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DOE OSTI2025

eDNAjoint: An R package for interpreting paired or semi‐paired environmental DNA and traditional survey data in a Bayesian framework

Abstract Environmental DNA (eDNA) sampling is increasingly used in surveys of species distribution as a potentially sensitive and efficient monitoring method. Yet access to modelling tools designed specifically for interpreting this new data type lags behind its ubiquity. While occupancy modelling software has dominated the analytical landscape for eDNA data analysis of single species, this type of model may not always be the most appropriate. The rate of eDNA detection often corresponds to species density, rather than just occupancy, and researchers often have access to observations from non‐genetic sampling methods at the same sites. To provide users access to a modelling framework designed to maximize the use of all available data, we developed an R package, eDNAjoint . The package provides an easy‐to‐use interface for fitting a ‘joint’ model that integrates data from paired or semi‐paired eDNA and traditional surveys in a Bayesian framework. The model can be used to estimate parameters like the probability of a false positive eDNA detection and mean catch rate at a site, and the package allows access to multiple model variations and Bayesian prior customization. Additional functionality can be used for model selection, summarising posteriors and comparing the relative sensitivities of the two survey methods. We demonstrate the use of eDNAjoint by fitting a variation of the model with site‐level covariates that scale the sensitivity of eDNA sampling relative to traditional sampling. The example workflow uses binary eDNA and seine count data for the endangered tidewater goby ( Eucyclogobius newberryi ) from a study by Schmelzle and Kinziger (2016). This use case includes a prior sensitivity analysis and an evaluation of the relationship between detection rates and environmental variables. eDNAjoint has the potential to greatly increase the range of users who will be able to rigorously analyse eDNA and traditional survey data in a Bayesian framework, understand if and how eDNA can improve monitoring practices, and gain confidence in the interpretability of eDNA data.

Keller, Abigail G. [Department of Environment Scie↗

DOE OSTI2025

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

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 OSTI2025

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

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

58 GEOSCIENCES↗

DOE OSTI2024

Bayesian Fit for the NOvA Three Flavor Oscillation Analysis

NOvA is a long baseline neutrino oscillation experiment, using Fermilab's NuMI beam and a functionally identical near and far detector. NOvA measures muon neutrino disappearance and electron neutrino appearance to probe neutrino oscillation parameters, including the large neutrino mixing angle, the mass ordering, and the CP-violating phase. NOvA has developed a Bayesian analysis in addition to its Frequentist analysis, using Markov Chain Monte Carlo. This Bayesian framework allows for measurements previously difficult to make with the Frequentist framework, such as the Jarlskog invariant and the reactor mixing angle. The details and status of the Bayesian Framework will be presented, as well as latest NOvA results on measurements of three-flavor oscillation parameters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Improving the Parameterization of Cloud and Rain Microphysics in E3SM using Novel Observationally-Constrained Bayesian Approach (Final Technical Report)

In this project, we sought to develop new cloud and rain microphysics frameworks within the Energy Exascale Earth System Model (E3SM). This work encompassed two primary avenues of research: 1) Further development of a Bayesian-based scheme called BOSS (Bayesian Observationally-constrained Statistical-physical Scheme) to represent cloud and rain microphysics, testing it in realistic high-resolution cloud models, and implementing it in E3SM; 2) Development of a methodology utilizing machine learning to enable computationally tractable use of tractable use of Markov chain Monte Carlo sampling for Bayesian parameter estimation in Earth system and cloud models. In this project, we adapted the BOSS microphysics scheme, originally formulated for rain-only, to include all liquid-phase microphysical processes for cloud and rain, in particular the processes that mediate between these two categories, for example the conversion from cloud to rain through collision and coalescence of drops. We constrained the scheme via comparison and testing against a detailed model that explicitly represents the evolution of cloud and rain particles, called a bin microphysics scheme.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

A Bayesian approach to the long-baseline neutrino oscillation sensitivity of DUNE

The sensitivity of the Deep Underground Neutrino Experiment (DUNE) to neutrino oscillation is evaluated using a Bayesian Markov Chain Monte Carlo (MCMC) approach. This analysis uses the same underlying sensitivity inputs as previous DUNE studies [Eur. Phys. J. C 80, 978 (2020)], and therefore does not present updated DUNE sensitivities, but instead explores the additional inferences accessible using a Bayesian approach. We present four-dimensional posterior probability distributions of the oscillation parameters, highlighting the breadth of correlation in the parameter space of interest, especially between $\sin^2 θ_{23}$ and $\sin^2 θ_{13}$. We exploit the flexibility of the Bayesian framework to incorporate parameter constraints post hoc and assess the impact of applying a reactor short-baseline $θ_{13}$ constraint. A significant increase in the sensitivity to the $θ_{23}$ octant is found when including the constraint. Posterior distributions of derived quantities can be easily constructed from MCMC results. This work presents the first study of DUNE's sensitivity to the Jarlskog invariant, $J$, a quantity that provides a parametrisation-independent measure of charge-parity violation in the leptonic sector.

Abbaslu, Saeed [IPM, Tehran] (ORCID:00000003356771↗

DOE OSTI2025

Bayesian optimization of PYTHIA 8 tunes

A new tune (set of model parameters) is found for the six most important parameters of the PYTHIA 8 final state parton shower and hadronization model using Bayesian optimization. The tune fits the Large Electron-Positron collider (LEPI) data from ALEPH better than the default tune in PYTHIA 8. To the best of our knowledge, we present the most comprehensive application of Bayesian optimization to the tuning of a parton shower and hadronization model using the LEPI data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

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.

Approximate Bayesian inference↗

DOE OSTI2025

Explainable multi-fidelity Bayesian neural network for distribution system state estimation

Distribution System State Estimation (DSSE) is frequently constrained by limited real-time measurements, the uncertainties introduced by distributed energy resources, and the presence of bad data. To address them, this paper proposes an enhanced Multi-Fidelity Bayesian Neural Network (MFBNN) DSSE approach. A low-fidelity layer based on a Deep Neural Network (DNN) is first pre-trained on pseudo-measurement data to learn fundamental state features. Subsequently, a high-fidelity Bayesian Neural Network (BNN) layer leverages limited but high-quality real-time measurements to refine these features, thereby achieving accurate DSSE. Additionally, the deep SHapley Additive exPlanation (SHAP) is developed to quantify the influence of measurement data on DSSE through dual perspectives of global feature importance and local nodal contributions, establishing a hierarchical explainability framework for machine learning-based DSSE. Comparative studies conducted on the IEEE 13-bus system and a real-world 2135-node system from Dominion Energy demonstrate that the proposed method excels in estimation accuracy, even under situations of high noise levels, bad data, and missing data. Further comparisons with Weighted Least Squares (WLS) and other machine learning-based DSSE approaches verify that the proposed framework offers higher accuracy, improved interpretability, and enhanced robustness.

Bad data↗

DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗

DOE OSTI2026

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with $\mathscr{O}$ (10 9 ) parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with $\mathscr{O}$ (10 8 ) inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Determining reference standard strength for neutron-irradiated reduced activation ferritic/martensitic steel F82H by Bayesian method

The deterministic approach widely adopted in the design of structural components relies on systematically defined design limits using empirically determined safety factors. However, this approach is not always appropriate because structures are subjected to a variety of loads in the practical environment, which may result in excessively conservative design limits. In recent years, a more rigorous probabilistic approach that incorporates material strength distributions has become an important solution. In the probabilistic approach, the probability density functions of material strength properties underpin the design criteria. Here, the objective of this study is to identify the density distribution functions that best describe tensile properties of irradiated F82H to define a reference strength for DEMO design. Due to the limited number of existing data, this study specifically employs a Bayesian prediction method based on Monte Carlo simulations to determine a material reference value with statistical reliability and to investigate its effectiveness. For example, the dependence of tensile properties of 300 °C irradiated materials on irradiation damage and the range predicted by 95% Bayesian estimation was evaluated. As a statistical model for the dose dependence of statistical parameters, the normal distribution exhibited a better fit for 0.2% proof strength and tensile strength, whereas the distribution of total elongation data gave comparable reference values for both the normal and Weibull distribution models. Both models gave comparable criteria for the distribution of total elongation data. The Weibull model also gave better results for uniform elongation. The function best describing the model was a logarithmic law for both 0.2% proof strength and tensile strength, while a power law for both total and uniform elongation, which allowed for more comprehensive data prediction of irradiation data with statistical accuracy for DEMO reactor design.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Bayesian optimization of entropy-stabilized metal fluoride conversion cathodes and their synthesis

Fluoride-based conversion cathodes are promising for next-generation Li ion batteries because of their high voltage and energy densities. High entropy earth abundant fluoride cathodes are attractive for sustainable battery because of the potentially higher cycling stability. While Ni and Co containing equimolar alloys stabilized by high entropy were considered previously, Ni and Co free non-equimolar metal alloy compositions might offer new opportunities to increase materials stability and average voltage. This opportunity was pursued using Bayesian optimization of average voltage for the computational prediction of (Fe x1 Cu x2 Zn x3 Mn x4 Mg x5 )F 2 cathode chemistries. Theoretical voltage, room temperature free energy, and electronic structure of potentially high voltage compositions were computed using density functional theory calculations. Here, the experimental realization of non-equimolar quinary Co and Ni free fluorides with stable rutile single phase and improved conversion reaction voltage by up to 28 % compared to the equimolar alloy demonstrated the power of Bayesian optimization methods for the computationally guided experimental synthesis of fluoride cathodes. Finally, non-equimolar cathode chemistries were found with cycling stability superior to known multi-element fluorides.

25 ENERGY STORAGE↗

DOE OSTI2025

Bayesian Entropy Neural Networks for physics-aware prediction

This article addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.

14 SOLAR ENERGY↗

DOE OSTI2025

A Bayesian framework to investigate radiation reaction in strong fields

Recent experiments aiming to measure phenomena predicted by strong-field quantum electrodynamics (SFQED) have done so by colliding relativistic electron beams and high-power lasers. In such experiments, measurements of collision parameters are not always feasible. However, precise knowledge of these parameters is required to accurately test SFQED. Here, we present a novel Bayesian inference procedure that infers collision parameters that could not be measured on-shot. This procedure is applicable to all-optical non-linear Compton scattering experiments investigating radiation reaction. The framework allows multiple diagnostics to be combined self-consistently and facilitates the inclusion of known information pertaining to the collision parameters. Using this Bayesian analysis, the relative validity of the classical, quantum-continuous and quantum-stochastic models of radiation reaction was compared for several test cases, which demonstrates the accuracy and model selection capability of the framework and highlight its robustness if the experimental values of fixed parameters differ from their values in the models.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Investigation of Ethane Dehydrogenation and Hydrogenolysis on Pt(111), Pt(211), and Pt(100): Bayesian Quantification and Correction of DFT-Based Enthalpic and Entropic Uncertainties

Computational investigations of heterogeneously catalyzed reactions using density functional theory (DFT) are often inaccurate, largely due to uncertainties in the choice of DFT functional (enthalpic uncertainty) and approximations for modeling adsorbate movement along the catalyst surface (entropic uncertainty). This work illustrates that both uncertainties are significant in the investigation of ethane dehydrogenation (EDH) and hydrogenolysis on Pt catalysts by considering the complete deconstruction of ethane on Pt(111), Pt(211), and Pt(100) using microkinetic modeling (MKM). Hence, this work uses both noncalibrated and Bayesian-calibrated MKMs to quantify and correct inaccuracies in macroscopic properties due to both uncertainties. A Bayesian approach to the correction of entropic errors was introduced using a “Modified Fermi Function (MFF)” to calibrate between the two bounds of entropy represented by the harmonic oscillator (HO) and free translator (FT) approximations. Regardless of enthalpic and entropic uncertainties, all three surfaces are capable of ethane activation; however, Pt(211) was found to be the most active and is largely responsible for methane production. Next, Pt(111) is largely responsible for acetylene production, and Pt(100) has the highest ethylene selectivity but is most susceptible to coking. By comparison of different calibrated models, the FT entropy approximation was found to better describe EDH under typical experimental conditions. Statistical evidence was found to support Pt(111) as the active site for EDH, assuming that one single site is responsible for the chemistry. On the three surfaces, competing second dehydrogenations to CH 2 CH 2 and CH 3 CH were observed as well as isomerization of CH 3 CH back to CH 2 CH 2 and deeper dehydrogenation of CH 3 CH. In conclusion, C–C cleavage was found to largely proceed via the CH 3 C intermediate on Pt(100) and Pt(111), while on Pt(211), it was via both CHC and CH 3 C.

Bayesian model selection↗

DOE OSTI2024

Identifying Green Solvent Mixtures for Bioproduct Separation Using Bayesian Experimental Design

Liquid–liquid extraction (LLE) is a widely used technique for the separation and purification of liquid-phase products with applications in various industries, including pharmaceuticals, petrochemicals, and renewable chemistry. A critical step in the design of an LLE process is the selection of appropriate solvents. This study presents a new methodology for identifying solvent mixtures for bioproduct separation using Bayesian experimental design (BED). Motivated by the need for environmentally friendly and effective separation methods, we address the challenge of selecting solvent systems that balance separation efficiency, selectivity, and environmental impact while also tackling the difficulty of separating multiple bioproducts using complex solvent systems. Our approach specifically seeks to predict product partition coefficients (log10 Kp values) as thermodynamic parameters underlying solvent selection. The iterative approach integrates Bayesian optimization with experimental measurements to guide solvent selection and leverages COSMO-RS simulations to enhance high-throughput experimentation. Using the design of solvent systems for the separation of lignin-derived aromatic products via centrifugal partition chromatography (CPC) as a case study, we show that within seven iterations/cycles of the methodology, we can identify new mixtures of green solvents that align with CPC design principles. Furthermore, these results demonstrate the efficacy of the BED framework in optimizing green solvent systems for complex separations, highlighting the potential of this method to advance the field of green chemistry and contribute to the development of sustainable industrial processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗