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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Sequential Kalman tuning of the t -preconditioned Crank-Nicolson algorithm: efficient, adaptive and gradient-free inference for Bayesian inverse problems

Ensemble Kalman Inversion (EKI) has been proposed as an efficient method for the approximate solution of Bayesian inverse problems with expensive forward models. However, when applied to the Bayesian inverse problem EKI is only exact in the regime of Gaussian target measures and linear forward models. Here, in this work we propose embedding EKI and Flow Annealed Kalman Inversion, its normalizing flow (NF) preconditioned variant, within a Bayesian annealing scheme as part of an adaptive implementation of the t-preconditioned Crank-Nicolson (tpCN) sampler. The tpCN sampler differs from standard pCN in that its proposal is reversible with respect to the multivariate t-distribution. The more flexible tail behaviour allows for better adaptation to sampling from non-Gaussian targets. Within our Sequential Kalman Tuning (SKT) adaptation scheme, EKI is used to initialize and precondition the tpCN sampler for each annealed target. The subsequent tpCN iterations ensure particles are correctly distributed according to each annealed target, avoiding the accumulation of errors that would otherwise impact EKI. We demonstrate the performance of SKT for tpCN on three challenging numerical benchmarks, showing significant improvements in the rate of convergence compared to adaptation within standard SMC with importance weighted resampling at each temperature level, and compared to similar adaptive implementations of standard pCN. The SKT scheme applied to tpCN offers an efficient, practical solution for solving the Bayesian inverse problem when gradients of the forward model are not available. Code implementing the SKT schemes for tpCN is available at https://github.com/RichardGrumitt/KalmanMC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

This paper analyzes hierarchical Bayesian inverse problems using techniques from highdimensional statistics. Furthermore, our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.

MAP estimation↗
DOE OSTI2026

Nuclear Data Adjustment for Nonlinear Applications in the OECD/NEA WPNCS SG14 Benchmark—A Bayesian Inverse UQ-Based Approach for Data Assimilation

The Organisation for Economic Co-operation and Development Working Party on Nuclear Criticality Safety has proposed a benchmark exercise to assess the performance of current nuclear data adjustment techniques applied to nonlinear applications and experiments with low correlation to applications. This work introduces Bayesian inverse uncertainty quantification (IUQ) employing scientific machine learning surrogate models as a method for nuclear data adjustments in this benchmark, and compares IUQ to the more traditional methods of generalized linear least squares (GLLS) and Monte Carlo Bayes (MOCABA). Posterior predictions from IUQ showed agreement with GLLS and MOCABA for linear applications. Here, when comparing GLLS, MOCABA, and IUQ posterior predictions to computed model responses using adjusted parameters, we observe that the GLLS predictions failed to replicate the computed response distributions for nonlinear applications, while MOCABA showed near agreement, and IUQ used the computed model responses directly. We also discuss observations on why experiments with low correlation to applications can be informative to nuclear data adjustments and identify some properties useful in selecting experiments for inclusion in nuclear data adjustment. Performance in this benchmark indicates potential for Bayesian IUQ in nuclear data adjustments.

Bayesian calibration↗
DOE OSTI2025

Nuclear Data Adjustment for Nonlinear Applications in the OECD/NEA WPNCS SG14 Benchmark -- A Bayesian Inverse UQ-based Approach for Data Assimilation

The Organization for Economic Cooperation and Development (OECD) Working Party on Nuclear Criticality Safety (WPNCS) proposed a benchmark exercise to assess the performance of current nuclear data adjustment techniques applied to nonlinear applications and experiments with low correlation to applications. This work introduces Bayesian Inverse Uncertainty Quantification (IUQ) as a method for nuclear data adjustments in this benchmark, and compares IUQ to the more traditional methods of Generalized Linear Least Squares (GLLS) and Monte Carlo Bayes (MOCABA). Posterior predictions from IUQ showed agreement with GLLS and MOCABA for linear applications. When comparing GLLS, MOCABA, and IUQ posterior predictions to computed model responses using adjusted parameters, we observe that GLLS predictions fail to replicate computed response distributions for nonlinear applications, while MOCABA shows near agreement, and IUQ uses computed model responses directly. We also discuss observations on why experiments with low correlation to applications can be informative to nuclear data adjustments and identify some properties useful in selecting experiments for inclusion in nuclear data adjustment. Performance in this benchmark indicates potential for Bayesian IUQ in nuclear data adjustments.

FOS: Computer and information sciences↗
DOE OSTI2025

Preliminary Results on Bayesian Inverse UQ for OECD/NEA WPNCS Subgroup 14 Benchmark Exercise for Error Recovery and Experimental Coverage

The Organization for Economic Cooperation and Development (OECD) Working Party on Nucelar Criticality Safety (WPNCS) has proposed a benchmark exercise representative of neutronic behavior in criticality experiments. Here, the goal is to develop confidence in data assimilation techniques used to adjust nuclear data. Participants are given synthetic experimental models with associated measured data and asked to estimate the model parameters given the model and measurements as well as provide predictions for separate application models. In this work, we performed data assimilation using Bayesian inverse Uncertainty Quantification (UQ) with machine learning surrogate models to produce posterior parameter distributions for the requested parameters and posterior predictive distributions for the requested responses. Several experimental models are shown to insufficiently inform the posterior parameter distributions for the applications involved. However, given sufficient experimental data, posterior parameter estimates yielded reduced uncertainty in the response predictions of interest while covering the experimental data.

Bayesian Inference↗
DOE OSTI2024

Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization

Abstract This paper presents a statistical forward model for a Compton imaging system, called Compton imager. This system, under development at the University of Illinois Urbana Champaign, is a variant of Compton cameras with a single type of sensors which can simultaneously act as scatterers and absorbers. This imager is convenient for imaging situations requiring a wide field of view. The proposed statistical forward model is then used to solve the inverse problem of estimating the location and energy of point-like sources from observed data. This inverse problem is formulated and solved in a Bayesian framework by using a Metropolis within Gibbs algorithm for the estimation of the location, and an expectation-maximization algorithm for the estimation of the energy. This approach leads to more accurate estimation when compared with the deterministic standard back-projection approach, with the additional benefit of uncertainty quantification in the low photon imaging setting.

Tarpau, Cécilia (ORCID:0000000286539490)↗
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2026

Source-Resolved Inversion of Elemental Carbon Emissions in California Using Log-Space Bayesian Inference

Elemental carbon (EC), operationally quantified by thermal-optical analysis, is widely used as a proxy for black carbon (BC) relevant to short-term climate forcing and public health. Current EC emission inventories remain highly uncertain, with persistent discrepancies between bottom-up and top-down estimates. In this study, we develop a source-resolved, log-space Bayesian inversion framework applied to estimate California’s statewide EC emissions in 2019. By integrating surface EC measurements from the EPA’s Air Quality System network with high-resolution source contributions simulated by a chemical transport model, we identify a one-third underestimation in the existing statewide EC inventory, requiring an increase of the total from a prior of 8.58 [5.49–13.75] Gg year–1 to a posterior estimate of 12.78 [10.71–15.37] Gg year–1. This discrepancy is primarily driven by substantial underestimations in the power and industrial and off-road mobile sectors. Furthermore, population-weighted exposure analysis reveals a marked sectoral divergence between emission mass and health burden: off-road mobile sources dominate both emissions and exposure, accounting for 31% of statewide exposure, while residential wood combustion contributes 26% of total exposure despite comprising only 19% of total emissions, due to its source proximity to population. These findings underscore the need to update sector-specific EC speciation profiles and demonstrate that mitigation strategies targeting off-road mobile sources and residential wood combustion are critical for reducing EC-related health impacts in California.

Zhang, Jie↗
DOE OSTI2025

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hierarchical Bayesian modeling for Inverse Uncertainty Quantification of system thermal-hydraulics code using critical flow experimental data

The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.

42 ENGINEERING↗
DOE OSTI2025

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference

In this work, we present two neural network approaches that approximate the solutions of static and dynamic conditional optimal transport (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference—particularly in the simulation-based (“likelihood-free”) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

pnnl/MCRASTA

McRasta (Markov Chain Rate and State Analysis) was developed to estimate parameter uncertainty in constitutive friction models via Bayesian inverse and Markov Chain Monte Carlo (MCMC) methods.

Fichera, Marissa [Pacific Northwest National Labor↗
DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

The Influence of Shallow Subsurface Properties on Particle Motion in Acoustic-Seismic Coupling

Atmospheric acoustic waves transmit energy into the solid Earth through air-to-ground coupling. These waves are recorded by seismic sensors and provide insight into both atmospheric phenomena and subsurface properties. Interpreting these signals is often challenging because they are modulated by subsurface structure and the incidence angle of the acoustic wave. This study examines acoustic--seismic coupling generated by the 2012 Camp Minden Explosion, which was recorded by hundreds of seismoacoustic stations. We apply a novel technique to quantify the seismic particle motion, model coupled waves with a propagator matrix approach, and apply a Bayesian inversion to infer properties of the shallow subsurface. Our analysis reveals that prograde motion is widespread and focused in low shear-wave velocity regions, such as the Mississippi Embayment, and retrograde motion is more common in higher shear-velocity areas. Inversion results at some stations produce plausible subsurface models with strong waveform fits, while inversions at other sites are less successful. These results indicate prograde particle motion in air-to-ground coupled waves is more prevalent than previously recognized and may serve as a diagnostic for shallow velocity structure. Our comprehensive modeling and inversion framework provides a potential method to extract layered near-surface properties from acoustic-seismic coupling observations.

58 GEOSCIENCES↗
DOE OSTI2025

Improved Bayesian regularization of inverse problems in vibrations and acoustics using noise-only measurements

Here, this paper studies Tikhonov regularization (ridge regression) parameter selection for problems in vibrations and acoustics. The selection method is based on a popular Bayesian method, but it incorporates measurements of sensor noise. The regularization parameter is closely related to the ratio of system input energy to noise energy, so noise measurements inform the inference procedure and improve parameter identification. In cases where standard Bayesian regularization identifies zero as the optimal regularization parameter, noise measurements guarantee a unique nonzero optimum. Sufficient theoretical criteria are developed for this guarantee. The method is verified in even-determined and under-determined configurations in an acoustic source localization simulation and a vibration load identification experiment. It is shown to yield significant improvements over existing empirical Bayesian regularization. Improvements are larger in the even-determined case and smaller in the under-determined case, wherein the inverse solution is less sensitive to the regularization parameter.

42 ENGINEERING↗