared with a classical weighted k-nearest neighbors (kNN) regressor. This statistical kNF-GBP model works even with low-quantity, low-quality initial training data, while being capable of realtime mass estimation. Unlike the kNN regressor, the GBP model produces a measure of uncertainty with its predictions. The proposed method is validated using curve-sampled driving data collected from multiple cloud-connected Class 8 regional haul diesel trucks. Both the kNN regressor and the kNF-GBP mass prediction model were able to predict payload mass with coefficients of determination above 0.97 with minimal data preprocessing.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

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 OSTI2019

Multidimensional sum-up rounding for integer programming in optimal experimental design

Here we present a numerical method for approximating the solution of convex integer programs stemming from optimal experimental design. The statistical setup consists of a Bayesian framework for linear inverse problems for which the direct relationship is described by a discretized integral equation. Specifically, we aim to find the optimal sensor placement from a set of candidate locations where data are collected with measurement error. The convex objective function is a measure of the uncertainty, described here by the trace or log-determinant of the posterior covariance matrix, for the discretized linear inverse problem solution. The resulting convex integer program is relaxed, producing a lower bound. An upper bound is obtained by extending the sum-up rounding approach to multiple dimensions. For this extension, we analyze its accuracy as a function of the discretization mesh size for a rectangular domain. We show asymptotic optimality of the integer solution defining the upper bound for different experimental design criteria (A- and D-optimal), by proving the convergence to zero of the gap between the upper and lower bounds as the mesh size goes to zero. The technique is illustrated on a two-dimensional gravity surveying problem for both A-optimal and D-optimal sensor placement where our designs yield better results compared with a thresholding rounding approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A Probabilistic Model-Based Diagnostic Framework for Nuclear Engineering Systems

A fault diagnostic framework was investigated in this study for applications in thermal–hydraulic systems of nuclear power plants. The proposed framework consists of quantitative model-based diagnosis, statistical change detection and probabilistic reasoning. The use of physics-based diagnostic models provides high detection sensitivity and allows noise and measurement uncertainty to be incorporated robustly. Performance-related parametric models for each component are constructed based on first principles. Numerical model residuals are generated using the concept of analytical redundancy. Statistical change detection methods are employed to detect non-zero residuals in the presence of uncertainty. The diagnosis task is performed using Bayesian inference to detect and localize possible faults. Application to a single-phase heat exchanger for demonstration showed that the proposed probabilistic framework can provide improved results in comparison with traditional approaches while remaining less sensitive to false alarms in the presence of measurement and modeling uncertainty.

Bayesian network↗

DOE OSTI2023

Uncertainty quantification for high explosive reactant and product equations of state

Equations of state (EOSs) are typically represented as physics-informed models with tunable parameters that are adjusted to replicate calibration data as closely as possible. Uncertainty quantification (UQ) allows for the development of an ensemble of EOS parameters that are consistent with the calibration data instead of a single EOS. In this work, we perform UQ for the reactant and product EOSs for a variety of high explosives (HEs). In doing so, we demonstrate a strategy for dealing with heterogeneous (both experimental and calculated) data. We also use a statistical distance metric to quantify the differences between the various HEs using the UQ results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗

DOE OSTI2025

Calibration of RAFM Micromechanical Model for Creep Using Bayesian Optimization for Functional Output

A Bayesian optimization procedure is presented for calibrating a multimechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on Fe(8–9)%Cr are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600°C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework (Huang et al., 2021, “Bayesian optimization of functional output in inverse problems,” Optim. Eng., 22, pp. 2553–2574). Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. In conclusion, validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel.

42 ENGINEERING↗

DOE OSTI2018

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this work, we propose a novel Bayesian stochastic inversion methodology, characterized by a tight coupling between a gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated spatial random field. Moreover, non-Gaussian full posterior probability distribution functions are estimated via an efficient LMCMC method on both the projected low-dimensional feature space and the recovered high-dimensional parameter space. We demonstrate this computational framework by integrating and adapting recent developments such as data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to solve inverse problems in linear elasticity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Machine Learning-Based Technique for Automated Sensor Characterization

The development of novel instrumentation requires an iterative cycle with three stages: design, prototyping, and testing. Recent advancements in simulation and nanofabrication techniques have significantly accelerated the design and prototyping phases. Nonetheless, detector characterization continues to be a major bottleneck in device development. During the testing phase, a significant time investment is required to characterize the device in different operating conditions and find optimal operating parameters. The total effort spent on characterization and parameter optimization can occupy a year or more of an expert s time. In this work, we present a novel technique for automated sensor calibration that aims to accelerate the testing stage of the development cycle. This technique leverages closed-loop Bayesian optimization (BO), using real-time measurements to guide parameter selection and identify optimal operating states. We demonstrate the method with a novel low-noise CCD, showing that the machine learning-driven tool can efficiently characterize and optimize operation of the sensor in a couple of days without supervision of a device expert.