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The Sensitivity of Variational Bayesian Neural Network Performance to Hyperparameters

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for model training (such as those made in variational inference) and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for variational BNNs by performing a global sensitivity analysis of variational BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of variational BNNs in real-world applications, we suggest that thorough hyperparameter tuning, including tuning of prior hyperparameters and loss function parameters, is essential for accurate UQ in variational BNNs.

97 MATHEMATICS AND COMPUTING

Jensen–Shannon divergence based novel loss functions for Bayesian neural networks

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback–Leibler (KL) divergence-based variational inference used in BNNs suffer from unstable optimization and challenges in approximating light-tailed posteriors due to the unbounded nature of the KL divergence. To resolve these issues, we formulate a novel loss function for BNNs based on a new modification to the generalized Jensen–Shannon (JS) divergence, which is bounded. In addition, we propose a Geometric JS divergence-based loss, which is computationally efficient since it can be evaluated analytically. We found that the JS divergence-based variational inference is intractable, and hence employed a constrained optimization framework to formulate these losses. Our theoretical analysis and empirical experiments on multiple regression and classification data sets suggest that the proposed losses perform better than the KL divergence-based loss, especially when the data sets are noisy or biased. Specifically, there are approximately 5% and 8% improvements in accuracy for a noise-added CIFAR-10 dataset and a regression dataset, respectively. There is about 13% reduction in false negative predictions of a biased histopathology dataset. Additionally, we quantify and compare the uncertainty metrics for the regression and classification tasks.

97 MATHEMATICS AND COMPUTING

Advanced Semi-Supervised Learning with Uncertainty Estimation for Phase Identification in Distribution Systems

The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION

Advanced Semi-Supervised Learning With Uncertainty Estimation for Phase Identification in Distribution Systems

The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION

Deep inference of simulated strong lenses in ground-based surveys

The large number of strong lenses discoverable in future astronomical surveys will likely enhance the value of strong gravitational lensing as a cosmic probe of dark energy and dark matter. However, leveraging the increased statistical power of such large samples will require further development of automated lens modeling techniques. We show that deep learning and simulation-based inference (SBI) methods produce informative and reliable estimates of parameter posteriors for strong lensing systems in ground-based surveys. We present the examination and comparison of two approaches to lens parameter estimation for strong galaxy-galaxy lenses — Neural Posterior Estimation (NPE) and Bayesian Neural Networks (BNNs). We perform inference on 1-, 5-, and 12-parameter lens models for ground-based imaging data that mimics the Dark Energy Survey (DES). We find that NPE outperforms BNNs, producing posterior distributions that are more accurate, precise, and well-calibrated for most parameters. For the 12-parameter NPE model, the calibration is consistently within <10% of optimal calibration for all parameters, while the BNN is rarely within 20% of optimal calibration for any of the parameters. Similarly, residuals for most of the parameters are smaller (by up to an order of magnitude) with the NPE model than the BNN model. This work takes important steps in the systematic comparison of methods for different levels of model complexity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Physics-based hybrid machine learning for critical heat flux prediction with uncertainty quantification

Critical heat flux (CHF) is a key quantity in nuclear system modeling due to its impact on heat transfer, safety margins, and reactor performance. This study develops and validates an uncertainty-aware hybrid modeling approach that combines machine learning with physics-based models to predict CHF in cases of dryout. The Biasi and Bowring empirical correlations were paired with three ML uncertainty quantification (UQ) techniques: deep neural network (DNN) ensembles, Bayesian neural networks (BNNs), and deep Gaussian processes (DGPs). A pure ML model without a base model was evaluated for comparison. Model performance was assessed under plentiful (7,350 points) and limited (9 points) training data scenarios using parity, uncertainty distributions, and calibration curves. Results show that the Biasi hybrid DNN ensemble achieved the best overall performance, with a mean absolute relative error of 1.846%, and well-calibrated uncertainty estimates. The BNN-based hybrids showed slightly higher error (2.14%) but superior uncertainty calibration. DGP models underperformed, with over 6% error and poor uncertainty calibration. All hybrid models outperformed pure machine learning configurations, demonstrating resistance against data scarcity. These findings indicate that hybrid modeling significantly improves predictive accuracy, interpretability, and resilience to data scarcity. The integration of uncertainty awareness provides actionable confidence in CHF predictions, which is vital for safety-critical decisions in nuclear applications. This hybrid approach offers a viable pathway for deploying ML models in reactor analysis tools while preserving domain knowledge and physical consistency.

22 GENERAL STUDIES OF NUCLEAR REACTORS

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.

97 MATHEMATICS AND COMPUTING

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