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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Transfer learning for analysis of collective and non-collective Thomson scattering spectra

Thomson scattering (TS) diagnostics provide reliable, minimally perturbative measurements of fundamental plasma parameters, such as electron density (⁠n e ) and electron temperature (⁠T e ⁠). Deep neural networks can provide accurate estimates of ⁠n e and T e when conventional fitting algorithms may fail, such as when TS spectra are dominated by noise, or when fast analysis is required for real-time operation. Although deep neural networks typically require large training sets, transfer learning can improve model performance on a target task with limited data by leveraging pre-trained models from related source tasks, where select hidden layers are further trained using target data. We present five architecturally diverse deep neural networks, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating n e and T e in both the collective and non-collective scattering regimes. We evaluate errors in n e and T e estimates as a function of training set size for models trained with and without transfer learning, and we observe decreases in model error from transfer learning when the training set contains ≲ 200 experimentally measured spectra.

Artificial neural networks↗
DOE OSTI2023

Fast and accurate reduced-order modeling of a MOOSE-based additive manufacturing model with operator learning

One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on existing simulation tools employed in AM. The goal of the present work is to construct a fast and accurate reduced-order model (ROM) for an AM model developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, ultimately reducing the time/cost of AM control and optimization processes. Our adoption of the operator learning (OL) approach enabled us to learn a family of differential equations produced by altering process variables in the laser’s Gaussian point heat source. More specifically, we used the Fourier neural operator (FNO) and deep operator network (DeepONet) to develop ROMs for time-dependent responses. Furthermore, we benchmarked the performance of these OL methods against a conventional deep neural network (DNN)-based ROM. Ultimately, we found that OL methods offer comparable performance and, in terms of accuracy and generalizability, even outperform DNN at predicting scalar model responses. The DNN-based ROM afforded the fastest training time. Furthermore, all the ROMs were faster than the original MOOSE model yet still provided accurate predictions. FNO had a smaller mean prediction error than DeepONet, with a larger variance for time-dependent responses. Unlike DNN, both FNO and DeepONet were able to simulate time series data without the need for dimensionality reduction techniques. Finally, the present work can help facilitate the AM optimization process by enabling faster execution of simulation tools while still preserving evaluation accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A robust deep learning workflow to predict multiphase flow behavior during geological C O 2 sequestration injection and Post-Injection periods

Simulation of multiphase flow in porous media is essential to manage the geologic CO 2 sequestration (GCS) process, and physics-based simulation approaches usually take prohibitively high computational cost due to the nonlinearity of the coupled physics. This paper contributes to the development and evaluation of a deep learning workflow that accurately and efficiently predicts the temporal-spatial evolution of pressure and CO 2 plumes during injection and post-injection periods of GCS operations. Based on a Fourier Neural Operator, the deep learning workflow takes input variables or features including rock properties, well operational controls and time steps, and predicts the state variables of pressure and CO 2 saturation. To further improve the predictive fidelity, separate deep learning models are trained for CO 2 injection and post-injection periods due to the difference in primary driving force of fluid flow and transport during these two phases. We also explore different combinations of features to predict the state variables. We use a realistic example of CO 2 injection and storage in a 3D heterogeneous saline aquifer, and apply the deep learning workflow that is trained from physics-based simulation data and emulate the physics process. Through this numerical experiment, we demonstrate that using two separate deep learning models to distinguish post-injection from injection period generates the most accurate prediction of pressure, and a single deep learning model of the whole GCS process including the cumulative injection volume of CO 2 as a deep learning feature, leads to the most accurate prediction of CO 2 saturation. For the post-injection period, it is key to use cumulative CO 2 injection volume to inform the deep learning models about the total carbon storage when predicting either pressure or saturation. The deep learning workflow not only provides high predictive fidelity across temporal and spatial scales, but also offers a speedup of 250 times compared to full physics reservoir simulation, and thus will be a significant predictive tool for engineers to manage the long-term process of GCS.

58 GEOSCIENCES↗
DOE OSTI2022

An MLIR-based Compiler Flow for System-Level Design and Hardware Acceleration

The generation of custom hardware accelerators for applications implemented within high-level productive programming frameworks requires considerable manual effort. To automate this process, we introduce \sodaopt, a compiler tool that extends the MLIR infrastructure. \sodaopt automatically searches, outlines, tiles, and pre-optimizes relevant code regions to generate high-quality accelerators through high-level synthesis. \sodaopt can support any high-level programming framework and domain-specific language that interface with the MLIR infrastructure. By leveraging MLIR, \sodaopt solves compiler optimization problems with specialized abstractions. Backend synthesis tools connect to \sodaopt through progressive intermediate representation lowerings. \sodaopt interfaces to a design space exploration engine to identify the combination of compiler optimization passes and options that provides high-performance generated designs for different backends and targets. We demonstrate the practical applicability of the compilation flow by exploring the automatic generation of accelerators for deep neural networks operators outlined at arbitrary granularity and by combining outlining with tiling on large convolution layers. Experimental results with kernels from the PolyBench benchmark show that \sodaopt high-level optimizations improve execution delays of synthesized accelerators up to 60x. We also show that for the selected kernels, our solution outperforms the current of state-of-the art in more than 70% of the benchmarks and provides better average speedup in 55% of them.

Bohm Agostini, Nicolas↗
DOE OSTI2024

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

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.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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 OSTI2025

Deep Learning–Assisted Multiobjective Optimization of Geological CO 2 Storage Performance under Geomechanical Risks

In geological CO 2 storage, designing the optimal well control strategy for CO 2 injection to maximize CO 2 storage while minimizing the associated geomechanical risks is not trivial. This challenge arises due to pressure buildup, CO 2 plume migration, the highly nonlinear nature of geomechanical responses to rock-fluid interaction, and the high computational cost associated with coupled flow and geomechanics simulations. In this paper, we introduce a novel optimization framework to address these challenges. The optimization problem is formulated as follows: maximize total CO 2 storage while minimizing geomechanical risks by adjusting the injection schedules within bounded constraints. The geomechanical risks are primarily driven by injection-induced pressure build-up, which is characterized by ground displacement and the induced microseismicity. We used the Fourier neural operator (FNO)-based deep learning model to construct surrogate models, replacing the time-consuming coupled flow and geomechanics simulations for evaluating the aforementioned objective functions. The developed surrogate models have been incorporated into a multiobjective optimization framework through a genetic algorithm to reduce the computational burden. The proposed optimization framework reduces the computational cost from approximately 2,400 hours, when using objective function evaluations based on physics-based simulations, to around 20 minutes. A set of Pareto-optimal solutions of the proposed workflow yields nontrivial optimal decisions, reducing the microseismicity potential and the vertical displacement. This Pareto front highlights the optimal trade-offs between CO 2 storage amount, safety, and ground displacement, emphasizing the need for careful optimization and management of injection strategies to achieve a balanced outcome. The novelty of this work is twofold. First, we demonstrate the importance of incorporating the minimization of the geomechanical risks as objective functions into the CO 2 storage optimization workflow to mitigate the potential risk of induced microseismicity and ground displacement. Second, we leverage the FNO-based surrogate models to optimize a real-field CO 2 storage operation.

42 ENGINEERING↗
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 OSTI2023

Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Recent advances in modeling large-scale, complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult. For these systems, often computationally inexpensive, but in general inaccurate models, known as the low-fidelity models, are available. Here in this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system's response and a low-fidelity response in the presence of a small training dataset from the true system's response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown physical systems.

MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Deep Koopman Neural Network for Analyzing High-Energy-Density Simulations of Electrical Wire Explosions

Megaampere-scale electrical wire experiments (EWEs) provide a platform for studying magnetohydrodynamic (MHD) instability growth in magneto-inertial fusion (MIF) devices. Even when nonlinear simulations of these experiments can digitally reproduce much of the experimentally observed instability growth, interpreting the results and understanding mode growth and evolution can be non-trivial. As a first step toward providing better interpretation of these simulation features, this work investigates the use of a deep neural network that uses Koopman operator theory to analyze the dynamics of pulsed-power-driven explosions of EWEs. This deep neural network is trained on 1-D resistive MHD simulations of EWEs. This neural network learns to transform the nonlinear data into a lower-dimensional representation where the time dynamics are linear. Layers of this neural network are shown to learn features of the simulations, including the locations of shock waves and different physical regimes of the simulation. Using the learned features, the network can compress a time state of the simulation consisting of 5120 data point into a 36-parameter lower-dimensional latent space embedding. Furthermore, these embeddings are shown to be clustered in the latent space by initial radius and time state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Deep Learning for Subsurface Flow: A Comparative Study of U‐Net, Fourier Neural Operators, and Transformers in Underground Hydrogen Storage

Subsurface flow research is essential for the sustainable management of natural resources and the environment. Deep learning (DL) has significantly advanced this field by developing efficient and accurate surrogate models to replace computationally expensive physics‐based simulations. These surrogate models are commonly used to predict the spatiotemporal evolution of state variables, such as gas saturation and reservoir pressure, in heterogeneous geological formations. Despite the various DL models applied to this task, there is a lack of studies systematically comparing their performance. This absence of comparative analysis leads to somewhat arbitrary DL model selection in subsurface flow research, resulting in suboptimal performance and potentially inaccurate predictions. To bridge this gap, we conduct a systematic comparison study of three popular DL architectures—U‐Net, Fourier Neural Operators (FNO), and Segmentation Transformer (SETR)—in surrogate modeling of underground hydrogen storage (UHS). We focus on UHS due to its promise of enhancing clean energy resilience and its cyclic operational conditions that represent common scenarios in various subsurface applications. We evaluate the models based on accuracy, training cost, and inference speed. The comparison shows that U‐Net achieves the highest accuracy, followed by SETR and FNO. Despite its lower accuracy, FNO has the highest inference speed. SETR offers competitive accuracy with the least training memory usage, demonstrating the potential of transformers in learning subsurface flow. Our results provide guidance for selecting DL models for surrogate modeling in a wide range of subsurface flow problems.

42 ENGINEERING↗
DOE OSTI2024

Speeding up and reducing memory usage for scientific machine learning via mixed precision

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets) stand out as the leading techniques for solving partial differential equations by incorporating both physical equations and experimental data. However, training PINNs and DeepONets require significant computational resources, including long computational times and large amounts of memory. In search of computational efficiency, training neural networks using half precision (float16) rather than the conventional single (float32) or double (float64) precision has gained substantial interest, given the inherent benefits of reduced computational time and memory consumed. However, we find that float16 cannot be applied to SciML methods, because of gradient divergence at the start of training, weight updates going to zero, and the inability to converge to a local minima. To overcome these limitations, we explore mixed precision, which is an approach that combines the float16 and float32 numerical formats to reduce memory usage and increase computational speed. Our experiments showcase that mixed precision training not only substantially decreases training times and memory demands but also maintains model accuracy. Here, we also reinforce our empirical observations with a theoretical analysis. The research has broad implications for SciML in various computational applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-time inference and extrapolation with Time-Conditioned UNet: Applications in hypersonic flows, incompressible flows, and global temperature forecasting

Neural Operators are fast and accurate surrogates for nonlinear mappings between functional spaces within training domains. Extrapolation beyond the training domain remains a grand challenge across all application areas. We present Time-Conditioned UNet (TC-UNet) as an operator learning method to solve time-dependent PDEs continuously in time without any temporal discretization, including in extrapolation scenarios. TC-UNet incorporates the temporal evolution of the PDE into its architecture by combining a parameter conditioning approach with the attention mechanism from the Transformer architecture. After training, TC-UNet makes real-time inferences on an arbitrary temporal grid. We demonstrate its extrapolation capability on a climate problem by estimating the global temperature for several years and also for inviscid hypersonic flow around a double cone. We propose different training strategies involving temporal bundling and sub-sampling. We demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals and zero-shot super-resolution time.

Deep learning↗
DOE OSTI2023

WavPool: A New Block for Deep Neural Networks

Modern deep neural networks comprise many operational layers, such as dense or convolutional layers, which are often collected into blocks. In this work, we introduce a new, wavelet-transform-based network architecture that we call the multi-resolution perceptron: by adding a pooling layer, we create a new network block, the WavPool. The first step of the multi-resolution perceptron is transforming the data into its multi-resolution decomposition form by convolving the input data with filters of fixed coefficients but increasing size. Following image processing techniques, we are able to make scale and spatial information simultaneously accessible to the network without increasing the size of the data vector. WavPool outperforms a similar multilayer perceptron while using fewer parameters, and outperforms a comparable convolutional neural network by ~ 10% on relative accuracy on CIFAR-10.

McDermott, Samuel D.↗
DOE OSTI2024

Multi-fidelity Fourier neural operator for fast modeling of large-scale geological carbon storage

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical simulators are required to train a model to accurately predict the complex physical behaviors associated with this process. In practice, the available training data are always limited in large-scale 3D problems due to the high computational cost. Therefore, we propose to use a multi-fidelity Fourier neural operator (FNO) to solve large-scale GCS problems with more affordable multi-fidelity training datasets. FNO has a desirable grid-invariant property, which simplifies the transfer learning procedure between datasets with different discretization. Here, we first test the model efficacy on a GCS reservoir model being discretized into 110 k grid cells. The multi-fidelity model can predict with accuracy comparable to a high-fidelity model trained with the same amount of high-fidelity data with 81% less data generation costs. We further test the generalizability of the multi-fidelity model on a same reservoir model with a finer discretization of 1 million grid cells. This case was made more challenging by employing high-fidelity and low-fidelity datasets generated by different geostatistical models and reservoir simulators. We observe that the multi-fidelity FNO model can predict pressure fields with reasonable accuracy even when the high-fidelity data are extremely limited. The findings of this study can help for better understanding of the transferability of multi-fidelity deep learning surrogate models.

58 GEOSCIENCES↗
DOE OSTI2020

Deep anomaly detection for industrial systems: a case study

We explore the use of deep neural networks for anomaly detection of industrial systems where the data are multivariate time series measurements. We formulate the problem as a self-supervised learning where data under normal operation are used to train a deep neural network autoregressive model, i.e., use a window of time series data to predict future data values. The aim of such a model is to learn to represent the system dynamic behavior under normal conditions, while expect higher model vs. measurement discrepancies under faulty conditions. In real world applications, many control settings are discrete in nature. In this paper, vector embedding and joint losses are employed to deal with such situations. Both LSTM and CNN based deep neural network backbones are studied on the Secure Water Treatment (SWaT) testbed datasets. Also, Support Vector Data Description (SVDD) method is adapted to such anomaly detection settings with deep neural networks. Evaluation methods and results are discussed based on the SWaT dataset along with potential pitfalls.

anomaly detection, deep neural network↗