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DOE OSTI2025

Robustness of Deep Learning Classification to Adversarial Input on GPUs: Asynchronous Parallel Accumulation Is a Source of Vulnerability

The ability of machine learning (ML) classification models to resist small, targeted input perturbations—known as adversarial attacks—is a key measure of their safety and reliability. We show that floating-point non associativity (FPNA) coupled with asynchronous parallel programming on GPUs is sufficient to result in misclassification, without any perturbation to the input. Additionally, we show that this misclassification is particularly significant for inputs close to the decision boundary and that standard adversarial robustness results may be overestimated up to 4.6 when not considering machine-level details. We first study a linear classifier, before focusing on standard Graph Neural Network (GNN) architectures and datasets used in robustness assessments. We develop a novel black-box attack using Bayesian optimization to discover external workloads that can change the instruction scheduling which bias the output of reductions on GPUs and reliably lead to misclassification. Motivated by these results, we present a new learnable permutation (LP) gradient-based approach to learning floating-point operation orderings that lead to misclassifications. The LP approach provides a worst-case estimate in a computationally efficient manner, avoiding the need to run identical experiments tens of thousands of times over a potentially large set of possible GPU states or architectures. Finally, using instrumentation-based testing, we investigate parallel reduction ordering across different GPU architectures under external background workloads, when utilizing multi-GPU virtualization, and when applying power capping. Our results demonstrate that parallel reduction ordering varies significantly across architectures under the first two conditions, substantially increasing the search space required to fully test the effects of this parallel scheduler-based vulnerability. These results and the methods developed here can help to include machine-level considerations into adversarial robustness assessments, which can make a difference in safety and mission critical applications.

Shanmugavelu, Sanjif [Maxeler Technologies, a Groq↗

DOE OSTI2016

Improved uncertainty quantification in nondestructive assay for nonproliferation

This paper illustrates methods to improve uncertainty quantification (UQ) for non-destructive assay (NDA) measurements used in nuclear nonproliferation. First, it is shown that current bottom-up UQ applied to calibration data is not always adequate, for three main reasons: (1) Because there are errors in both the predictors and the response, calibration involves a ratio of random quantities, and calibration data sets in NDA usually consist of only a modest number of samples (3–10); therefore, asymptotic approximations involving quantities needed for UQ such as means and variances are often not sufficiently accurate; (2) Common practice overlooks that calibration implies a partitioning of total error into random and systematic error, and (3) In many NDA applications, test items exhibit non-negligible departures in physical properties from calibration items, so model-based adjustments are used, but item-specific bias remains in some data. Therefore, improved bottom-up UQ using calibration data should predict the typical magnitude of item-specific bias, and the suggestion is to do so by including sources of item-specific bias in synthetic calibration data that is generated using a combination of modeling and real calibration data. Second, for measurements of the same nuclear material item by both the facility operator and international inspectors, current empirical (top-down) UQ is described for estimating operator and inspector systematic and random error variance components. A Bayesian alternative is introduced that easily accommodates constraints on variance components, and is more robust than current top-down methods to the underlying measurement error distributions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

A Dirichlet process mixture model for automatic {sup 18}F-FDG PET image segmentation: Validation study on phantoms and on lung and esophageal lesions

Purpose: The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on {sup 18}F-fluorodeoxyglucose positron emission tomography ({sup 18}F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. Methods: The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracy was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10–37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Results: Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This “calibration curve” was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. Conclusions: The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗

DOE OSTI2026

Uncertainty quantification and reliability assessment for intermodal freight transportation

Intermodal freight optimization models support cost-effective, low-emission, and timely goods movement by coordinating trucks, rail, and barges. These models determine optimal flows, routing, and modal switches while respecting infrastructure and operational constraints. However, their real-world utility is often undermined by pervasive uncertainties-such as fluctuating transportation costs and emissions, variable terminal capacities, and uncertain freight demand-that distort key performance outcomes, including total system cost, carbon footprint, and transit time reliability. This study presents a structured framework for quantifying uncertainty in intermodal freight transportation (IFT) optimization. The framework evaluates how input uncertainty affects system performance and reliability, a critical need for ensuring that model-based decisions remain robust under real-world variability, especially amid volatile fuel prices, shifting demand, and growing disruptions. It integrates three complementary methods: (1) Sobol-based global sensitivity analysis to identify influential parameters affecting cost, emissions, and transit time, (2) Monte Carlo-based capacity perturbation analysis to assess robustness under probabilistic facility disruptions, and (3) Monte Carlo filtering with Bayesian inference to detect threshold-based performance vulnerabilities. The results highlight diesel truck unit cost as the dominant driver of variability. To improve system resilience, planners should prioritize uncertainty in fuel-related parameters when designing intermodal strategies.

Intermodal freight transportation↗

DOE OSTI2020

Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model – Application to realistic N -body simulations

ABSTRACT Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z’s tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $\Delta \bar{z} \approx 0.05,$ the final biases in the posterior are $\Delta \bar{z} \lesssim 0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Deep-inelastic and quasielastic electron scattering from A = 3 nuclei

We perform a combined analysis of inclusive electron scattering data from $A=3$ nuclei in the deep-inelastic and quasielastic scattering regions, using Monte Carlo analysis methods and the nuclear weak binding approximation to establish the range over which the data can be described within the same theoretical framework. Comparison with quasielastic $^3$He cross sections from SLAC and Jefferson Lab suggests that most features of the $x \gtrsim 1$ data can be reasonably well described in the impulse approximation with finite-$Q^2$ nuclear smearing functions for momentum transfers $Q^2 \gtrsim 1$~GeV$^2$. For the DIS region, we analyze the recent $^3$He to deuterium cross section ratio from the Jefferson Lab E03-103 experiment to explore the possible isospin dependence of the nuclear effects. We discuss the implications of this for the MARATHON experiment, and outline how a Bayesian analysis of $^3$He, $^3$H and deuterium data can robustly determine the free neutron structure function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Automated Bayesian high-throughput estimation of plasma temperature and density from emission spectroscopy

Here, this paper introduces a novel approach for automated high-throughput estimation of plasma temperature and density using atomic emission spectroscopy, integrating Bayesian inference with sophisticated physical models. We provide an in-depth examination of Bayesian methods applied to the complexities of plasma diagnostics, supported by a robust framework of physical and measurement models. Our methodology is demonstrated using experimental observations in the field of magneto-inertial fusion, focusing on individual and sequential shot analyses of the Plasma Liner Experiment at LANL. The results demonstrate the effectiveness of our approach in enhancing the accuracy and reliability of plasma parameter estimation and in using the analysis to reveal the deep hidden structure in the data. This study not only offers a new perspective of plasma analysis but also paves the way for further research and applications in nuclear instrumentation and related domains.

Bayesian inference↗

DOE OSTI2016

Bayesian analysis of the flutter margin method in aeroelasticity

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Improvement and generalization of ABCD method with Bayesian inference

To find New Physics or to refine our knowledge of the Standard Model at the LHC is an enterprise that involves many factors, such as the capabilities and the performance of the accelerator and detectors, the use and exploitation of the available information, the design of search strategies and observables, as well as the proposal of new models. We focus on the use of the information and pour our effort in re-thinking the usual data-driven ABCD method to improve it and to generalize it using Bayesian Machine Learning techniques and tools. We propose that a dataset consisting of a signal and many backgrounds is well described through a mixture model. Signal, backgrounds and their relative fractions in the sample can be well extracted by exploiting the prior knowledge and the dependence between the different observables at the event-by-event level with Bayesian tools. We show how, in contrast to the ABCD method, one can take advantage of understanding some properties of the different backgrounds and of having more than two independent observables to measure in each event. In addition, instead of regions defined through hard cuts, the Bayesian framework uses the information of continuous distribution to obtain soft-assignments of the events which are statistically more robust. To compare both methods we use a toy problem inspired by pp\to hh\to b\bar b b \bar b p p → h h → b b ‾ b b ‾ , selecting a reduced and simplified number of processes and analysing the flavor of the four jets and the invariant mass of the jet-pairs, modeled with simplified distributions. Taking advantage of all this information, and starting from a combination of biased and agnostic priors, leads us to a very good posterior once we use the Bayesian framework to exploit the data and the mutual information of the observables at the event-by-event level. We show how, in this simplified model, the Bayesian framework outperforms the ABCD method sensitivity in obtaining the signal fraction in scenarios with 1% and 0.5% true signal fractions in the dataset. We also show that the method is robust against the absence of signal. We discuss potential prospects for taking this Bayesian data-driven paradigm into more realistic scenarios.

Alvarez, Ezequiel↗

DOE OSTI2021

High-energy-density-physics measurements in implosions using Bayesian inference

Convergent high-energy-density (HED) experimental platforms are used to study matter under some of the most extreme conditions that can be produced on Earth, comparable to the interior of stars. There are many challenges in using these systems for fundamental measurements currently being addressed by new analysis methods, such as the combination of a reduced physics model and Bayesian inference, allowing a self-consistent inference of physical quantities with a robust error analysis. These methods in combination with simple (as compared to inertial confinement fusion implosions) implosion platforms, which can be modified to show sensitivity to different physical mechanisms of interest, are used to study the physical properties of matter under extreme conditions. This work discusses a subset of implosion targets for studying opacity effects, electron-ion equilibration, and thermal conductivity and, as an example, a system consisting of a thick-shelled, gas-filled laser-direct-drive implosion is used to show how a reduced model and Bayesian inference can help inform experimental design decisions such as diagnostic choice. It is shown that for this system that a combination of neutron and x-ray self-emission diagnostics is critical for constraining the details of the thermodynamic states in the system and that the conductivity exponent in a Spitzer like framework can be constrained to the 30% level in deuterium at gigabar conditions. Furthermore, this process can be applied to many HED systems to make underlying model assumptions explicit and facilitate experimental design and analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

mBEEF-vdW: Robust fitting of error estimation density functionals

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.

36 MATERIALS SCIENCE↗

DOE OSTI2015

A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems

One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or ‘spot’. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods – which involve the analysis of blur caused by a structured aperture – can be used to obtain the spot’s spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Lastly, synthetic data-sets are used to demonstrate accurate reconstruction, while real data taken with high-energy X-ray imaging systems are used to demonstrate applicability and feasibility.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Systematic Bayesian evaluation of resonance parameters in 19 Ne for the 15 O ⁡(𝛼, 𝛾)⁢ 19 Ne and 18 F ⁡(𝑝, 𝛼)⁢ 15 O reactions

Here, we present a comprehensive evaluation of the nuclear structure properties of 19 Ne using a novel and rigorous Bayesian statistical framework. Precise characterization of 19 Ne resonance parameters is critical for accurately determining reaction rates of the astrophysically significant 15 O ⁡(𝛼, 𝛾)⁢ 19 Ne and 18 F ⁡(𝑝, 𝛼)⁢ 15 O reactions, which govern breakout from the hot CNO cycle in x-ray bursts and influence 𝛾-ray emission in novae, respectively. By reconstructing likelihood functions from published experimental data—including asymmetric uncertainties and upper or lower limits—we derive posterior distributions for resonance energies, decay widths, and branching ratios. Our Bayesian approach systematically incorporates previously reported discrepancies among measurements, providing a statistically robust and consistent treatment of these uncertainties. The evaluated resonance parameters and associated uncertainties provide crucial input for stellar nucleosynthesis modeling, contributing to a refined understanding of explosive astrophysical phenomena.

Kim, Sohyun H. [Sungkyunkwan Univ., Suwon (Republi↗

DOE OSTI2021

Bayesian Spatially Varying Multi-Regularization Image Deblurring

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Since blur and noise are inevitably present in any imaging system, the images must be \deblurred" to extract the full information content. Mathematically, image deblurring is an ill-posed inverse problem that requires regularization. The regularization, in turn, has a large effect on the deblurred image: different regularization strengths, and types, lead to drastically different reconstructions. Moreover, many images contain a mixture of smooth and sharp features which suggests the use of multi-regularization, i.e., varying the type of regularization (e.g. Tikhonov or total variation) across the image. We address these issues by formulating the image deblurring problem within a hierarchical Bayesian framework in which we spatially adapt the strength of the regularization and also vary the regularization type across the image. In this way, the image itself, along with corresponding regularization strength at each pixel, are described jointly by a posterior distribution which we can sample by Markov chain Monte Carlo (MCMC) methods. We illustrate our techniques on simplified test problems and apply them to high-energy X-ray images taken at the Nevada National Security Site. Numerical tests show that our new method is robustly applicable and increases the quality of the image reconstruction when compared to other (Bayesian) methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Dark Energy Survey Year 3 results: optimized $w$CDM simulation-based inference with weak lensing map-level hybrid statistics

We present cosmological constraints from the Dark Energy Survey Year 3 (DES Y3) weak lensing data using hierarchical hybrid statistics within a Bayesian simulation-based inference framework that is based on the Gower Street simulations. To maximize the precision of the inference, we have developed a new, information-theory based, data compression of the weak lensing maps to just seven highly informative summary statistics. The hybrid scheme exploits the high information content of the power spectrum, compressing both the power spectrum and neural-based summaries that are designed to extract further information. Our simulation-based approach enables principled forward modelling of all major sources of systematic uncertainty and survey properties into realistic mock observations, including the survey mask, photometric redshift uncertainties, intrinsic galaxy alignments, multiplicative shear calibration bias, source galaxy clustering, non-Gaussian shape noise, and non-linear structure formation. The summary statistics are then used in a Bayesian simulation-based inference pipeline. The inference is validated through coverage tests and checks for robustness against baryonic feedback. Assuming a $w$CDM cosmology, our analysis yields $S_8 = 0.808 \pm 0.017$, $Ω_{\rm m} = 0.325 \pm 0.024$, and $w < -0.766$ (marginalized posterior 68 per cent credible intervals). This rigorous combination of information theory, physics- and neural network-based extreme data compression, and principled Bayesian analysis improves the figure of merit for $(Ω_{\rm m}, S_8, w)$ by 60 per cent over the previous state-of-the-art, and by almost a factor of 3 over two-point analyses of the same data. They are the most precise joint constraints on $(Ω_{\rm m}, S_8, w)$ from weak gravitational lensing data alone of any survey to date. We intend to apply this analysis to the more recent DES Y6 data.

Williamson, J. [University Coll. London]↗

DOE OSTI2014

WE-E-BRE-05: Ensemble of Graphical Models for Predicting Radiation Pneumontis Risk

Purpose: We propose a prior knowledge-based approach to construct an interaction graph of biological and dosimetric radiation pneumontis (RP) covariates for the purpose of developing a RP risk classifier. Methods: We recruited 59 NSCLC patients who received curative radiotherapy with minimum 6 month follow-up. 16 RP events was observed (CTCAE grade ≥2). Blood serum was collected from every patient before (pre-RT) and during RT (mid-RT). From each sample the concentration of the following five candidate biomarkers were taken as covariates: alpha-2-macroglobulin (α2M), angiotensin converting enzyme (ACE), transforming growth factor β (TGF-β), interleukin-6 (IL-6), and osteopontin (OPN). Dose-volumetric parameters were also included as covariates. The number of biological and dosimetric covariates was reduced by a variable selection scheme implemented by L1-regularized logistic regression (LASSO). Posterior probability distribution of interaction graphs between the selected variables was estimated from the data under the literature-based prior knowledge to weight more heavily the graphs that contain the expected associations. A graph ensemble was formed by averaging the most probable graphs weighted by their posterior, creating a Bayesian Network (BN)-based RP risk classifier. Results: The LASSO selected the following 7 RP covariates: (1) pre-RT concentration level of α2M, (2) α2M level mid- RT/pre-RT, (3) pre-RT IL6 level, (4) IL6 level mid-RT/pre-RT, (5) ACE mid-RT/pre-RT, (6) PTV volume, and (7) mean lung dose (MLD). The ensemble BN model achieved the maximum sensitivity/specificity of 81%/84% and outperformed univariate dosimetric predictors as shown by larger AUC values (0.78∼0.81) compared with MLD (0.61), V20 (0.65) and V30 (0.70). The ensembles obtained by incorporating the prior knowledge improved classification performance for the ensemble size 5∼50. Conclusion: We demonstrated a probabilistic ensemble method to detect robust associations between RP covariates and its potential to improve RP prediction accuracy. Our Bayesian approach to incorporate prior knowledge can enhance efficiency in searching of such associations from data. The authors acknowledge partial support by: 1) CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council (Grant number: 432290) and 2) The Terry Fox Foundation Strategic Training Initiative for Excellence in Radiation Research for the 21st Century (EIRR21)

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗