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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improving Predictions Under Uncertainty of Material Plasma Device Operations

Understanding the properties of materials when exposed to various plasma temperatures and fluxes is essential to the building and operating of fusion reactors. The Material Plasma Exposure eXperiment (MPEX) is an instrument currently being developed by the Department of Energy (DOE) for this purpose. MPEX is expected to come online in stages over the next five years. Proto-MPEX, the predecessor to MPEX, operated from 2014 to 2021, and was designed to understand the generation of plasma temperatures and fluxes at orders of magnitude below what will be obtained by MPEX. This work uses the recently developed stochastic neural network (SNN), a machine learning technique capable of operating under uncertainty to provide a surrogate model for the Proto-MPEX device. We demonstrate that SNN outperforms Bayesian neural network (BNN), a standard in the field of machine learning with uncertainty. The development of a robust surrogate of the Proto-MPEX will aid in the commissioning and operation of the MPEX device.

Archibald, Rick↗
DOE OSTI2023

Missing data in multi-omics integration: Recent advances through artificial intelligence

Biological systems function through complex interactions between various ‘omics (biomolecules), and a more complete understanding of these systems is only possible through an integrated, multi-omic perspective. This has presented the need for the development of integration approaches that are able to capture the complex, often non-linear, interactions that define these biological systems and are adapted to the challenges of combining the heterogenous data across ‘omic views. A principal challenge to multi-omic integration is missing data because all biomolecules are not measured in all samples. Due to either cost, instrument sensitivity, or other experimental factors, data for a biological sample may be missing for one or more ‘omic techologies. Recent methodological developments in artificial intelligence and statistical learning have greatly facilitated the analyses of multi-omics data, however many of these techniques assume access to completely observed data. A subset of these methods incorporate mechanisms for handling partially observed samples, and these methods are the focus of this review. We describe recently developed approaches, noting their primary use cases and highlighting each method's approach to handling missing data. We additionally provide an overview of the more traditional missing data workflows and their limitations; and we discuss potential avenues for further developments as well as how the missing data issue and its current solutions may generalize beyond the multi-omics context.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Exploring Data Set Bias and Decision Support with Predictive Uncertainty Through Bayesian Approximations and Convolutional Neural Networks

Individual seismic catalogs can contain multiscale observations from fault level to global scales and associated waveforms from discrete events reflect crustal structure across many different scales and locations. Seismic network aperture, geographic location, and observation distance may not provide informative guidance or intuition on how different catalogs will behave across models trained under different conditions. We rely on uncertainty to provide guardrails for when to trust model decisions, but understanding when our uncertainty is trustworthy is an open challenge. Here, in this work, we explore Bayesian approximation methods for assigning predictive uncertainty in seismic event classification problems. We find that computationally expensive Bayesian approximations do not outperform simple ensemble methods. We also find that when exploiting multiple seismic event catalogs, joint training with data from all the catalogs combined with Bayesian approximations and supervised training for classification can obscure bias and result in less robust uncertainty while also not providing substantial performance benefits compared to training individual models for each catalog.

58 GEOSCIENCES↗
DOE OSTI2023

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

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↗
DOE OSTI2026

Boron Coordination in Multicomponent Glasses: Analytical Models and Machine Learning With Uncertainty

Borosilicate glasses are extensively used in a variety of applications from kitchenware to nuclear waste immobilization due to the strong network formed by the Si-O-B bond that makes it resistant to chemical corrosion and gives it a low thermal expansion. Boron, however, exists in both trigonal BO3 and tetrahedral BO4 bonds in glass systems, which impacts the chemical durability and thermal resistance of the glass, amongst other properties. Boron coordination (N4), or the ratio of the amount of BO4 to BO3 within a glass, may aid in predicting these properties but is difficult to derive without experimental data due to the complexity of impacts from varied glass compositions and processing factors. For this reason, compositional models have been developed to predict boron coordination, but the models typically include a limited number of glass components. To help fill this gap in the models, in this work, a diverse multicomponent glass dataset of 809 glasses is compiled from a literature search, and then a number of analytical and machine learning (ML) models are trained on the dataset. Previously developed modified Bernstein and modified Du Stebbins analytical models were fitted to update parameters with the new dataset. Then, partially Bayesian neural networks, Gaussian process regressor, and heteroskedastic deterministic neural networks were evaluated. The ML models examined all have different strategies to overcome the potential for overfitting as a result of a limited training dataset, and return results that account for model uncertainty, which can be valuable for understanding model reliability. For the first time, cooling rate is introduced as an input parameter for ML models, showing consistent improvements in performance and solidifying the importance of including parameters outside of composition alone for N4 prediction. The machine learning models examined here show promise in accurate predictions of boron coordination in borosilicate glasses, all achieving R2 values of 0.91.

boron coordination↗
DOE OSTI2022

Probabilistic Neural Computing with Stochastic Devices

Abstract The brain has effectively proven a powerful inspiration for the development of computing architectures in which processing is tightly integrated with memory, communication is event‐driven, and analog computation can be performed at scale. These neuromorphic systems increasingly show an ability to improve the efficiency and speed of scientific computing and artificial intelligence applications. Herein, it is proposed that the brain's ubiquitous stochasticity represents an additional source of inspiration for expanding the reach of neuromorphic computing to probabilistic applications. To date, many efforts exploring probabilistic computing have focused primarily on one scale of the microelectronics stack, such as implementing probabilistic algorithms on deterministic hardware or developing probabilistic devices and circuits with the expectation that they will be leveraged by eventual probabilistic architectures. A co‐design vision is described by which large numbers of devices, such as magnetic tunnel junctions and tunnel diodes, can be operated in a stochastic regime and incorporated into a scalable neuromorphic architecture that can impact a number of probabilistic computing applications, such as Monte Carlo simulations and Bayesian neural networks. Finally, a framework is presented to categorize increasingly advanced hardware‐based probabilistic computing technologies.

Misra, Shashank↗
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 OSTI2021

Photometric redshifts for the S-PLUS Survey: Is machine learning up to the task?

The Southern Photometric Local Universe Survey (S-PLUS) is a novel project that aims to map the Southern Hemisphere using a twelve filter system, comprising five broad-band SDSS-like filters and seven narrow-band filters optimized for important stellar features in the local universe. In this paper we use the photometry and morphological information from the first S-PLUS data release (S-PLUS DR1) cross-matched to unWISE data and spectroscopic redshifts from Sloan Digital Sky Survey DR15. We explore three different machine learning methods (Gaussian Processes with GPz and two Deep Learning models made with TensorFlow) and compare them with the currently used template-fitting method in the S-PLUS DR1 to address whether machine learning methods can take advantage of the twelve filter system for photometric redshift prediction. Using tests for accuracy for both single-point estimates such as the calculation of the scatter, bias, and outlier fraction, and probability distribution functions (PDFs) such as the Probability Integral Transform (PIT), the Continuous Ranked Probability Score (CRPS) and the Odds distribution, we conclude that a deep-learning method using a combination of a Bayesian Neural Network and a Mixture Density Network offers the most accurate photometric redshifts for the current test sample. In conclusion, it achieves single-point photometric redshifts with scatter (σ NMAD ) of 0.023, normalized bias of -0.001, and outlier fraction of 0.64% for galaxies with r_auto magnitudes between 16 and 21.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Integrating field observations and process-based modeling to predict watershed water quality under environmental perturbations

Watersheds play a critical role in supplying water resources needed for human use and ecosystem health. Understanding and predicting how, when, and where changes in the quantity and quality of water resources occur under different environmental stresses including extreme events is crucial for sustainable management of water resources under a changing environment. However, few studies have attempted to quantify or identify the factors and process interactions controlling the impact of extreme events across water-shed systems. Only few large-scale studies include coordinated monitoring and modeling efforts, which limits our ability to assess the large-scale impact of extreme events on water supply and quality. Methods are lacking to propagate uncertainty in process understanding through an integrated hydro-biogeochemical model framework and evaluate its importance, thus failing to take full advantage of the information potentially available through transformative advances in characterization technologies from high-resolution mass spectrometry to airborne and satellite-based remote sensing. There are consequent risks to our nations water security and to human and ecosystem health that may become exacerbated with the increasing frequency of extreme events that is projected for the coming decades. This paper reviews the current status of watershed science for both water quantity and quality and identifies critical gaps in our current knowledge and modeling capability in addressing the emergent needs in predicting watershed hydrologic and biogeochemical responses (i.e., water quantity and quality) under natural and anthropogenic perturbations. We highlight the need to (1) understand how environmental perturbations including extreme events like floods and droughts propagate through watershed systems and assess their short- and long-term impacts on watershed biogeochemistry, water quality and their recovery pathways; (2) develop and improve a watershed water quality model that reflects the state of scientific understanding gained from observations; and (3) construct a data-model fusion system for watershed characterization, process identification, and mechanistic model parameterization. A large base of modeling, monitoring and data capabilities have been built by various federal government agencies given the relevance of water to their critical missions. An emerging need is to build an integrated national capability for watershed water availability and quality that can address water-related missions across multiple federal agencies.

13 HYDRO ENERGY↗
DOE OSTI2024

Electronic structure prediction of multi-million atom systems through uncertainty quantification enabled transfer learning

The ground state electron density — obtainable using Kohn-Sham Density Functional Theory (KS-DFT) simulations — contains a wealth of material information, making its prediction via machine learning (ML) models attractive. However, the computational expense of KS-DFT scales cubically with system size which tends to stymie training data generation, making it difficult to develop quantifiably accurate ML models that are applicable across many scales and system configurations. Here, we address this fundamental challenge by employing transfer learning to leverage the multi-scale nature of the training data, while comprehensively sampling system configurations using thermalization. Our ML models are less reliant on heuristics, and being based on Bayesian neural networks, enable uncertainty quantification. We show that our models incur significantly lower data generation costs while allowing confident — and when verifiable, accurate — predictions for a wide variety of bulk systems well beyond training, including systems with defects, different alloy compositions, and at multi-million-atom scales. Moreover, such predictions can be carried out using only modest computational resources.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Uranium particle age dating, aggregation, and model age best estimators

We present important aspects of uranium particle age dating by Large-Geometry Secondary Ion Mass Spectrometry (LG-SIMS) that can introduce bias and increase model age uncertainties, especially for small, young, and/or low-enriched particles. This metrology is important for applications related to International Nuclear Safeguards. We explore influential factors related to model age estimation, including the effects of evolving surface chemistry on inter-element measurements of particles (e.g., Th and U), detector background, and aggregation methods using simulated and actual particle samples. We introduce a new model age estimator, called “mid68”, that supplements 95% confidence intervals, providing a “best estimate” and uncertainty about the most likely age. The mid68 estimator can be calculated using the Feldman and Cousins method or Bayesian methods and provides a value with a symmetric uncertainty that can be used for calculations and approximate aggregation of processed model age values when the raw data and correction factors are not available. For particles yielding low 230 Th counts amidst nonzero detector background, their underlying model age probability distributions are asymmetric, so the mid68 estimator provides additional robust information regarding the underlying model age likelihood. This study provides a comprehensive and timely examination of critical aspects of uranium particle age dating as more laboratories establish particle chronometry capabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantified uncertainties in fission yields from machine learning

As machine learning methods gain traction in the nuclear physics community, especially those methods that aim to propagate uncertainties to unmeasured quantities, it is important to understand how the uncertainty in the training data coming either from theory or experiment propagates to the uncertainty in the predicted values. Gaussian Processes and Bayesian Neural Networks are being more and more widely used, in particular to extrapolate beyond measured data. However, studies are typically not performed on the impact of the experimental errors on these extrapolated values. In this work, we focus on understanding how uncertainties propagate from input to prediction when using machine learning methods. We use a Mixture Density Network (MDN) to incorporate experimental error into the training of the network and construct uncertainties for the associated predicted quantities. Systematically, we study the effect of the size of the experimental error, both on the reproduced training data and extrapolated predictions for fission yields of actinides.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

EFIT-Prime: Probabilistic and physics-constrained reduced-order neural network model for equilibrium reconstruction in DIII-D

We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Overview and Recommendations for Cyber Risk Assessment in Nuclear Power Plants

Digital instrumentation and control (I&C) systems are being deployed in nuclear power plants (NPPs) for both existing and advanced reactor designs. As I&C systems become more digitized to allow features like near autonomous control and remote operation, they introduce greater cyber risk to NPPs. Cyberattacks targeting industrial control systems (ICSs) are growing in both qualities and capabilities, which indicates that cybersecurity needs to be an integral part of risk assessment in the industry. Although there are some risk assessment methods in traditional information technology (IT) cybersecurity, the differences between IT and ICS cybersecurity make it infeasible to apply these risk assessment methods directly to ICSs. Some research has focused on risk assessment methods for ICSs, but few studies focus on applications to NPPs. Ideal risk frameworks for the nuclear industry are dynamic and account for system dependencies; this survey review focuses on such risk assessment methods both in and outside the nuclear field. In this article, the major challenges in cybersecurity risk assessment research are pointed out, and further research suggestions and considerations for cyber risk assessment in I&C systems are identified.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗