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This presentation is on Bayesian evaluation framework for imperfect differential and integral data or models. This presentation includes a particular focus on common assumptions used in Bayesian ND evaluations. Additionally, this presentation highlights the benefits of a generalized form of the Bayes' theorem.
This presentation is on generalized Bayesian framework for evaluation of integral benchmark experiments. This presentation starts off with assumptions and approximations used with Bayes Theorem. then an overview of approximations used by ORNL codes, and Generalized Bayesian Monto Carlo (GBMC). The presentation then details out a precise framework. This presentation then concludes with considerations.
A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in Ref. [2]. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized data are perfect. 2. Normality: The prior and posterior PDF are normal. 3. Linearity: The model is linear. In this work we outline how the framework in [1] could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in [1] to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implementing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS and the stochastic method, respectively. The graphic in Figure 1 categorizes the methods discussed in terms of the assumptions that they employ to determine posterior PDFs.
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We present recent advances in the R-matrix formalism as well as the Bayesian evaluation framework for improved nuclear data evaluations. The advances in the R matrix formalism include: 1) direct processes, 2) doorway, as well as multistep, processes, and 3) various forms of the Reich-Moore approximation for eliminated capture channels. Furthermore, to address unreasonably small posterior uncertainties often encountered in nuclear data evaluations of large data sets using the conventional form of the Bayes’ theorem, we introduce imperfections (of the data or the model) as a formal evaluation tool for taming the evaluated uncertainties in harmony with Bayes’ theorem. These theoretical advances were motivated by the nuclear data evaluations of differential resolved resonance cross section data using the code SAMMY, as well as the integral benchmark experiments using the SCALE code system, being performed at Oak Ridge National Laboratory for the Nuclear Criticality Safety Program. Some pedagogical applications of the new formalism, as well as a snapshot of the SAMMY modernization efforts, will be presented.
Nuclear data evaluation methods conventionally make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.
The R-Matrix code SAMMY is a widely used nuclear data evaluation code focused on the resolved range, which includes corrections for experimental effects. The code is still mostly written in Fortran 77, and uses a memory management system suitable for the time of its initial writing (1984). A modernization effort is under way to bring the code in-line with modern software development practices. A continuous-integration testing framework was added, automating the large existing set of test cases. It is run on every commit. The memory management was updated to current standard practices suitable for modern software analysis tools. The code can be obtained from https://code.ornl.gov/RNSD/SAMMY. The resonance parameters and covariance information are now stored in C++ objects shared by SAMMY and AMPX, the processing code that generates nuclear data libraries for SCALE. This allows for easier maintenance and access to the resonance parameters inside and outside of SAMMY. This feature is already used by accessing and changing parameters in memory in the Bayesian Monte Carlo Evaluation Framework for Cross Sections Nuclear Data and Integral Benchmark Experiments project, Further plans include the switch to the ENDF reading and writing routines in AMPX, as these routines are more robust, easier to maintain, and support more features. Of note here is support for the new GNDS format. Previously it wasn’t easy to share the full covariance matrix for evaluations containing more than one isotope due to limitations on the ENDF format; this is now supported in GNDS. The data are currently available in a binary SAMMY format and can be exported to GNDS to make them more widely available and sharable. The next step will be to use the same resonance processing code at 0K in AMPX and SAMMY as one of the available Reich-Moore R-Matrix formalism. The first step toward this goal is to isolate the reconstruction into a module that takes resonance parameters as its input and does not depend on SAMMY global parameters. This goal has been achieved and it should now be possible to more easily change the resonance formalism and add enhancements as the Phenomenological R-Matrix parameterization of direct, doorway, and compound nuclear reactions discussed elsewhere on this conference. This concerted modernization and enhancement effort provides multiple advantages to the nuclear data community. It will allow parameter optimization using enhanced formalisms, including experimental effects, that better match complex experimental data. Then those evaluated parameters can immediately be passed off to AMPX to be reconstructed with the exact same cross section model and be put into a data library for subsequent testing using SCALE and the Valid Benchmark suite or other suitable benchmark suites.
We present the first results from Bayesian AnalYsis of Multiple AGN in X-rays (BAYMAX), a tool that uses a Bayesian framework to quantitatively evaluate whether a given Chandra observation is more likely a single or dual point source. Although the most robust method of determining the presence of dual active galactic nuclei (AGNs) is to use X-ray observations, only sources that are widely separated relative to the instrumentʼs point-spread function are easy to identify. It becomes increasingly difficult to distinguish dual AGNs from single AGNs when the separation is on the order of Chandraʼs angular resolution (<1″). Using likelihood models for single and dual point sources, BAYMAX quantitatively evaluates the likelihood of an AGN for a given source. Specifically, we present results from BAYMAX analyzing the lowest-mass dual AGN candidate to date, SDSS J0914+0853, where archival Chandra data shows a possible secondary AGN ∼ 0"3 from the primary. Analyzing a new 50 ks Chandra observation, results from BAYMAX shows that SDSS J0914+0853 is most likely a single AGN with a Bayes factor of 13.5 in favor of a single point source model. Further, posterior distributions from the dual point source model are consistent with emission from a single AGN. We find a very low probability of SDSS J0914+0853 being a dual AGN system with a flux ratio f>0.3 and separation r>0"3. Overall, BAYMAX will be an important tool for correctly classifying candidate dual AGNs in the literature, as well as studying the dual AGN population where past spatial resolution limits have prevented systematic analyses.
AbstractBayesian Metabolic Control Analysis (BMCA) has emerged as a promising framework for inferring metabolic control coefficients in data-limited scenarios by integrating Bayesian inference with linlog rate laws. However, its predictive accuracy and limitations remain underexplored. This study systematically evaluates BMCA’s ability to infer elasticity values, flux control coefficients (FCCs), and concentration control coefficients (CCCs) under varying data availability conditions using three synthetic metabolic network models. Our findings highlight the strengths and weaknesses of BMCA, guiding its application in metabolic engineering and emphasizing the need for methodological refinements.Author summaryUnderstanding how enzymes control metabolic pathways is crucial for optimizing biomanufacturing and synthetic biology applications. Bayesian Metabolic Control Analysis (BMCA) is a promising computational method that integrates Bayesian inference with metabolic control analysis to estimate key control parameters, even in cases with limited experimental data. However, the accuracy and limitations of BMCA remain unclear. In this study, we systematically evaluate BMCA using three synthetic metabolic networks to determine how different types of physiological data impact its predictive performance. We find that BMCA requires flux and enzyme concentration data for accurate predictions, while external metabolite concentrations contribute little. Additionally, BMCA fails to predict elasticity values beyond a magnitude of 1.5 and reliably infer allosteric regulation, even when strong regulatory interactions exist. In addition, BMCA does not accurately rank metabolic control points, which may limit its utility in identifying key enzymes in engineered pathways. Our work provides practical insights into when and how BMCA can be applied, guiding future research in metabolic modeling and control analysis.
In this work, generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We perform inverse modeling and compute the posterior distribution of the critical hydrological parameters that are subject to great uncertainty in the Community Land Model (CLM) for a given value of the output LH. The unknown parameters include those that have been identified as the most influential factors on the simulations of surface and subsurface runoff, latent and sensible heat fluxes, and soil moisture in CLM4.0. We set up the inversion problem in the Bayesian framework in two steps: (i) building a surrogate model expressing the input–output mapping, and (ii) performing inverse modeling and computing the posterior distributions of the input parameters using observation data for a given value of the output LH. The development of the surrogate model is carried out with a Bayesian procedure based on the variable selection methods that use gPC expansions. Our approach accounts for bases selection uncertainty and quantifies the importance of the gPC terms, and, hence, all of the input parameters, via the associated posterior probabilities.
We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.
Bayesian Metabolic Control Analysis (BMCA) is a promising framework for inferring metabolic control coefficients in data-limited scenarios, combining Bayesian inference with linear-logarithmic (lin-log) rate laws. These metabolic control coefficients quantify how changes in enzyme activities affect steady-state fluxes and metabolite concentrations across a metabolic network. However, its predictive accuracy and limitations remain underexplored. This study systematically evaluates BMCA’s ability to infer elasticity values, flux control coefficients (FCC), and concentration control coefficients (CCC) under varying data availability conditions using three synthetic metabolic network models. We demonstrate that BMCA predictions are highly dependent on the inclusion of flux and enzyme concentration data, with the omission of these datasets leading to severe inaccuracies. In our synthetic, enzyme-perturbation datasets, external metabolite concentrations had minimal impact and, in some cases, their exclusion improved predictions; when external-nutrient perturbations were introduced and those concentrations were observed, gains were at most modest. Additionally, we find that posterior estimation with both ADVI and HMC can underestimate large-magnitude elasticities in our synthetic settings, with ADVI showing somewhat higher variance under strong up-regulation; thus, recovering |elasticity| ≳ 1.5 remains challenging regardless of the inference engine. ADVI also fails to accurately infer allosteric interactions, even when regulatory effects are strong. While BMCA maintains reasonable accuracy in partially recovering the rankings of the highest FCC values, its estimates of absolute values remain constrained by prior assumptions and data limitations. Our findings reveal the BMCA algorithm’s strengths and weaknesses, providing guidance on its application in metabolic engineering, and highlighting the need for methodological refinements to enhance its predictive capabilities.
In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.
We present progress in utilizing a machine learning (ML) assisted optimization framework to study the trends in a parameter space defined by spectrally shaped, high-intensity, petawatt-class (8 J, 45 fs) laser pulses interacting with solid targets and give the first simulation-based overview of predicted trends. A neural network (NN) incorporating uncertainty quantification is trained to predict the number of hot electrons generated by the laser–target interaction as a function of pulse shaping parameters. The predictions of this NN serve as the basis function for a Bayesian optimization framework to navigate this space. For post-experimental evaluation, we compare two separate neural network (NN) models. One is based solely on data from experiments, and the other is trained only on ensemble particle-in-cell simulations. Reviewing the predicted and observed trends across the experiment-capable laser parameter search space, we find that both ML models predict a maximal increase in hot electron generation at a level of approximately 12%–18%; however, no statistically significant enhancement was observed in experiments. On direct comparison of the NN models, the average discrepancy is 8.5%, with a maximum of 30%. Since shot-to-shot fluctuations in experiments affect the observations, we evaluate the behavior of our optimization framework by performing virtual experiments that vary the number of repeated observations and the noise levels. Here, we discuss the implications of such a framework for future autonomous exploration platforms in high-repetition-rate experiments.
The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.
The widespread integration of deep neural networks in developing data-driven surrogate models for high-fidelity simulations of complex physical systems highlights the critical necessity for robust uncertainty quantification techniques and credibility assessment methodologies, ensuring the reliable deployment of surrogate models in consequential decision-making. Here, this study presents the Occam Plausibility Algorithm for surrogate models (OPAL-surrogate), providing a systematic framework to uncover predictive neural network-based surrogate models within the large space of potential models, including various neural network classes and choices of architecture and hyperparameters. The framework is grounded in hierarchical Bayesian inferences and employs model validation tests to evaluate the credibility and prediction reliability of the surrogate models under uncertainty. Leveraging these principles, OPAL-surrogate introduces a systematic and efficient strategy for balancing the trade-off between model complexity, accuracy, and prediction uncertainty. The effectiveness of OPAL-surrogate is demonstrated through two modeling problems, including the deformation of porous materials for building insulation and turbulent combustion flow for ablation of solid fuels within hybrid rocket motors.
Applications of new techniques in machine learning are speeding up progress in research in various fields. In this work, we construct and evaluate a deep neural network (DNN) to be used within a Bayesian statistical framework as a faster and more reliable alternative to the Gaussian process (GP) emulator of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate beam energies. We found strong evidence of the DNN being able to emulate the IBUU simulator's prediction on the strengths of protons' directed and elliptical flow very efficiently even with small training datasets and with accuracy about ten times higher than the GP. Here, limitations of our present work and future improvements are also discussed.
While the fabrication of graded materials by directed energy deposition (DED) has led to accelerated materials discovery, the ability to rapidly explore sufficiently large material composition spaces is limited due to the time-intensive nature of conventional materials characterization techniques. The present study investigates the viability of small punch test (SPT) protocols for rapidly evaluating DED-fabricated alloy mixtures of stainless steel 316L (316L) and Inconel 625 (IN625). The SPT protocols evaluated in this study include both the recently established two-step Bayesian estimation framework as well as the empirical relationships established in prior literature. It is shown that these protocols are capable of reliably and quantitatively tracking the changes in the mechanical properties of the alloy mixtures studied. Enhancement of mechanical properties was observed with the addition of IN625 to 316L, which is attributed to the austenite stabilization in the matrix and the formation of fine δ - Ni3Nb precipitates. It is shown that CALPHAD-based Scheil model simulations predicted the formation of different precipitate phases for each composition. The novel protocols presented in this paper open new avenues for high throughput material explorations for additive manufacturing.