SEARCH · Search NASA
Results for “deep bayesian neural networks”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Native Implementation of TensorFlow-Trained Deep and Bayesian Neural Networks in Fortran
Explore the source record for details and available documents.
A Framework for the Analysis of Deep Neural Networks in Autonomous Aerospace Applications using Bayesian Statistics
Deep Neural Networks (DNNs) are considered to be key components in many autonomous systems. Applications range from vision-based obstacle avoidance to intelligent/learning control and planning. Safety-critical applications as found in the aerospace domain require that the behavior of the DNN is validated and tested rigorously for safety of the autonomous system (AUS). In this paper, we present a framework to support testing of DNNs and the analysis of the network structure. Our framework employs techniques from statistical modeling and active learning to effectively generate test cases for DNN safety testing and performance analysis. We will present results of a case study on a physics-based Deep recurrent residual neural network (DR-RNN), which has been trained to emulate the aerodynamics behavior of a fixed-wing aircraft.
Posterior Regularized Bayesian Neural Network incorporating soft and hard knowledge constraints
Neural Networks (NNs) have been widely used in supervised learning due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. Furthermore, the experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.
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.
Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?
Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.
Uncertainty quantification of a deep learning fuel property prediction model
Deep learning models are being widely used in the field of combustion. Given the black-box nature of typical neural network based models, uncertainty quantification (UQ) is critical to ensure the reliability of predictions as well as the training datasets, and for a principled quantification of noise and its various sources. Deep learning surrogate models for predicting properties of chemical compounds and mixtures have been recently shown to be promising for enabling data-driven fuel design and optimization, with the ultimate goal of improving efficiency and lowering emissions from combustion engines. In this study, UQ is performed for a multi-task deep learning model that simultaneously predicts the research octane number (RON), Motor Octane Number (MON), and Yield Sooting Index (YSI) of pure components and multicomponent blends. The deep learning model is comprised of three smaller networks: Extractor 1, Extractor 2, and Predictor, and a mixing operator. The molecular fingerprints of individual components are encoded via Extractor 1 and Extractor 2, the mixing operator generates fingerprints for mixtures/blends based on linear mixing operation, and the predictor maps the fingerprint to the target properties. Two different classes of UQ methods, Monte Carlo ensemble methods and Bayesian neural networks (BNNs), are employed for quantifying the epistemic uncertainty. Combinations of Bernoulli and Gaussian distributions with DropConnect and DropOut techniques are explored as ensemble methods. All the DropConnect, DropOut and Bayesian layers are applied to the predictor network. Aleatoric uncertainty is modeled by assuming that each data point has an independent uncertainty associated with it. The results of the UQ study are further analyzed to compare the performance of BNN and ensemble methods. Although this study is confined to UQ of fuel property prediction, the methodologies are applicable to other deep learning frameworks that are being widely used in the combustion community.
DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories
This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.
Uncertainty Quantification for the Image Segmentation Task [Slides]
This report provides information about image segmentation, including challenges, experiment results and future efforts.
Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors
With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.
Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling
Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.
Semi-supervised Bayesian Low-shot Learning
Deep neural networks (NNs) typically outperform traditional machine learning (ML) approaches for complicated, non-linear tasks. It is expected that deep learning (DL) should offer superior performance for the important non-proliferation task of predicting explosive device configuration based upon observed optical signature, a task which human experts struggle with. However, supervised machine learning is difficult to apply in this mission space because most recorded signatures are not associated with the corresponding device description, or “truth labels.” This is challenging for NNs, which traditionally require many samples for strong performance. Semi-supervised learning (SSL), low-shot learning (LSL), and uncertainty quantification (UQ) for NNs are emerging approaches that could bridge the mission gaps of few labels and rare samples of importance. NN explainability techniques are important in gaining insight into the inferential feature importance of such a complex model. In this work, SSL, LSL, and UQ are merged into a single framework, a significant technical hurdle not previously demonstrated. Exponential Average Adversarial Training (EAAT) and Pairwise Neural Networks (PNNs) are chosen as the SSL and LSL methods of choice. Permutation feature importance (PFI) for functional data is used to provide explainability via the Variable importance Explainable Elastic Shape Analysis (VEESA) pipeline. A variety of uncertainty quantification approaches are explored: Bayesian Neural Networks (BNNs), ensemble methods, concrete dropout, and evidential deep learning. Two final approaches, one utilizing ensemble methods and one utilizing evidential learning, are constructed and compared using a well-quantified synthetic 2D dataset along with the DIRSIG Megascene.
Efficient Subset Simulation using Hamiltonian Neural Network enhanced Markov Chain Monte Carlo Methods
The Monte Carlo method delivers an unbiased estimate of the probability of failure. However, the variance of the estimate depends on the number of evaluated samples. This number must be very large for estimations of a low probability of failure. If the evaluation of each sample is computationally expensive, the crude Monte Carlo simulation strategy is impracticable. Therefore, subset simulations are used to reduce the required number of evaluations. Subset simulations require a Markov Chain Monte Carlo sampler, such as the random walk Metropolis-Hastings algorithm. The algorithm, however, struggles with sampling in low-probability regions, especially if they are narrow. As a consequence, advanced Markov Chain Monte Carlo simulations have been developed. In particular, the Hamiltonian Monte Carlo method explores the target distribution rapidly. Driven by the idea of Hamiltonian dynamics, this sampler provides a non-random walk through the target distribution. The incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results for reliability analysis. One downside of the Hamiltonian Monte Carlo method is that gradient evaluations are computationally expensive, especially when dealing with high-dimensional problems and evaluating long trajectories. We show that integrating Hamiltonian neural networks in Hamiltonian Monte Carlo simulations significantly speeds up the sampling task. Furthermore, the enhancement of adaptive trajectory length within the Hamiltonian Monte Carlo results in the efficient proposal of the following states. Based on this recent enhancement, we provide a fast sampling strategy for subset simulations using Hamiltonian neural networks to replace the evaluation of the gradient and significantly speed up the Hamiltonian Monte Carlo simulation.
Lowering the computational barrier: Partially Bayesian neural networks for transparency in medical imaging AI
Deep Neural Networks (DNNs) can provide clinicians with fast and accurate predictions that are highly valuable for high-stakes medical decision-making, such as in brain tumor segmentation and treatment planning. However, these models largely lack transparency about the uncertainty in their predictions, potentially giving clinicians a false sense of reliability that may lead to grave consequences in patient care. Growing calls for Transparent and Responsible AI have promoted Uncertainty Quantification (UQ) to capture and communicate uncertainty in a systematic and principled manner. However, traditional Bayesian UQ methods remain prohibitively costly for large, million-dimensional tumor segmentation DNNs such as the U-Net. In this work, we discuss a computationally-efficient UQ approach via the partially Bayesian neural networks (pBNN). In pBNN, only a single layer, strategically selected based on gradient-based sensitivity analysis, is targeted for Bayesian inference. We illustrate the effectiveness of pBNN in capturing the full uncertainty for a 7.8-million parameter U-Net. We also demonstrate how practitioners and model developers can use the pBNN's predictions to better understand the model's capabilities and behavior.
Bayesian Inference with Latent Hamiltonian Neural Networks (L-HNNs)
When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS). However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice. We propose Hamiltonian neural networks (HNNs) with HMC and NUTS for solving Bayesian inference problems [1, 2]. Once trained, HNNs do not require gradients of the target density while sampling. Moreover, they satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well suited for use within HMC and NUTS because stationarity can be shown. We also propose an HNN extension called latent HNNs (L-HNNs), which predict latent variable outputs. Compared to HNNs, L-HNNs offer improved expressivity and a reduction in integration errors. Finally, we propose employing L-HNNs in NUTS with an online error monitoring scheme to prevent degeneracy of the sampling in regions of low probability density. We demonstrate L-HNNs in NUTS with online error monitoring by using several example cases involving complex, heavy-tailed, and high local curvature probability densities. Overall, L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring improved the effective sample size (ESS) per gradient by an order of magnitude.
Learning functional priors and posteriors from data and physics
In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.
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.
Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination
Post-training model compression can reduce the inference costs of deep neural networks, but uncompressed training still consumes enormous hardware resources and energy. To enable low-energy training on edge devices, it is highly desirable to directly train a compact neural network from scratch with a low memory cost. Low-rank tensor decomposition is an effective approach to reduce the memory and computing costs of large neural networks. However, directly training low-rank tensorized neural networks is a very challenging task because it is hard to determine a proper tensor rank a priori, and the tensor rank controls both model complexity and accuracy. Here, this paper presents a novel end-to-end framework for low-rank tensorized training. We first develop a Bayesian model that supports various low-rank tensor formats (e.g., CANDECOMP/PARAFAC, Tucker, tensor-train, and tensor-train matrix) and reduces neural network parameters with automatic rank determination during training. Then we develop a customized Bayesian solver to train large-scale tensorized neural networks. Our training methods shows orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the experiments. On a very large deep learning recommendation system with over 4.2 ×10 9 model parameters, our method can reduce the parameter number to 1.6 ×10 5 automatically in the training process (i.e., by 2.6 ×10 4 times) while achieving almost the same accuracy. Code is available at https://github.com/colehawkins/bayesian-tensor-rank-determination.