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DOE OSTI2019

Cataloging the visible universe through Bayesian inference in Julia at petascale

A key task in astronomy is to locate astronomical objects in images and to characterize them according to physical parameters such as brightness, color, and morphology. This task, known as cataloging, is challenging for several reasons: many astronomical objects are much dimmer than the sky background, labeled data is generally unavailable, overlapping astronomical objects must be resolved collectively, and the datasets are enormous – terabytes now, petabytes soon. In this work, we infer an astronomical catalog from 55 TB of imaging data using Celeste, a Bayesian variational inference code written entirely in the high-productivity programming language Julia. Using over 1.3 million threads on 650,000 Intel Xeon Phi cores of the Cori Phase II supercomputer, Celeste achieves a peak rate of 1.54 DP PFLOP/s. Celeste is able to jointly optimize parameters for 188 M stars and galaxies, loading and processing 178 TB across 8192 nodes in 14.6 min. To achieve this, Celeste exploits parallelism at multiple levels (cluster, node, and thread) and accelerates I/O through Cori’s burst buffer. Julia’s native performance enables Celeste to employ high-level constructs without resorting to hand-written or generated low-level code (C/C++/Fortran) while still achieving petascale performance.

Regier, Jeffrey↗

DOE OSTI2019

Model-Based Localizatiion in a Shallow Ocean Environment: A Sequential Bayesian/Optimization Approach

The shallow ocean is a dynamically changing medium leading to nonstationary statistical behavior when subjected to temperature, wind, surface variations, bottom interactions, noise and extraneous disturbances as well as other conditions that render it a uniquely challenging environment — especially from a signal processing perspective. Processors must account for and adapt to such instantaneous changes in order to be effective. Thus, a processor is required to “adapt” to these environmental variations while simultaneously providing meaningful estimates that are necessary for such applications as detection, localization, inversion and enhancement. In this paper, we develop a parametrically adaptive, sequential Bayesian processor capable of jointly estimating both modal functions and environmental parameters to provide enhanced estimates for a focused optimizer capable locating a target in the noisy shallow ocean environment.

42 ENGINEERING↗

DOE OSTI2020

A Hybrid Gradient Method to Designing Bayesian Experiments for Implicit Models

Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g.,having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound [1]. However, the approach in [1] requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES)combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.

Zhang, Jiaxin↗

DOE OSTI2024

A comprehensive review of dwell time optimization methods in computer-controlled optical surfacing

Dwell time plays a vital role in determining the accuracy and convergence of the computer-controlled optical surfacing process. However, optimizing dwell time presents a challenge due to its ill-posed nature, resulting in non-unique solutions. To address this issue, several well-known methods have emerged, including the iterative, Bayesian, Fourier transform, and matrix-form methods. Despite their independent development, these methods share common objectives, such as minimizing residual errors, ensuring dwell time's positivity and smoothness, minimizing total processing time, and enabling flexible dwell positions. This paper aims to comprehensively review the existing dwell time optimization methods, explore their interrelationships, provide insights for their effective implementations, evaluate their performances, and ultimately propose a unified dwell time optimization methodology.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Uncertainty quantification of mass models using ensemble Bayesian model averaging

Developments in the description of the masses of atomic nuclei have led to various nuclear mass models that provide predictions for masses across the whole chart of nuclides. These mass models play an important role in understanding the synthesis of heavy elements in the rapid neutron capture ( r ) process. However, it is still a challenging task to estimate the size of uncertainty associated with the predictions of each mass model. In this work, a method called ensemble Bayesian model averaging (EBMA) is introduced to quantify the uncertainty of one-neutron separation energies (S 1 n ) which are directly relevant in the calculations of r -process observables. Here, this Bayesian method provides a natural way to perform model averaging, selection, and uncertainty quantification, by combining the mass models as a mixture of normal distributions whose parameters are optimized against the experimental data, employing the Markov chain Monte Carlo method using the no-u-turn sampler. The EBMA model optimized with all the experimental S 1 n from the AME2003 nuclides are shown to provide reliable uncertainty estimates when tested with the new data in the AME2020.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Integrated Risk-Informed Condition Based Maintenance Capability and Automated Platform: Technical Report 1

Due to continuing global energy market trends, driven heavily by the abundant preserves of natural gas, there is an immediate need to reduce costs associated with operation and maintenance (O&M) for the current domestic nuclear power industry and for future reactor developments. This is to ensure that nuclear power generation remains an economically competitive and viable option in the energy market. O&M costs include labor-intensive preventive maintenance (PM) programs, which involve manually-performed inspection, calibration, testing, and maintenance of plant assets at periodic frequency and time-based replacement of assets, irrespective of their condition. This has resulted in an expensive, labor-centric business model to achieve high capacity factors. Fortunately, there are technologies (advanced sensors, data analytics, and risk assessment methodologies) that can enable the transition from a labor-centric business model to a technology-centric business model. The technology-centric business model will result in a significant reduction of PM activities, laying the foundation for real-time condition assessment of plant assets, reducing overall labor and part costs. To enable this transition, PKMJ Technical Services LLC is partnering with the U.S. Department of Energy’s Idaho National Laboratory (operated by the Battelle Energy Alliance, LLC) and the Public Services Enterprise Group (PSEG) Nuclear, LLC in the Integrated Risk-Informed Condition-Based Maintenance Capability and Automated Platform Project. In this report, the configuration of a digital cloud platform using Microsoft Azure is discussed, data from the PSEG Salem Nuclear Generating Station Units 1 & 2 are imported into a digital cloud platform, and the data is used for an evaluation of several key areas: cost impact analysis, risk-informed model development, and preventive maintenance strategy optimization. First, the cost impact analysis reviews which plant assets are potential good candidates for condition-based monitoring. Next, INL utilized the data in their local environment to develop the risk-informed model; which provides estimates of failure rates and probability of failures of assets based upon their past performance. The developed model is performed on assets selected from the cost impact analysis. Lastly, engineers assess the preventive maintenance strategy for the selected assets at PSEG against maintenance strategies in the nuclear industry for similar assets to potentially identify acceptable justification for the extension of current maintenance frequencies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

A Graphical Model for Fusing Diverse Microbiome Data

This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high-dimensional features, in this case, transcripts, collected from different treatments. In such datasets, there are no explicit correspondences between the communities and each corresponds to different factors, making data fusion challenging. We introduce a flexible multinomial-Gaussian generative model for jointly modeling such count data. This latent variable model jointly characterizes the observed data through a common multivariate Gaussian latent space that parameterizes the set of multinomial probabilities of the transcriptome counts. The covariance matrix of the latent variables induces a covariance matrix of co-dependencies between all the transcripts, effectively fusing multiple data sources. We present a computationally scalable variational Expectation-Maximization (EM) algorithm for inferring the latent variables and the parameters of the model. Here, the inferred latent variables provide a common dimensionality reduction for visualizing the data and the inferred parameters provide a predictive posterior distribution. In addition to simulation studies that demonstrate the variational EM procedure, we apply our model to a bacterial microbiome dataset.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Improved naive Bayesian probability classifier in predictions of nuclear mass

Recently, novel statistical methods such as neural networks and Bayesian learning methods are implemented to describe the nuclear masses. Based on previous studies, an improved naive Bayesian probability (iNBP) classifier is proposed to study the nuclear masses by refining the results of sophisticated nuclear models. In the iNBP method, the prediction for nuclear masses is treated as a classification problem. The residuals are classified into several groups to generate prior and conditional probabilities, and the posterior probabilities are further determined by the Bayesian formula. We choose the expectation with maximum probability as the final prediction. Reliability of the iNBP method is assessed by analyzing the global optimizations and the extrapolating capabilities. Here, the iNBP method exhibits impressive improvements on global descriptions for different mass models. Moreover, the method shows robust extrapolating capabilities. Results demonstrate the iNBP method can be applied to predict the nuclear masses of unknown regions. Considering the local mass relations, the iNBP method can offer considerable fine-tuning of the mass descriptions from nuclear models. The methodology proposed in this paper can also be applied to other model-based extrapolations of nuclear observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Effect of thermal conditioning on the initiation threshold of secondary high‐explosives

While most performance metrics of high–explosive (HE) based devices like detonation velocity, detonation pressure, and energy output are expected to degrade over time, the evolution of initiation threshold appears less clear, with claims of both increasing and decreasing trends in threshold having been made in the literature. This work analyzes D–optimally designed sequential binary test data for a few thermally conditioned porous–powder and polymer–bonded HE initiator systems using a Bayesian likelihood method employing the probit regression model. Here we find that in most cases the initiation threshold decreases (i.e., sensitivity increases) upon accelerated thermal conditioning. However, such results are nuanced and influenced by factors like the contact area of initiating stimulus, HE characteristics like density and specific surface area, as well as possible thermally induced changes to other materials and interfaces involved.

36 MATERIALS SCIENCE↗

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 OSTI2021

PNNL-CompBio/bayesian-inference

Bayesian Metabolic Inference is a platform to integrate genome-scale multi-omics data into an iterative method to obtain optimized recommendations for optimal target compound production. This method uses a variational inference approach to approximate new posterior data to analyze in order to obtain useful correlations and control coefficients.

Kumar, Neeraj↗

DOE OSTI2025

Conin

SAND2025-07645O Conin is a Python library that supports constrained analysis of probabilistic graphical models (PGMs). It enables constrained inference and learning for hidden Markov models, Bayesian networks, dynamic Bayesian networks, and Markov networks. Conin interfaces with the pgmpy library to specify general probabilistic graphical models with a variety of optimization solvers to support learning and inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Hart, William [Sandia National Lab. (SNL-CA), Live↗

DOE OSTI2022

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗

DOE OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗

DOE OSTI2026

Physicochemical and Performance Characterization of Six Commercial Organic Solvent Nanofiltration Membranes

This work introduces a novel, gradient-free metamaterial design method based on Gaussian process regression to represent the density field of a unit cell. The dimension of the design space is determined by the covariance matrix dimension in the Gaussian process regression. We propose compressing this matrix using an autoencoder, enabling the decoder to generate the density field and effectively reduce the originally large design space to a lower-dimensional subspace. In this compressed space, we employ an active learning method, Bayesian Adaptive Direct Search (BADS), for efficient exploration of the design space. We demonstrate that for simple 2D designs aimed at maximizing unit cell stiffness, our method yields results comparable to those of standard topology optimization. Furthermore, we extend our approach to various mechanical problems, from linear elasticity to hyperelastic large deformation and elasto-plasticity under finite deformation, to 3D metamaterial design. This illustrates the method’s versatility and effectiveness across a range of applications.

Wu, Haoran↗

DOE OSTI2023

Deep Sigma Point Processes-Assisted Chance-Constrained Power System Transient Stability Preventive Control

Here this paper proposes a deep sigma point processes (DSPP)-assisted chance-constrained power system transient stability preventive control method to deal with uncertain renewable energy and loads-induced stability risk. The traditional transient stability-constrained preventive control is reformulated as a chance-constrained optimization problem. To deal with the computational bottleneck of the time-domain simulation-based probabilistic transient stability assessment, the DSPP is developed. DSPP is a parametric Bayesian approach that allows us to predict system transient stability with high computational efficiency while accurately quantifying the confidence intervals of the predictions that can be used to inform system instability risk. To this end, with a given preset confidence probability, we embed DSPP into the primal dual interior point method to help solve the chance-constrained preventive control problem, where the corresponding Jacobian and Hessian matrices are derived. Comparison results with other existing methods show that the proposed method can significantly speed up preventive control while maintaining high accuracy and convergence

97 MATHEMATICS AND COMPUTING↗