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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 OSTI2020

Solving differential equations using deep neural networks

Recent work on solving partial differential equations (PDEs) with deep neural networks (DNNs) is presented. The paper reviews and extends some of these methods while carefully analyzing a fundamental feature in numerical PDEs and nonlinear analysis: irregular solutions. First, the Sod shock tube solution to the compressible Euler equations is discussed and analyzed. This analysis includes a comparison of a DNN-based approach with conventional finite element and finite volume methods, and demonstrates that the DNN is competitive in terms of degrees of freedom required for a given accuracy. Further, the DNN-based approach is extended to consider performance improvements and simultaneous parameter space exploration. Next, a shock solution to compressible magnetohydrodynamics (MHD) is solved for, and used in a scenario where experimental data is utilized to enhance a PDE system that is a priori insufficient to validate against the observed/experimental data. This is accomplished by enriching the model PDE system with source terms that are then inferred via supervised training with synthetic experimental data. The resulting DNN framework for PDEs enables straightforward system prototyping and natural integration of large data sets (be they synthetic or experimental), all while simultaneously enabling single-pass exploration of an entire parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A Bayesian Learning Approach to Wireless Outdoor Heatmap Construction using Deep Gaussian Process

We present a novel Bayesian learning approach to outdoor radio heatmap construction utilizing deep Gaussian process (GP). The proposed approach employs a two-layer hierarchy which consists of two cascaded Gaussian processes that are capable of modeling more complex input-output relations than standard single-layer Gaussian processes. Since deriving the exact model likelihood is challenging, a lower bound is optimized instead so that gradient descent-based methods can be performed to find out the optimal model parameters. Typically, inducing points are used in GPs to facilitate low-rank approximation of covariance (kernel) matrices for computation speedup. However, the inaccuracy induced by inducing points can accumulate when stacking multiple layers of GP which may hinder the performance of deep GP. Moreover, since inducing points need to be learned, having them at all layers of deep GP also incurs computational burden. To overcome the above challenges, in contrast to the canonical deep GP model, we use a modified architecture where a full standard GP resides in the first layer and inducing points are only introduced for the second layer. This modified architecture strikes a balance between model accuracy and training complexity. In the proposed model, the noise parameter of the first GP layer is also eliminated to improve the training efficiency as the noise parameter at the output of the second layer suffices to model the uncertainty in the output. The proposed approach is evaluated on real-world datasets, in the form of location-Received Signal Strength (RSS) pairs, collected from the Platform for Open Wireless Data-driven Experimental Research (POWDER) located at the campus of the University of Utah. Experiment results show that the proposed approach can achieve smaller prediction errors on various training and testing data configurations than DNN-based and GP-based methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simultaneous energy and mass calibration of large-radius jets with the ATLAS detector using a deep neural network

The energy and mass measurements of jets are crucial tasks for the Large Hadron Collider experiments. This paper presents a new calibration method to simultaneously calibrate these quantities for large-radius jets measured with the ATLAS detector using a deep neural network (DNN). To address the specificities of the calibration problem, special loss functions and training procedures are employed, and a complex network architecture, which includes feature annotation and residual connection layers, is used. The DNN-based calibration is compared to the standard numerical approach in an extensive series of tests. The DNN approach is found to perform significantly better in almost all of the tests and over most of the relevant kinematic phase space. In particular, it consistently improves the energy and mass resolutions, with a 30% better energy resolution obtained for transverse momenta $p$ T > $500$ GeV.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Graph interpolating activation improves both natural and robust accuracies in data-efficient deep learning

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning (DL) research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high-dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace–Beltrami equation on a high-dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation integrates the advantages of both deep learning and manifold learning. Compared to the conventional DNNs with the softmax function as output activation, the new framework demonstrates the following major advantages: First, it is better applicable to data-efficient learning in which we train high capacity DNNs without using a large number of training data. Second, it remarkably improves both natural accuracy on the clean images and robust accuracy on the adversarial images crafted by both white-box and black-box adversarial attacks. Third, it is a natural choice for semi-supervised learning. This paper is a significant extension of our earlier work published in NeurIPS, 2018. For reproducibility, the code is available at https://github.com/BaoWangMath/DNN-DataDependentActivation .

Mathematics↗
DOE OSTI2022

DNN-based policies for stochastic AC OPF

We report a prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF formulations consider simple control policies such as affine policies that are mathematically simple and resemble many policies used in current practice. Motivated by the efficacy of machine learning (ML) algorithms and the potential benefits of general control policies for cost and constraint enforcement, we put forth a deep neural network (DNN)-based policy that predicts the generator dispatch decisions in real time in response to uncertainty. The weights of the DNN are learnt using stochastic primal–dual updates that solve the SOPF without the need for prior generation of training labels and can explicitly account for the feasibility constraints in the SOPF. The advantages of the DNN policy over simpler policies and their efficacy in enforcing safety limits and producing near optimal solutions are demonstrated in the context of a chance constrained formulation on a number of test cases.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

In this paper, we present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available and allows for training DNNs when no direct measurements of the functions of interest are available. We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods. For the non-linear diffusion PDE model with a fully unknown constitutive relationship (i.e., no measurements of constitutive relationship are available), the physics informed DNN method can accurately estimate the non-linear constitutive relationship based on state measurements only. Finally, we demonstrate that the proposed method remains accurate in the presence of measurement noise.

42 ENGINEERING↗
DOE OSTI2025

Predicting critical heat flux with uncertainty quantification and domain generalization using conditional variational autoencoders and deep neural networks

Deep generative models (DGMs) can generate synthetic data samples that closely resemble the original dataset, addressing data scarcity. In this work, we developed a conditional variational autoencoder (CVAE) to augment critical heat flux (CHF) data used for the 2006 Groeneveld lookup table. To compare with traditional methods, a fine-tuned deep neural network (DNN) regression model was evaluated on the same dataset. Both models achieved small mean absolute relative errors, with the CVAE showing more favorable results. Uncertainty quantification (UQ) was performed using repeated CVAE sampling and DNN ensembling. The DNN ensemble improved performance over the baseline, while the CVAE maintained consistent results with less variability and higher confidence. Both models achieved small errors inside and outside the training domain, with slightly larger errors outside. Altogether, the CVAE performed better than the DNN in predicting CHF and exhibited better uncertainty behavior.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Towards Low-Overhead Resilience for Data Parallel Deep Learning

Data parallel techniques have been widely adopted both in academia and industry as a tool to enable scalable training of deep learning models. At scale, DL training jobs can fail due to software or hardware bugs, may need to be preempted or terminated due to unexpected events, or may perform suboptimally because they were misconfigured. Under such circumstances, there is a need to recover and/or reconfigure data-parallel DL training jobs on-the-fly, while minimizing the impact on the accuracy of the DNN model and the runtime overhead. In this regard, state-of-art techniques adopted by the HPC community mostly rely on checkpoint-restart, which inevitably leads to loss of progress, thus increasing the runtime overhead. In this paper we explore alternative techniques that exploit the properties of modern deep learning frameworks (overlapping of gradient averaging and weight updates with local gradient computations through pipeline parallelism) to reduce the overhead of resilience/elasticity. To this end we introduce a failure simulation framework and two resilience strategies (immediate mini-batch rollback and lossy forward recovery), which we study compared with checkpoint-restart approaches in a variety of settings in order to understand the trade-offs between the accuracy loss of the DNN model and the runtime overhead.

data-parallel training↗
DOE OSTI2021

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

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↗
DOE OSTI2023

Efficient learning of power grid voltage control strategies via model-based deep reinforcement learning

Here this article proposes a model-based deep reinforcement learning (DRL) method to design emergency control strategies for short-term voltage stability problems in power systems. Recent advances show promising results for model-free DRL-based methods in power systems control problems. But in power systems applications, these model-free methods have certain issues related to training time (clock time) and sample efficiency; both are critical for making state-of-the-art DRL algorithms practically applicable. DRL-agent learns an optimal policy via a trial-and-error method while interacting with the real-world environment. It is also desirable to minimize the direct interaction of the DRL agent with the real-world power grid due to its safety-critical nature. Additionally, the state-of-the-art DRL-based policies are mostly trained using a physics-based grid simulator where dynamic simulation is computationally intensive, lowering the training efficiency. We propose a novel model-based DRL framework where a deep neural network (DNN)-based dynamic surrogate model (SM), instead of a real-world power grid or physics-based simulation, is utilized within the policy learning framework, making the process faster and more sample efficient. However, having stable training in model-based DRL is challenging because of the complex system dynamics of large-scale power systems. We addressed these issues by incorporating imitation learning to have a warm start in policy learning, reward-shaping, and multi-step loss in surrogate model training. Finally, we achieved 97.5% reduction in samples and 87.7% reduction in training time for an application to the IEEE 300-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Deep Learning-Assisted Real-Time Forward Modeling of Electromagnetic Logging in Complex Formations

Higher dimensional (i.e., 2-D and 3-D) modeling is indispensable to correctly evaluate the responses of electromagnetic logging tools in complex formation environments. However, limited by the high computational cost of rigorous modeling such as finite difference method and the finite element method, the real-time applications in the well logging industry primarily rely on the 1-D forward solver, which would result in erroneous formation evaluation for complex scenarios. As a result, aiming at realizing fast modeling for electromagnetic logging tools in complex formations, this paper proposes a general framework assisted by deep neural networks (DNNs). The framework consists of three modules: earth model classification, parameter extraction, and surrogate construction. Separate DNNs are trained and tested for different modules. The accuracy and efficiency of the DNN assisted fast modeling are validated by several experiments. Here, this study finds that the fast modeling assisted by DNNs is able to calculate the tool responses and reconstruct the subsurface formations in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A DNN surrogate unsteady aerodynamic model for wind turbine loads calculations

A recurrent deep-neural network (DNN) surrogate model capable of modeling the unsteady aerodynamic response and dynamic stall behavior of wind turbine blades has been developed and validated for use in engineering design codes. The model is trained using a subset of the oscillating airfoil experiments conducted at the Ohio State University wind tunnel. The predictions from our DNN model show excellent agreement with the measured data and, in all cases, a marked improvement over the state-of-the-art unsteady aerodynamic models. The DNN-based unsteady aerodynamics model was integrated with OpenFAST to perform full-turbine load computations for the NREL-5MW rotor. The largest differences are observed for the inboard stations, particularly in the pitching moment response, when using the new surrogate model compared to the other models available in OpenFAST.

17 WIND ENERGY↗
DOE OSTI2022

Enhanced physics-constrained deep neural networks for modeling vanadium redox flow battery

Numerical simulation has become indispensable in advancing cost-effective process optimization and control of flow batteries. We propose an enhanced version of the physics-constrained deep neural network (PCDNN) approach to provide high-accuracy voltage predictions in the vanadium redox flow batteries (VRFBs). The purpose of the PCDNN approach is to enforce the physics-based zero-dimensional (0D) VRFB model in a neural network to assure model generalization for various battery operation conditions. However, limited by the simplifications of the 0D model, the PCDNN cannot capture sharp voltage changes in the extreme SOC regions. To improve the accuracy of voltage prediction at extreme ranges, we introduce a second (enhanced) DNN to mitigate the prediction errors carried from the 0D model itself and call the resulting approach enhanced PCDNN (ePCDNN). By comparing with experimental data, we demonstrate that the ePCDNN approach can accurately capture the voltage response throughout the charge–discharge cycle, including the tail region of the voltage discharge curve. The loss function for training the ePCDNN is designed to be flexible by adjusting the weights of the physics-constrained DNN and the enhanced DNN. In conclusion, this allows the ePCDNN framework to be transferable to battery systems with variable physical model fidelity.

25 ENERGY STORAGE↗
DOE OSTI2025

Resistive Switching of Spinel Li 4 Ti 5 O 12 Lithium-Ion Battery Material for Neuromorphic Computing

The rapid rise of AI has exposed significant limitations in conventional Von Neumann computing architecture, particularly in regard to speed and energy efficiency. To address these challenges, researchers are exploring a brain-inspired neuromorphic architecture that mimics biological neural networks, enabling massive parallel processing with reduced power consumption for complex AI computational demands. Recent interest has focused on utilizing battery electrodes and solid electrolyte materials for their resistive switching properties in developing a neuromorphic architecture. These properties are precisely tuned through local- and bulk-level chemical composition modifications via voltage bias stimuli. In this study, we demonstrate fabricating a three-terminal lithium-ion electrochemical transistor based on lithium titanium oxide (Li 4 Ti 5 O 12 ), a popular lithium-ion battery anode material. We deposited and characterized LTO thin films using RF sputtering, demonstrating a 6 orders of magnitude increase in electronic conductivity upon lithiation, with conductivity plateauing after 20% lithiation. Density functional theory calculations revealed transformation from the insulating to conducting state, supported by experimental characterization through X-Ray Photoelectron Spectroscopy (XPS) and Direct Current (DC) polarization analyses. The fabricated transistor consisted of LTO as the channel layer, gold as source/drain terminals, lithium phosphorus oxynitride (LiPON) as the lithium-ion conductor, and copper as the gate terminal. The device exhibited clear hysteresis in transfer characteristics due to lithium insertion/extraction processes. Long-term potentiation (LTP) and long-term depression (LTD) measurements showed an asymmetric ratio of 1.425 and maximum/minimum conductance ratio of 7.83. When implemented in a deep neural network (DNN) for MNIST handwritten digit recognition, the device achieved 92.03% accuracy over 20 training epochs. Detailed transport mechanism analysis revealed the crucial role of oxygen vacancies and interface effects in device operation. Our preliminary findings establish LTO-based lithium-ion electrochemical transistors as promising candidates for energy-efficient neuromorphic computing applications, offering potential solutions to traditional Von Neumann architecture limitations.

25 ENERGY STORAGE↗
DOE OSTI2020

FPDeep: Scalable Acceleration of CNN Training on Deeply-Pipelined FPGA Clusters

In this paper, we propose a framework called FPDeep, which uses a hybrid of model and layer paral- lelism to configure distributed reconfigurable clusters to train DNNs. This approach has numerous benefits. First, the design does not suffer from batch size growth. Second, novel workload and weight partitioning leads to balanced loads of both among nodes. And third, the entire system is fine-grained pipeline. This leads to high parallelism and utilization and also minimizes the time features need to be cached while waiting for back-propagation.

Wang, Tianqi↗