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At least 613 records · Page 34

Hierarchical Inference of the Lensing Convergence from Photometric Catalogs with Bayesian Graph Neural Networks

Abstract We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ( κ ) from photometric measurements of galaxies along a given line of sight (LOS). The method is of particular interest in strong gravitational time-delay cosmography (TDC), where characterizing the “external convergence” ( κ ext ) from the lens environment and LOS is necessary for precise Hubble constant ( H 0 ) inference. Starting from a large-scale simulation with a κ resolution of ∼1′, we introduce fluctuations on galaxy–galaxy lensing scales of ∼1″ and extract random sight lines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1000 sight lines, the BGNN infers the individual κ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of κ precisely and without bias (within the 2 σ credible interval), resulting in a contribution to the H 0 error budget well under 1%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sight line, extracts a stronger κ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the κ ext characterization for precision TDC. The code is available as a public Python package, Node to Joy ⏬ .

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical tools for a better optical model

Background: Modern statistical tools provide the ability to compare the information content of observables and provide a path to explore which experiments would be most useful to give insight into and constrain theoretical models. Purpose: Here we study three such tools in the context of nuclear reactions with the goal of constraining the optical potential. Method: The three statistical tools examined are (i) the principal component analysis, (ii) the sensitivity analysis based on derivatives, and (iii) the Bayesian evidence. We first apply these tools to a toy-model case, comparing the form of the imaginary part of the optical potential. Then we consider two different reaction observables, elastic angular distributions and polarization data for reactions on 48 Ca and 208 Pb at two different beam energies. Results: For the toy-model case, we find significant discrimination power in the sensitivities and the Bayesian evidence, showing clearly that the volume imaginary term is more useful to describe scattering at higher energies. When comparing between elastic cross sections and polarization data using realistic optical models, sensitivity studies indicate that both observables are roughly equally sensitive but the variability of the optical model parameters is strongly angle dependent. The Bayesian evidence shows some variability between the two observables, but the Bayes factor obtained is not sufficient to discriminate between angular distributions and polarization. Conclusions: From the cases considered, we conclude that, in general, elastic scattering angular distributions have similar impact in constraining the optical potential parameters compared with the polarization data. The angular ranges for the optimum experimental constraints can vary significantly with the observable considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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.

Zepeda, Cuevas [Chicago U., KICP]↗

Automating Sensor Characterization with Bayesian Optimization

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.

Cuevas-Zepeda, Julian [Chicago U., KICP; Chicago U↗

Unbinned extraction of $γ$ from $B\to DK$ with normalizing flows

We introduce an unbinned method for extracting the CKM angle $γ$ from the decay chain $B^\pm \to (D \to K_S π^+ π^-) K^\pm$ using normalizing flows (NFs). The NFs, trained on $D$ decay data, learn a faithful continuous representation of the amplitude and strong phase variation over the $D\to K_Sπ^+π^-$ Dalitz plot whose fidelity improves with increased data sample sizes. With this input, the $B$ decay data can be used to extract the parameters $r_B$, $δ_B$, and $γ$. We test the method on Monte Carlo generated data, where it successfully recovers the injected value of $γ$ within uncertainties. The present implementation propagates statistical uncertainties from finite training data via an ensemble of independently trained flows, and does not attempt to capture the effects of systematic experimental errors. We explore two versions of the method that differ in how the trigonometric constraint on phase variation is encoded, and comment on the possible extension to Bayesian NFs, which would provide direct uncertainty estimates on the learned densities without requiring ensemble training.

Grossman, Yuval [Cornell U., LEPP]↗

Optimizing collimator positions using bayesian optimization in the Fermilab MI-8 transfer line

Collimators are used to minimize losses and to remove particles that would otherwise get lost downstream and irradiate the machine. Finding the optimal jaw positions is time consuming and with the upstream beam properties changing, the collimation settings would need to be readjusted each time. Therefore, a method to optimize collimator positions and to operate them at full capacity in a short time is required for loss control downstream. A study of collimator positions was conducted and a machine learning (ML) model was developed to predict optimal collimator positions. Bayesian Optimization (BO) was used to calculate new jaw positions from the ML model. The results of BO and usage of ML for better performance of the collimation system are presented in this paper.

Babacan, Betiay [Fermilab]↗