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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 OSTI2021

GOOML Big Kahuna Forecast Modeling and Genetic Optimization Files

This submission includes example files associated with the Geothermal Operational Optimization using Machine Learning (GOOML) Big Kahuna fictional power plant, which uses synthetic data to model a fictional power plant. A forecast was produced using the GOOML data model framework and fictional input data, and a genetic optimization is included which determines optimal flash plant parameters. The inputs and outputs associated with the forecast and genetic optimization are included. The input and output files consist of data, configuration files, and plots. A link to the Physics-Guided Neural Networks (phygnn) GitHub repository is also included, which augments a traditional neural network loss function with a generic loss term that can be used to guide the neural network to learn physical or theoretical constraints. phygnn is used by the GOOML framework to help integrate its machine learning models into the relevant physics and engineering applications. Note that the data included in this submission are intended to provide a demonstration of GOOML's capabilities. Additional files that have not been released to the public are needed for users to run these models and reproduce these results. Units can be found in the readme data resource.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine Learning-Assisted High-Temperature Reservoir Thermal Energy Storage Optimization: Numerical Modeling and Machine Learning Input and Output Files

This data set includes the numerical modeling input files and output files used to synthesize data, and the reduced-order machine learning models trained from the synthesized data for reservoir thermal energy storage site identification. In this study, a machine-learning-assisted computational framework is presented to identify High-Temperature Reservoir Thermal Energy Storage (HT-RTES) site with optimal performance metrics by combining physics-based simulation with stochastic hydrogeologic formation and thermal energy storage operation parameters, artificial neural network regression of the simulation data, and genetic algorithm-enabled multi-objective optimization. A doublet well configuration with a layered (aquitard-aquifer-aquitard) generic reservoir is simulated for cases of continuous operation and seasonal-cycle operation scenarios. Neural network-based surrogate models are developed for the two scenarios and applied to generate the Pareto fronts of the HT-RTES performance for four potential HT-RTES sites. The developed Pareto optimal solutions indicate the performance of HT-RTES is operation-scenario (i.e., fluid cycle) and reservoir-site dependent, and the performance metrics have competing effects for a given site and a given fluid cycle. The developed neural network models can be applied to identify suitable sites for HT-RTES, and the proposed framework sheds light on the design of resilient HT-RTES systems. All the simulations and the neural network model were done by Idaho National Laboratory. A detailed description of the work was reported in publication linked below.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗
DOE OSTI2024

Physics-informed machine learning of the correlation functions in bulk fluids

The Ornstein–Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks and physics-informed neural operator networks, are explored to solve the OZ equation. The physics-informed machine learning models demonstrate great accuracy and high efficiency in solving the forward and inverse OZ problems of various bulk fluids. The results highlight the significant potential of physics-informed machine learning for applications in thermodynamic state theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Smart Preprocessing & Robust Integration Emulator

To achieve the desired particle size of biomass feedstocks during preprocessing for trouble-free handling and conversion to produce biofuels and bioproducts, the raw materials must undergo a crucial milling process. The particle size of biomass plays a critical role in subsequent biofuel manufacturing, where a larger area-to-volume ratio facilitates efficient synthesis while balancing the impact of moisture on biomass storage. To optimize biofuel production efficiency and overcome these challenges, it is imperative to accurately predict the particle size distribution (PSD) of the biomass in the design of efficient preprocessing systems. The population balance model (PBM), upon empirical calibration and validation, can provide rapid prediction of post-milling PSD of granular biomass. However, PSD has limitations related to mass conservation and the absence of moisture considerations. To overcome these drawbacks, a deep learning model called the enhanced deep neural operator (DNO+) is implemented in the code. This model not only retains the capabilities of the PBM in handling complex mapping functions but also incorporates additional factors influencing the system. By considering various experimental conditions such as sieve size and moisture content, the trained DNO+ model can effectively predict the PSD after milling for any given feed PSD. To further reduce the reliance on experimental data, the PBM is integrated into the DNO+ model, resulting in a physics-informed DNO+ (PIDNO+). The PIDNO+ model addresses the non-conservation of quality exhibited by the PBM while inheriting the advantages of the DNO+ model in considering multiple influencing factors. Moreover, the PIDNO+ model significantly reduces the amount of data required for model training. Both deep learning models, i.e., DNO+ and PIDNO+, are excellent in predictive performance, offering swift and accurate machine learning-based predictions. The use of this code that contains these models will assist in guiding the proper milling equipment selection and operational conditions to achieve the desired biomass particle sizes, ensuring the efficiency of subsequent biofuel and bioproduct production processes.

Xia, Yidong [Idaho National Laboratory (INL), Idah↗
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

UQpy Version 4.2: Uncertainty quantification with Python

We introduce a new module for the UQpy software package which extends its capabilities into the field of Scientific Machine Learning. This module builds on PyTorch to create a flexible and robust platform for uncertainty quantification in machine learning. The scientific machine learning module of UQpy introduces custom layers, neural networks, and neural network trainers that are compatible with torch version 2.2.2 and allow for “plug and play” integration into existing torch code.

Neural networks↗
DOE OSTI2025

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their “space” and “time”) as well as their effective parameters are all emergent , i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the “space,” the “time” and the “parameter” axes of a tensor. Once the data become organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative examples are based (i) on a simple advection–diffusion model; (ii) on a previously developed vertex-plus-signaling model of Drosophila embryonic development; and (iii) on two complex dynamic network models (one neuronal and one coupled oscillator model) for which no obvious smooth embedding geometry is known a priori. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.

generative models↗
DOE OSTI2025

Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem

Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator (DeepONet) to solve wave propagation problems described by the Helmholtz equation in a domain without scatterers but at different wavenumbers and with a complex absorbing boundary condition. We then design two classes of fast meta-solvers by combining DeepONet with either relaxation methods, such as Jacobi and Gauss-Seidel, or with Krylov methods, such as GMRES and BiCGStab, using the trunk basis of DeepONet as a coarse-scale preconditioner. We leverage the spectral bias of neural networks to account for the lower part of the spectrum in the error distribution while the upper part is handled inexpensively using relaxation methods or fine-scale preconditioners. The meta-solvers are then applied to solve scattering problems with different shape of scatterers, at no extra training cost. We first demonstrate that the resulting meta-solvers are shape-agnostic, fast, and robust, whereas the standard standalone solvers may even fail to converge without the DeepONet. We then apply both classes of meta-solvers to scattering from a submarine, a complex three-dimensional problem. We achieve very fast solutions, especially with the DeepONet-Krylov methods, which require orders of magnitude fewer iterations than any of the standalone solvers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Deep Learning Accelerated History Matching and Forecasting in Geologic CO 2 Sequestration [Slides]

We have successfully developed a predictive workflow for the Geologic CO 2 Sequestration using a deep learning model based on the Fourier Neural Operator. The workflow has high accuracy for predicting pressure & saturation during the injection and post-injection periods and has decent accuracy for predicting water and CO 2 production rates during injection period. It is necessary to train exclusive DNN models for pressure prediction in long term GCS, but for saturation prediction, we can use a single model to predict it.

58 GEOSCIENCES↗
DOE OSTI2021

A domain wall-magnetic tunnel junction artificial synapse with notched geometry for accurate and efficient training of deep neural networks

Inspired by the parallelism and efficiency of the brain, several candidates for artificial synapse devices have been developed for neuromorphic computing, yet a nonlinear and asymmetric synaptic response curve precludes their use for backpropagation, the foundation of modern supervised learning. Spintronic devices—which benefit from high endurance, low power consumption, low latency, and CMOS compatibility—are a promising technology for memory, and domain-wall magnetic tunnel junction (DW-MTJ) devices have been shown to implement synaptic functions such as long-term potentiation and spike-timing dependent plasticity. In this work, we propose a notched DW-MTJ synapse as a candidate for supervised learning. Using micromagnetic simulations at room temperature, we show that notched synapses ensure the non-volatility of the synaptic weight and allow for highly linear, symmetric, and reproducible weight updates using either spin transfer torque (STT) or spin–orbit torque (SOT) mechanisms of DW propagation. We use lookup tables constructed from micromagnetics simulations to model the training of neural networks built with DW-MTJ synapses on both the MNIST and Fashion-MNIST image classification tasks. Accounting for thermal noise and realistic process variations, the DW-MTJ devices achieve classification accuracy close to ideal floating-point updates using both STT and SOT devices at room temperature and at 400 K. Our work establishes the basis for a magnetic artificial synapse that can eventually lead to hardware neural networks with fully spintronic matrix operations implementing machine learning.

42 ENGINEERING↗
DOE OSTI2023

Toward learning Lattice Boltzmann collision operators

In this work, we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data were generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws and symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Synergistic learning with multi-task DeepONet for efficient PDE problem solving

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Finally, our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

42 ENGINEERING↗
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗
DOE OSTI2023

Generalized Quantum Convolution for Multidimensional Data

The convolution operation plays a vital role in a wide range of critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. In existing implementations, particularly in quantum neural networks, convolution operations are usually approximated by the application of filters with data strides that are equal to the filter window sizes. One challenge with these implementations is preserving the spatial and temporal localities of the input features, specifically for data with higher dimensions. In addition, the deep circuits required to perform quantum convolution with a unity stride, especially for multidimensional data, increase the risk of violating decoherence constraints. In this work, we propose depth-optimized circuits for performing generalized multidimensional quantum convolution operations with unity stride targeting applications that process data with high dimensions, such as hyperspectral imagery and remote sensing. We experimentally evaluate and demonstrate the applicability of the proposed techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

NN-OpInf

SAND2026-18878O The NN-OpInf tool is a PyTorch-based approach to operator inference that uses composable, structure-preserving neural networks to represent nonlinear operators. Operator inference is a machine learning method for inferring low-dimensional systems from data and polynomial models for system dynamics. However, many systems do not conform to polynomial structures, which NN-OpInf addresses by parameterizing operators with neural networks. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗