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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 OSTI2022

A Classification of G -invariant Shallow Neural Networks

When trying to fit a deep neural network (DNN) to a G-invariant target function with G a group, it only makes sense to constrain the DNN to be G-invariant as well. However, there can be many different ways to do this, thus raising the problem of “G-invariant neural architecture design”: What is the optimal Ginvariant architecture for a given problem? Before we can consider the optimization problem itself, we must understand the search space, the architectures in it, and how they relate to one another. In this paper, we take a first step towards this goal; we prove a theorem that gives a classification of all G-invariant single-hidden-layer or “shallow” neural network (G-SNN) architectures with ReLU activation for any finite orthogonal group G, and we prove a second theorem that characterizes the inclusion maps or “network morphisms” between the architectures that can be leveraged during neural architecture search (NAS). The proof is based on a correspondence of every G-SNN to a signed permutation representation of G acting on the hidden neurons; the classification is equivalently given in terms of the first cohomology classes of G, thus admitting a topological interpretation. The G-SNN architectures corresponding to nontrivial cohomology classes have, to our knowledge, never been explicitly identified in the literature previously. Using a code implementation, we enumerate the G-SNN architectures for some example groups G and visualize their structure. Lastly, we prove that architectures corresponding to inequivalent cohomology classes coincide in function space only when their weight matrices are zero, and we discuss the implications of this for NAS.

Agrawal, Devanshu↗
DOE OSTI2024

Performance Comparison of Machine Learning Models for Ultrasonic Nondestructive Evaluation of Alkali-Silica Reaction in Concrete

Alkali-silica reaction (ASR) causes concrete degradation, leading to cracking, rebar corrosion, and reduced structural integrity, which raises safety concerns. Ultrasonic nondestructive evaluation (NDE) effectively assesses concrete properties and monitors ASR progression. However, its deployment and analysis require specialized expertise and subjective interpretation. As computational power increases, artificial intelligence (AI) and machine learning (ML) algorithms are increasingly being used to automate NDE data analysis across various industries for AI-assisted automation. Regulatory agencies are adapting to this technological shift, prompting a need to evaluate current ML technologies’ capabilities and limitations in assessing concrete material properties and damage. This report presents a comparative analysis of four ML regression models for predicting concrete material damage induced by ASR expansion using long-term ultrasonic data monitoring. The models investigated include linear regression (LR), support vector regression (SVR), shallow neural networks (NN), and deep neural networks (DNN). LR, SVR, and shallow NN models use features extracted from ultrasonic signals, whereas the DNN model processes time-domain ultrasonic signals and frequency spectra directly. The study systematically compared the models’ performance from various perspectives, including model input, prediction performance, and generalization ability. The findings indicate significant variability in model performance, with some ML algorithms achieving very high or very low prediction accuracy depending on the preprocessing and feature engineering (extraction and selection) applied. Key insights include the observation that shallow ML models (LR, SVR, and shallow NNs) require meticulous preprocessing and feature extraction to achieve high accuracy. In contrast, the DNN model, although it bypasses the need for feature engineering, necessitates extensive preprocessing to mitigate noise and computational demands. The SVR model emerged as the top performer among the shallow models, and the DNN model exhibited superior performance on specific datasets but struggled with generalization across specimens from different batches. Additionally, the SVR model is sensitive to temperature variations, whereas the DNN model is robust in this regard. Using recurrent neural networks is recommended for future ASR expansion prediction studies. Recurrent neural networks’ inherent ability to capture temporal dependencies and long-term patterns makes them well suited for analyzing sequential ultrasonic monitoring data. Overall, the results and conclusions of this study could provide insights into the capabilities and effectiveness of ML when applied to ultrasonic NDE data and help identify best practices for using ML for ultrasonic NDE of concrete material properties.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient solutions of fermionic systems using artificial neural networks

In this study, we explore the similarities and differences between variational Monte Carlo techniques that employ conventional and artificial neural network representations of the ground-state wave function for fermionic systems. Our primary focus is on shallow neural network architectures, specifically the restricted Boltzmann machine, and we examine unsupervised learning algorithms that are appropriate for modeling complex many-body correlations. We assess the advantages and drawbacks of conventional and neural network wave functions by applying them to a range of circular quantum dot systems. Our findings, which include results for systems containing up to 90 electrons, emphasize the efficient implementation of these methods on both homogeneous and heterogeneous high-performance computing facilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Topological and Dynamical Representations for Radio Frequency Signal Classification

Radio Frequency (RF) signals are found throughout our world, carrying over-the-air information for both digital and analog uses with applications ranging from WiFi to the radio. One area of focus in RF signal analysis is determining the modulation schemes employed in these signals which is crucial in many RF signal processing domains from secure communication to spectrum monitoring. This work investigates the accuracy and noise robustness of novel Topological Data Analysis (TDA) and dynamic representation based approaches paired with a small convolution neural network for RF signal modulation classification with a comparison to state-of-the-art deep neural network approaches. We show that using TDA tools, like Vietoris-Rips and lower star filtrations, and the Takens' embedding in conjunction with a standard shallow neural network we can capture the intrinsic dynamical, geometric, and topological features of the underlying signal's manifold, offering informative representations of the RF signals. Our approach is effective in handling the modulation classification task and is notably noise robust, outperforming the commonly used deep neural network approaches in mode classification. Moreover, our fusion of dynamical and topological information is able to attain similar performance to deep neural network architectures with significantly smaller training datasets.

Myers, Audun D.↗
DOE OSTI2022

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs–Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Inverse Analysis with Variational Autoencoders: A Comparison of Shallow and Deep Networks

Inverse problems are applied to determine unknown properties by matching observational data with a physical model that often takes many parameters as input. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented involving regularization with a technique known as a variational autoencoder (VAE), which is trained to map a high-dimensional parameter space with a complex structure to a low-dimensional latent space with a simple structure. We apply this approach to unconditioned realizations of the parameters (heterogeneous hydraulic fields) for a hydrogeological inverse problem. Two types of hydraulic conductivity fields are used to evaluate the characterization for the different levels of heterogeneity complexity of the physical inputs. This approach keeps the computational cost of generating the training data low. The reason is unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any groundwater flow model forward runs. In addition, this approach applies regularization on a low-dimensional latent space from the VAE and increases optimization efficiency through automatic differentiation. Furthermore, two different neural network (NN) structures are tested for their utility in using the VAE for inverse analysis. The performance of a deep, convolutional neural network strongly depends on the dimensionality of the latent space, which requires tuning. In contrast, a shallow, dense neural network provides consistently accurate characterization without tuning. Furthermore, our approach evaluates the advantages of the shallow, dense neural network over the deep, convolutional one and enables future application to a wide range of inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2021

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

hp -VPINNs: Variational physics-informed neural networks with domain decomposition

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto the space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the entire computational domain, while the test space contains piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with a local learning algorithm that can efficiently localize the network parameter optimization. Here, we demonstrate the advantages of hp-VPINNs in both accuracy and training cost for several numerical examples of function approximation and in solving differential equations.

42 ENGINEERING↗
DOE OSTI2020

Predicting Small Molecule Transfer Free Energies by Combining Molecular Dynamics Simulations and Deep Learning

Accurately predicting small molecule partitioning and hydrophobicity is critical in the drug discovery process. There are many heterogeneous chemical environments within a cell and entire human body. For example, drugs must be able to cross the hydrophobic cellular membrane to reach their intracellular targets, and hydrophobicity is an important driving force for drug–protein binding. Atomistic molecular dynamics (MD) simulations are routinely used to calculate free energies of small molecules binding to proteins, crossing lipid membranes, and solvation but are computationally expensive. Machine learning (ML) and empirical methods are also used throughout drug discovery but rely on experimental data, limiting the domain of applicability. We present atomistic MD simulations calculating 15,000 small molecule free energies of transfer from water to cyclohexane. This large data set is used to train ML models that predict the free energies of transfer. We show that a spatial graph neural network model achieves the highest accuracy, followed closely by a 3D-convolutional neural network, and shallow learning based on the chemical fingerprint is significantly less accurate. A mean absolute error of ~4 kJ/mol compared to the MD calculations was achieved for our best ML model. We also show that including data from the MD simulation improves the predictions, tests the transferability of each model to a diverse set of molecules, and show multitask learning improves the predictions. This work provides insight into the hydrophobicity of small molecules and ML cheminformatics modeling, and our data set will be useful for designing and testing future ML cheminformatics methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Correspondence between neuroevolution and gradient descent

Abstract We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Real-time confinement regime detection in fusion plasmas with convolutional neural networks and high-bandwidth edge fluctuation measurements

Abstract A real-time detection of the plasma confinement regime can enable new advanced plasma control capabilities for both the access to and sustainment of enhanced confinement regimes in fusion devices. For example, a real-time indication of the confinement regime can facilitate transition to the high-performing wide-pedestal (WP) quiescent H-mode, or avoid unwanted transitions to lower confinement regimes that may induce plasma termination. To demonstrate real-time confinement regime detection, we use the 2D beam emission spectroscopy (BES) diagnostic system to capture localized density fluctuations of long wavelength turbulent modes in the edge region at a 1 MHz sampling rate. BES data from 330 discharges in either L-mode, H-mode, quiescent H (QH)-mode, or WP QH-mode were collected from the DIII-D tokamak and curated to develop a high-quality database to train a deep-learning classification model for real-time confinement detection. We utilize the 6×8 spatial configuration with a time window of 1024 µ s and recast the input to obtain spectral-like features via fast Fourier transform preprocessing. We employ a shallow 3D convolutional neural network for the multivariate time-series classification task and utilize a softmax in the final dense layer to retrieve a probability distribution over the different confinement regimes. Our model classifies the global confinement state on 44 unseen test discharges with an average F 1 score of 0.94, using only ∼1 ms snippets of BES data at a time. This activity demonstrates the feasibility for real-time data analysis of fluctuation diagnostics in future devices such as ITER, where the need for reliable and advanced plasma control is urgent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Exploring the universality of hadronic jet classification

The modeling of jet substructure significantly differs between Parton Shower Monte Carlo (PSMC) programs. Despite this, we observe that machine learning classifiers trained on different PSMCs learn nearly the same function. This means that when these classifiers are applied to the same PSMC for testing, they result in nearly the same performance. This classifier universality indicates that a machine learning model trained on one simulation and tested on another simulation (or data) will likely be optimal. Our observations are based on detailed studies of shallow and deep neural networks applied to simulated Lorentz boosted Higgs jet tagging at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Learning high-dimensional parametric maps via reduced basis adaptive residual networks

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_v$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.

42 ENGINEERING↗
DOE OSTI2023

Automated Quantification of Wind Turbine Blade Leading Edge Erosion from Field Images

Wind turbine blade leading edge erosion is a major source of power production loss and early detection benefits optimization of repair strategies. Two machine learning (ML) models are developed and evaluated for automated quantification of the areal extent, morphology and nature (deep, shallow) of damage from field images. The supervised ML model employs convolutional neural networks (CNN) and learns features (specific types of damage) present in an annotated set of training images. The unsupervised approach aggregates pixel intensity thresholding with calculation of pixel-by-pixel shadow ratio (PTS) to independently identify features within images. The models are developed and tested using a dataset of 140 field images. The images sample across a range of blade orientation, aspect ratio, lighting and resolution. Each model (CNN v PTS) is applied to quantify the percent area of the visible blade that is damaged and classifies the damage into deep or shallow using only the images as input. Both models successfully identify approximately 65% of total damage area in the independent images, and both perform better at quantifying deep damage. The CNN is more successful at identifying shallow damage and exhibits better performance when applied to the images after they are preprocessed to a common blade orientation.

Aird, Jeanie A.↗