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At least 1,081 records · Page 60

A Robust Estimate of Continental-Scale Terrestrial Carbon Sinks Using GOSAT XCO 2 Retrievals

Satellite XCO 2 retrievals could improve the estimates of surface carbon fluxes, but it remains unknown on what scales these estimates are robust. Here, we use the time-dependent Bayesian synthesis top-down method and prior net ecosystem exchanges (NEEs) from 12 terrestrial biosphere models (TBMs) to infer the monthly carbon fluxes of 51 land regions with constraints by GOSAT XCO 2 retrievals. We find that the uncertainty (standard deviation of 12 TBMs) reduction rates (uncertainty reduction rate (URR)) decrease significantly at decreasing spatial scales. On the continental-scale, the mean URR is about 57%, and the annual and seasonal cycle estimates of NEE are rather robust. The evaluation shows that the posterior CO 2 concentrations are significantly improved at the continental scale. Our study suggests that the GOSAT XCO 2 can only promise a robust continental-scale NEE estimate and improving the XCO 2 accuracy is an effective way to achieve robust estimates on smaller scales under current spatial coverage.

58 GEOSCIENCES↗

Quantification of the effect of uncertainty on impurity migration in PISCES-A simulated with GITR

A Bayesian inference strategy has been used to estimate uncertain inputs to global impurity transport code (GITR) modeling predictions of tungsten erosion and migration in the linear plasma device, PISCES-A. This allows quantification of GITR output uncertainty based on the uncertainties in measured PISCES-A plasma electron density and temperature profiles (n e , T e ) used as inputs to GITR. The technique has been applied for comparison to dedicated experiments performed for high (4 × 10 22 m –2 s –1 ) and low (5 × 10 21 m –2 s –1 ) flux 250 eV He–plasma exposed tungsten (W) targets designed to assess the net and gross erosion of tungsten, and corresponding W impurity transport. The W target design and orientation, impurity collector, and diagnostics, have been designed to eliminate complexities associated with tokamak divertor plasma exposures (inclined target, mixed plasma species, re-erosion, etc) to benchmark results against the trace impurity transport model simulated by GITR. The simulated results of the erosion, migration, and re-deposition of W during the experiment from the GITR code coupled to materials response models are presented. Specifically, the modeled and experimental W I emission spectroscopy data for a 429.4 nm line and net erosion through the target and collector mass difference measurements are compared. Furthermore, the methodology provides predictions of observable quantities of interest with quantified uncertainty, allowing estimation of moments, together with the sensitivities to plasma temperature and density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On data set tensions and signatures of new cosmological physics

ABSTRACT Can new cosmic physics be uncovered through tensions amongst data sets? Tensions in parameter determinations amongst different types of cosmological observation, especially the ‘Hubble tension’ between probes of the expansion rate, have been invoked as possible indicators of new physics, requiring extension of the ΛCDM paradigm to resolve. Within a fully Bayesian framework, we show that the standard tension metric gives only part of the updating of model probabilities, supplying a data co-dependence term that must be combined with the Bayes factors of individual data sets. This shows that, on its own, a reduction of data set tension under an extension to ΛCDM is insufficient to demonstrate that the extended model is favoured. Any analysis that claims evidence for new physics solely on the basis of alleviating data set tensions should be considered incomplete and suspect. We describe the implications of our results for the interpretation of the Hubble tension.

Cortês, Marina (ORCID:0000000304853767)↗

Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials

Properties of soft materials are influenced by their anisotropic structuring under nonequilibrium fields. Although anisotropic structure-property relationships have been extensively explored theoretically, comparison to experiments requires determination of the microstructural orientation probability distribution function (OPDF) of microstructural elements. Small angle scattering (SAS) measurements encode information about the OPDF, but tools to navigate this connection are incomplete. Here, we develop and validate an explicit framework to link arbitrary OPDFs to SAS measurements. Specifically, we propose, validate, and apply a method, maximum a posteriori scattering inference (MAPSI), whereby the OPDF may be obtained from SAS measurements using a Bayesian estimation method. Using this method, we obtain estimates of the full 3D OPDF for two model semidilute fd-virus (rodlike) dispersions at concentrations that are approximately equal to and twice the overlap concentration. From the OPDF, we calculate its second and fourth moments and compare these to predictions for a dilute suspension of rigid rods and to a recent theory for semidilute suspensions. Finally, we use both the theoretical and measured moments to calculate the stress, both for dilute and semidilute suspensions. These predictions are not only compared to each other, but also to measured values of the shear stress, and point to new insights into the behavior of suspensions of highly elongated particles in the transition between dilute and semidilute behavior. We also use this new framework to provide perspective on the connection between scalar parameterizations of scattering and the OPDF that have frequently been used in the past. Here, the new tools developed in this work provide an unprecedented path toward experimental validation of dynamical theories of rodlike colloids and polymers, and for measurement of nonequilibrium structures and stresses of other complex fluids and soft materials with SAS.

36 MATERIALS SCIENCE↗

Probabilistic Power Flow Based on a Gaussian Process Emulator

In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator has allowed us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method.

42 ENGINEERING↗

Artificial Reasoning System for Symptom-Based Conditional Failure Probability Estimation Using Bayesian Network

Advances in nuclear power technologies require enhanced capabilities for operator advice and autonomous control. One of the first tasks in the development of such capabilities is the formulation of symptom-based conditional failure probabilities for structures, systems, and components (SSCs) of interest, for which the primary goal is to aid plant personnel in deducing the probabilistic performance status of the monitored SSCs and in detecting impending faults/failure. The task of conditional failure probability estimation is a bidirectional inference problem and shall be logically tackled by the Bayesian network (BN) approach. As a knowledge-based artificial intelligence tool and a probabilistic graphical model, BN offers the capability of reasoning under uncertainty and graphical representation emulating the physical behavior of the target SSC. This paper provides a systematic overview of the BN technique and the software tools for handling implementation of BN models, along with the associated knowledge representation and reasoning paradigm. Both operational data and expert judgement can be readily incorporated into the knowledge base of a BN model. The challenges with data availability are highlighted, and the general approach to target SSC identification is presented. Our focus is upon failure-prone and risk-important balance of plant assets, especially cases having strong operator involvement. An exemplary case study on the failure of a motor-driven centrifugal pump is also conducted to demonstrate the usefulness and technical feasibility of the proposed artificial reasoning system using an expert system shell.

Zhao, Xingang↗

Maximized Information Gain of Next Generation Pulsed Power Using Optimized Design of Z-Machine Experiments

This project develops a Bayesian optimization approach to extracting insights from Z Machine experimental data to determine if and how these insights can be used to extrapolate to a larger facility. The primary goal is to address the scientific challenge of informing how confidently experimental conditions can be predicted on a next generation facility, the design of which requires the reliable extrapolation of current high energy density technologies to regimes yet unobserved, except by costly high-fidelity computational models. Maximizing the use of presently available data and understanding how it informs future endeavors is critically important to enable transformative pulsed power and the science of extreme conditions. We explore a Bayesian optimization approach to experimental design which combines information theory, experimental data, and computational modeling to explore how information gain can be maximized.

97 MATHEMATICS AND COMPUTING↗

Harnessing Uncertainty through Functional Data Analysis in Gas Breakthrough Data

Detecting subsurface explosions from radionuclide gas migration through rock fractures is an effective way to identify nuclear activity. Los Alamos National Laboratory (LANL) has developed simulation methods, based on data from the 1962 Hardhat underground nuclear test, to predict gas breakthrough times at the surface. However, these methods rely on an imperfect understanding of the relationship between rock damage and fracture permeability. Our clinic project studies methods for predicting breakthrough curves that characterize total mass produced as a function of time, as well as quantifying the uncertainty associated with these predictions. The model that is currently employed to relate damage to permeability uses an empirically motivated power-law expression, with a range of parameter values that are compatible with the experimental Hardhat data. We develop emulators, built from functional data analysis techniques and trained on simulation data, that rapidly predict the gas breakthrough curve given a damage field and given the parameter values of the power-law equation. Using Bayesian regression, we address the problem of uncertainty quantification in our emulators. Finally, in order to test the robustness of the model, we further validate it on a damage field representing different physical conditions.

58 GEOSCIENCES↗

DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories

This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Bayesian Optimization for Reactor Design Optimization

This study present a test case in which the Bayesian Optimization method is applied to a simulation-based reactor core design optimization problem. The test case aims to showcase the potential of an automated design optimization algorithm for reactor designs by streamlining the reactor core design workflow, given the high computational cost of simulations. The contributions of this work are threefold. First, the existing HTGR model is converted into a simulation-based design optimization test case by developing a pipeline that enables modification of key design parameters and evaluates design performance based on simulation outputs. Second, Bayesian Optimization is implemented and adapted to demonstrate the feasibility of automatic design optimization for nuclear reactor core. Proposed approach leverages Gaussian Process models to characterize the relationship between design variables and performance metrics, while incorporating novel acquisition functions that balance exploration of the design space with exploitation of promising configurations. This implementation lays the foundation for the future developments of reactor design optimization algorithms.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Bayesian quantification of observability and equation of state of twin stars

The possibility of discovering twin stars, two neutron stars (NSs) with the same mass but different radii, is usually studied in forward modelings by using a restricted number of NS matter equations of state (EOSs) encapsulating a first-order phase transition from hadronic to quark matter (QM). Informing our likelihood function with the NS radius data from GW170817 and using a metamodel with nine parameters capable of mimicking most NS EOSs available in the literature, we conduct a Bayesian quantification of the observability and underlying EOSs of twin stars. Of the accepted EOSs, between 12 and 18% yield twin stars, depending on the restrictions we place on the second branch. The possibility of twin stars remains robust even under recent observational constraints. Here, we show that many of these twin star scenarios are observable with currently available levels of accuracy in measuring NS radii. We also present the marginalized posterior probability density functions (PDFs) of every EOS parameter for each of four mass-radius correlation topologies. We find that the inferred EOS depends sensitively on not only whether twin stars are present, but also the category of twin stars, indicating that the observation of twin stars would provide a strong constraint on the underlying EOS. In particular, for two coexisting hybrid stars having QM cores at different densities, the PDF for QM speed of sound squared 𝑐$^2_{qm}$ has two peaks, one below and another above the conformal limit 𝑐$^2_{qm}$ = 1/3 predicted by perturbative QCD.

QCD in nuclear reactions↗

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗

Uncertainty quantification in machine learning for engineering design and health prognostics: A tutorial

On top of machine learning (ML) models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Towards this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. In conclusion, two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage (case study 1) and the remaining useful life prediction of turbofan engines (case study 2).

97 MATHEMATICS AND COMPUTING↗

Multi-objective Bayesian alloy design using multi-task Gaussian processes

In design applications, correlations among material properties (such as the tendency for stronger materials to be less ductile) are often neglected. This approach is echoed in multi-objective optimization techniques which treat each performance characteristic as an independent objective, aiming to optimize scalar functions and find optimal Pareto fronts. However, this overlooks the statistical relationships between performance characteristics inherent in a material system. To address this, we propose the use of Bayesian optimization, a highly efficient black-box optimization algorithm known for constructing Gaussian processes (GPs) – uncorrelated surrogates - to model objective functions. Rather than evaluating multiple GPs for each objective function separately, we argue for a shift towards jointly modeling these objective functions, considering their statistical correlations. This integrated approach utilizes naturally occurring relationships among material properties, providing additional information to enhance the performance of the design framework. This requires the replacement of multiple independent GPs with a single multi-task GP, employing a correlation matrix to construct a multi-task kernel function, wherein each task corresponds to a single objective function. Here, we anticipate this refined methodology will better leverage material correlations, improving design optimization results.

36 MATERIALS SCIENCE↗

Optimization of simulated high-field side lower hybrid current drive coupling using machine learning predictions of scrape-off layer density

Lower hybrid current drive (LHCD) is a potential source of non-inductive off-axis current drive (CD) for tokamaks. Although LHCD has been successfully deployed on a number of tokamaks, it is highly sensitive to the scrape-off layer (SOL) conditions local to the LHCD launcher. Large gaps between the launcher and plasma core, SOL turbulence, or edge density perturbations due to edge-localized modes can hamper CD or cause large reflected power. These coupling issues in part motivated the installation of an LHCD launcher on the high-field side (HFS) of DIII-D. On the HFS, the SOL is less turbulent and more controllable compared to the low-field side. This quiescence may result in more predictable edge conditions and thus a more predictable CD. Here, in this work, HFS SOL reflectometry measurements are predicted from global plasma parameters using machine learning models. The SOL predictions coupled with the full-wave simulation of the LHCD launcher allow for the prediction of reflected power, directivity, and arcing risk before the discharge. Launcher performance is then optimized using multi-objective Bayesian optimization, finding the shot parameters that result in an optimal SOL density that maximizes CD while minimizing the risk of arcing. The predictions and optimizations of LHCD performance are then accelerated using a surrogate model of the full-wave LHCD simulation.

Bayesian optimization↗