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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Spike-and-Slab Shrinkage Priors for Structurally Sparse Bayesian Neural Networks

Network complexity and computational efficiency have become increasingly significant aspects of deep learning. Sparse deep learning addresses these challenges by recovering a sparse representation of the underlying target function by reducing heavily overparameterized deep neural networks. Specifically, deep neural architectures compressed via structured sparsity (e.g., node sparsity) provide low-latency inference, higher data throughput, and reduced energy consumption. In this article, we explore two well-established shrinkage techniques, Lasso and Horseshoe, for model compression in Bayesian neural networks (BNNs). To this end, we propose structurally sparse BNNs, which systematically prune excessive nodes with the following: 1) spike-and-slab group Lasso (SS-GL) and 2) SS group Horseshoe (SS-GHS) priors, and develop computationally tractable variational inference, including continuous relaxation of Bernoulli variables. We establish the contraction rates of the variational posterior of our proposed models as a function of the network topology, layerwise node cardinalities, and bounds on the network weights. Furthermore, we empirically demonstrate the competitive performance of our models compared with the baseline models in prediction accuracy, model compression, and inference latency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗
NASA NTRS2018

Augmented Reality Data Generation for Training Deep Learning Neural Network

One of the major challenges in deep learning is retrieving sufficiently large labeled training datasets, which can become expensive and time consuming to collect. A unique approach to training segmentation is to use Deep Neural Network (DNN) models with a minimal amount of initial labeled training samples. The procedure involves creating synthetic data and using image registration to calculate affine transformations to apply to the synthetic data. The method takes a small dataset and generates a highquality augmented reality synthetic dataset with strong variance while maintaining consistency with real cases. Results illustrate segmentation improvements in various target features and increased average target confidence.

Torres, Gil↗
DOE OSTI2025

Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can happen to be difficult or impossible to train accurately. Here, we present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training a longer chain, gradually increasing the expressivity of the learnt model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to learn progressively features of a solution which could have been hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

FY24 Progress Report: SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking

Algorithms for Machine Learning (ML) and data analysis for the 3013 Surveillance Program have been developed in an ongoing collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). The objective of the algorithms is to automate the identification of corrosion and crack formation in the Inner Container Closure Weld Region (ICCWR) of the canister system used to store Pu-bearing material. Data for corrosion and cracking is collected from large binary files generated by a Laser Confocal Microscope (LCM), the Wide Area 3D Measurement System (WAMS), or,in a recent proposal, by a Scanning Electron Microscope (SEM). The ML software uses the physical attributes in the data files (e.g., one or more of: height, color, and 16-bit grayscale values as functions of position in a plane projection) to detect signs of surface corrosion and cracking after being trained on similar data, with the features to be detected. Although the initial scope included screening for broader indicators of corrosion, e.g., pitting, identification of potential cracks was prioritized for the past several years at the request of program leadership. Labeled training data is essential to developing the ML algorithm, and enhancements to data labeling capability have been developed to address this essential precursor to application of ML routines. Efficient labeling is particularly important in view of the large volume of data required to train ML algorithms and the relative rarity of cracks in the ICCWR data set. The updated program will read binary data from either LCM, WAMS or SEM files, interrogate data attributes, facilitate user labeling of data for training ML algorithms, execute ML algorithms, output parameters from trained ML algorithms, report ML model accuracy with respect to labeled data, and generate graphical representations for various analyses. In FY24, hourglass neural networks (HNNs) that were initiated in FY22 were further developed and tested using available LCM data, and their performance was tested against that of the alternative U-Net Neural Network algorithm structure. HNNs along with previously developed Convolutional Neural Networks (CNNs) and Deep Neural Networks (DNNs) comprise a suite of ML tools for identification of cracks in the ICCWR

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRSDate not supplied

Runtime Monitoring for Unmanned Aerospace Systems with Neural Network Components

AI components (e.g., Deep Neural Networks) are increasingly used in unmanned Aerospace systems for safety-relevant applications. Rigorous Verification and Validation methods for such components are still in their infancy and thus, monitoring of the AI's behavior during runtime is essential. In this paper, we will present a runtime-monitoring architecture, which combines the advanced statistical analysis framework SYSAI (System Analysis using Statistical AI) with temporal and probabilistic runtime monitoring carried out by R2U2 (Realizable, Responsive, and Unobtrusive Unit). Learned statistical models of complex systems with AI components are produced by the SYSAI framework and provide detailed information to enable the R2U2 runtime monitor to efficiently perform advanced safety and performance checks in nominal and off-nominal conditions. We will present initial results of our tool set and architecture on a case study, a DNN-based autonomous centerline tracking system (ACT).

Yuning He↗
DOE OSTI2025

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗
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

Development and Evaluation of a General Drag Model for Gas-Solid Flows via Deep Learning

This project presents the development and evaluation of a general drag model for gas–solid multiphase flows using deep learning techniques. A comprehensive database of more than 4,000 experimental and numerical data points for spherical and non spherical particles was compiled, incorporating geometric features such as sphericity, aspect ratio, and orientation. Several predictive approaches—including traditional em pirical correlations, machine learning, and deep neural networks—were benchmarked, with the proposed Drag Coefficient Correlation-aided Deep Neural Network (DCC DNN) demonstrating superior accuracy. To account for particle–particle interactions, additional drag data were generated using CFD-based simulations of packed and flu idized beds, leading to the development of a retrained model capable of incorporat ing volume fraction effects. Integration of the trained model with the MFiX CFD solver was achieved using FTorch, enabling drag predictions during discrete element method (DEM) simulations. Validation against experimental data for single particles and fluidized beds confirmed the model’s improved predictive ability, particularly for non-spherical geometries. While the model performed strongly under fluidized con ditions, limitations remained in unfluidized regimes, suggesting a need for expanded datasets. Overall, this study demonstrates the feasibility of combining deep learning with physics-informed CFD to improve drag modeling for gas–solid flows, with promis ing implications for scaling multiphase simulations in industrial applications.

42 ENGINEERING↗