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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy and efficiency. In this work, we demonstrate that the failure of plain physics-informed neural networks arises from the significant discrepancy in the convergence rate of residuals at different training points, where the slowest convergence rate dominates the overall solution convergence. Based on these observations, we propose a pointwise adaptive weighting method that balances the residual decay rate across different training points. The performance of our proposed adaptive weighting method is compared with current state-of-the-art adaptive weighting methods on benchmark problems for both physics-informed neural networks and physics-informed deep operator networks. In conclusion, through extensive numerical results we demonstrate that our proposed approach of balanced residual decay rates offers several advantages, including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.

Balanced convergence rate↗
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 OSTI2026

A variational framework for residual-based adaptivity in neural PDE solvers and operator learning

Residual-based adaptive strategies are widely used in scientific machine learning yet remain largely heuristic. We introduce a variational framework that formalizes these methods through convex transformations of the residual, where different transformations correspond to distinct objective functionals. For instance, exponential weights target uniform error minimization, while linear weights recover quadratic error minimization. This perspective reveals adaptive weighting as a means of selecting sampling distributions that optimize a primal objective, directly linking discretization choices to error metrics. This principled approach yields three key benefits: it enables systematic design of adaptive schemes, reduces discretization error by lowering estimator variance, and enhances learning dynamics by improving gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across diverse optimizers and architectures. Our results provide a theoretical perspective for residual-based adaptivity and establish a foundation for principled discretization and training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

ExtremeMETA: High-speed Lightweight Image Segmentation Model by Remodeling Multi-channel Metamaterial Imagers

Deep neural networks (DNNs) have heavily relied on traditional computational units, such as CPUs and GPUs. However, this conventional approach brings significant computational burden, latency issues, and high power consumption, limiting their effectiveness. This has sparked the need for lightweight networks such as ExtremeC3Net. Meanwhile, there have been notable advancements in optical computational units, particularly with metamaterials, offering the exciting prospect of energy-efficient neural networks operating at the speed of light. Yet, the digital design of metamaterial neural networks (MNNs) faces precision, noise, and bandwidth challenges, limiting their application to intuitive tasks and low-resolution images. In this study, we proposed a large kernel lightweight segmentation model, ExtremeMETA. Based on ExtremeC3Net, our proposed model, ExtremeMETA maximized the ability of the first convolution layer by exploring a larger convolution kernel and multiple processing paths. With the large kernel convolution model, we extended the optic neural network application boundary to the segmentation task. To further lighten the computation burden of the digital processing part, a set of model compression methods was applied to improve model efficiency in the inference stage. The experimental results on three publicly available datasets demonstrated that the optimized efficient design improved segmentation performance from 92.45 to 95.97 on mIoU while reducing computational FLOPs from 461.07 MMacs to 166.03 MMacs. The large kernel lightweight model ExtremeMETA showcased the hybrid design’s ability on complex tasks.

large convolution kernel↗
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 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

A Neural Optimizer With Decision-Focused Learning for Optimal Energy Storage Operation

Here, this article introduces a neural optimizer-based framework for optimizing battery energy storage system (BESS) control for grid services, including demand charge and energy cost reduction. By leveraging decision-focused learning (DFL), the proposed framework ensures seamless integration and adaptation, significantly enhancing control performance. A patch time-series transformer is employed for peak load forecasting, incorporating aleatoric uncertainty quantification to account for forecasting uncertainties within the decision-making process. The framework utilizes a solver-in-the-loop approach to generate optimal BESS actions, which are then used to train the neural optimizer-based agent. By co-optimizing both BESS operational modes and output power within the NN, the system achieves improved performance and robustness. After initial training, the forecasting and control models are jointly fine-tuned to account for forecasting errors, further improving decision precision and efficiency through DFL. Case studies are performed to validate the performance of the framework using multiple real-world datasets, demonstrating superior performance in monthly peak load forecasting compared to state-of-the-art models. In addition, the results are compared against existing decision-making approaches. The results demonstrate a reduction in monthly peak forecasting error by approximately 15% across various performance measures and achieve an optimization gap for BESS operation that is about three times smaller compared to existing methods.

Kim, Hyeonjin [Pacific Northwest National Laborato↗
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↗
DOE OSTI2026

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 OSTI2024

On the Training and Generalization of Deep Operator Networks

Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.

deep operator networks↗
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 OSTI2025

Particle hit clustering and identification using point set transformers in liquid argon time projection chambers

Liquid argon time projection chambers are often used in neutrino physics and dark-matter searches because of their high spatial resolution. The images generated by these detectors are extremely sparse, as the energy values detected by most of the detector are equal to 0, meaning that despite their high resolution, most of the detector is unused in a particular interaction. Instead of representing all of the empty detections, the interaction is usually stored as a sparse matrix, a list of detection locations paired with their energy values. Traditional machine learning methods that have been applied to particle reconstruction such as convolutional neural networks (CNNs), however, cannot operate over data stored in this way and therefore must have the matrix fully instantiated as a dense matrix. Operating on dense matrices requires a lot of memory and computation time, in contrast to directly operating on the sparse matrix. We propose a machine learning model using a point set neural network that operates over a sparse matrix, greatly improving both processing speed and accuracy over methods that instantiate the dense matrix, as well as over other methods that operate over sparse matrices. Compared to competing state-of-the-art methods, our method improves classification performance by 14%, segmentation performance by more than 22%, while taking 80% less time and using 66% less memory. Compared to state-of-the-art CNN methods, our method improves classification performance by more than 86%, segmentation performance by more than 71%, while reducing runtime by 91% and reducing memory usage by 61%.

calibration and fitting methods↗
DOE OSTI2025

Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications

In this work we introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level overlapping additive Schwarz preconditioner. The neural network parameters are decomposed into groups (subdomains) with overlapping regions. In addition, the network’s feed-forward structure is indirectly imposed through a novel subdomain-wise synchronization strategy and a coarse-level training step. Through a series of numerical experiments, which consider physicsinformed neural networks and operator learning approaches, we demonstrate that the proposed two-level preconditioner significantly speeds up the convergence of the standard (LBFGS) optimizer while also yielding more accurate machine learning models. Moreover, the devised preconditioner is designed to take advantage of model-parallel computations, which can further reduce the training time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

ELECTRIFICATION OF A HEAVY-DUTY OFF-ROAD MATERIAL HANDLER: ENERGY SAVINGS AND EMISSION REDUCTIONS

Federal regulations are driving the adoption of electrification technologies to reduce carbon dioxide equivalent (CO2e) emissions, a metric that quantifies the global warming potential of various greenhouse gases in terms of carbon dioxide (CO2). Although no specific CO2 regulations exist for heavy-duty off-road machines, future reductions are likely, given stricter emissions standards for on-road vehicles. The heavy-duty off-road sector offers significant fuel-saving potential, as its focus has traditionally been on reliability and performance rather than fuel efficiency. This dissertation examines fuel and CO2e savings opportunities on a heavy-duty off-road material handler, the Pettibone Cary-Lift 204i, from stock configuration to simple modifications to a complete teardown and reconfiguration of the machine with a plug-in series hybrid architecture using electrified hydraulics. The study begins by modeling the baseline machine’s fuel and energy consumption, calibrating with experimental data from custom operating cycles. An energy analysis identifies key areas for fuel savings. Two simple powertrain modifications result in a combined 16.2% fuel savings. Next, a Pugh-style analysis narrows a list of electrified architectures, leading to high-fidelity models that evaluate total lifetime CO2e and costs. Higher electrification levels reduce CO2e emissions but increase costs, and electricity grid emissions significantly impact CO2e for plug-in architectures. A plug-in series hybrid is chosen for the project. In its base control form, 49% fuel and 29% CO2e savings are expected from the plug-in series hybrid compared to the baseline machine. Further savings are pursued through regenerative braking (6.3%) and load-following hydraulic control (17.8%), totaling 24.1% fuel savings, and leading to a total of 61% fuel and 41% CO2e savings compared to the baseline. Battery chemistries and charging strategies are also analyzed for cost and CO2e impacts, finding LFP batteries as superior due to longevity, and overnight level 2 charging usually at a lower cost but resulting in higher emissions than opportunity DC fast-charging (DCFC). DCFC emissions are highly dependent on grid emissions, and DCFC cost is highly dependent on grid demand charges. Finally, artificial intelligence is applied to operating cycle recognition. Neural network accuracy ranges from 81% to 99%, with applications to worksite efficiency and safety improvements.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Heterogeneous Point Set Transformers for Segmentation of Multiple View Particle Detectors

NOvA is a long-baseline neutrino oscillation experiment that detects neutrino particles from the NuMI beam at Fermilab. Before data from this experiment can be used in analyses, raw hits in the detector must be matched to their source particles, and the type of each particle must be identified. This task has commonly been done using a mix of traditional clustering approaches and convolutional neural networks (CNNs). Due to the construction of the detector, the data is presented as two sparse 2D images: an XZ and a YZ view of the detector, rather than a 3D representation. We propose a point set neural network that operates on the sparse matrices with an operation that mixes information from both views. Our model uses less than 10% of the memory required using previous methods while achieving a 96.8% AUC score, a higher score than obtained when both views are processed independently (85.4%).

Robles, Edgar E. [UC, Irvine (main)]↗
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↗