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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Design of Hopfield Networks Based on Superconducting Coupled Oscillators

The global energy shortage has driven the development of many energy-efficient computational platforms beyond Moore's law, among which brain-inspired neuromorphic computing is one of the promising solutions. Associative memory and pattern recognition are important computations solved by brain-inspired Hopfield networks. Classical Hopfield networks store memories via fixed point attractors of their dynamics. In oscillatory Hopfield networks, these attractors are replaced by periodic orbits. Here, we design an oscillatory Hopfield network based on coupled superconducting oscillators. We first employ a mathematical phase reduction approach to map networks of coupled superconducting rapid single flux quantum (RSFQ) ring oscillators to coupled Kuramoto phase-oscillator networks. We use this theory to numerically optimize the hardware's mutual inductances in order to directly match the phase-reduced superconducting oscillators to a model of phase-oscillator-based Hopfield networks. The resulting network can store multiple oscillatory phase-locked memory patterns and recover the patterns based on the initial phase conditions. As different pattern recognition tasks, or learning, require tunable connectivity strengths between the oscillatory nodes, we further employ a coupler circuit that enables tuning the coupling strength between two oscillators by applying an external flux. We demonstrate the functionality of our design through numerical simulations of a small example network with oscillators operating at 86 GHz and recognizing patterns within 10 ns. Our approach enables the learning and retrieval of dynamical memory patterns with a wide range of applications where rhythmic dynamic output is beneficial.

Cheng, Ran↗
NASA NTRS1988

Simulation tests of the optimization method of Hopfield and Tank using neural networks

The method proposed by Hopfield and Tank for using the Hopfield neural network with continuous valued neurons to solve the traveling salesman problem is tested by simulation. Several researchers have apparently been unable to successfully repeat the numerical simulation documented by Hopfield and Tank. However, as suggested to the author by Adams, it appears that the reason for those difficulties is that a key parameter value is reported erroneously (by four orders of magnitude) in the original paper. When a reasonable value is used for that parameter, the network performs generally as claimed. Additionally, a new method of using feedback to control the input bias currents to the amplifiers is proposed and successfully tested. This eliminates the need to set the input currents by trial and error.

Paielli, Russell A.↗
DOE OSTI2018

Non-convex Multi-species Hopfield Models

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different intensities. Thus, this system contains two of the main ingredients of modern deep neural-network architectures: Hebbian interactions to store patterns of information and multiple layers coding different levels of correlations. The model is completely solvable in the low-load regime with a suitable generalization of the Hamilton–Jacobi technique, despite the Hamiltonian can be a non-definite quadratic form of the Mattis magnetizations. The family of multi-species Hopfield model includes, as special cases, the 3-layers Restricted Boltzmann Machine with Gaussian hidden layer and the Bidirectional Associative Memory model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accuracy and capacity of modern Hopfield networks with synaptic noise.

We study the retrieval accuracy and capacity of modern Hopfield networks of with two-state (Ising) spins interacting via modified Hebbian 𝑛 -spin interactions. In particular, we consider systems where the interactions deviate from the Hebb rule through additive or multiplicative noise or through clipping or deleting interactions. We find that the capacity scales as 𝑁𝑛−1 with the number of spins 𝑁 in all cases, but with a prefactor reduced compared to the Hebbian case. For 𝑛=2 our results agree with the previously known results for the conventional 𝑛=2 Hopfield network.

Bhattacharjee, Sharba↗
DOE OSTI2021

Preliminary Assessment of Qiskit Quantum Simulator Capabilities for Development of Quantum Hopfield Neural Network for Anomaly Detection Applications (Q4 Report)

Quantum information processing offers potentially faster performance compared to the classical counterpart. The goal of this work is to investigate performance of Quantum Hopfield Neural Network for applications to anomaly detection. Preliminary study consist of assessment of computational capabilities of Qiskit quantum simulator. Eventual objective is to implement Quantum Hopfield Network algorithm for detection of weak nuisance and anomaly signal in the presence of strong and highly varying background in gamma radiation data measured during environmental screening.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1980

Electron-impact excitation of the singlet states of N2. I - The Birge-Hopfield system /b 1 pi u - X 1 Sigma g +/

Results of a study of the electron-impact excitation of the b 1 pi u state of N2, one of the singlet states thought to be excited by precipitating electrons in the auroral zones, and of its predissociation and radiative relaxation through the emission of the Birge-Hopfield band system (b 1 pi u - X 1 Sigma g +) are presented. A collimated electron beam was passed through N2 gas producing a variety of atomic states through dissociative excitation, and the radiation resulting from relaxation of these states was observed by VUV and visible-IR monochromators. Absolute emission cross sections for 11 Birge-Hopfield bands are obtained for energies from threshold to 500 eV, and used to calculate the absolute transition probabilities for BH(1, v-prime) bands and the variation of the electric dipole moment with internuclear distance. With the exception of the v-prime equals 1, 5 and 6 vibrational levels, all b 1 pi u levels are found to predissociate with a specific predissociation branching ratio greater than 0.99, representing a major source of nitrogen atoms.

Zipf, E. C.↗
NASA NTRS1986

Comparison between sparsely distributed memory and Hopfield-type neural network models

The Sparsely Distributed Memory (SDM) model (Kanerva, 1984) is compared to Hopfield-type neural-network models. A mathematical framework for comparing the two is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independently of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. However, the total number of stored bits per matrix element is the same in the two models, as well as for extended models with higher order interactions. The models are also compared in their ability to store sequences of patterns. The SDM is extended to include time delays so that contextual information can be used to cover sequences. Finally, it is shown how a generalization of the SDM allows storage of correlated input pattern vectors.

Keeler, James D.↗
DOE OSTI2025

Detection of Isotopes in Urban Source Search Low-Count Gamma Spectra Using Hopfield Neural Networks

Source search campaigns involve measurements of background gamma-ray spectra with a mobile detector-spectrometer traveling along arbitrarily chosen trajectories over a wide screening area. Radiation counts are typically measured with a tellurium-doped sodium iodide [NaI(Tl)] scintillator detector-spectrometer in short acquisition intervals, usually 1 s. The objective is to detect orphan isotopes with half-lives shorter than those of the isotopes in the natural background. In principle, radioisotopes can be identified by their unique gamma emission spectrum. However, detecting orphan isotopes in search data is challenging because low counts measured in short acquisition intervals result in incomplete spectral lines. In this study, we investigate the performance of a Hopfield neural network (HNN) that implements an auto-associative memory for the detection of isotopes of interest in an urban search campaign. The HNN is trained on one example of gamma spectra with well-resolved spectral lines of each isotope of interest. During testing, the auto-associative memory implementation of the HNN processes low-count gamma spectra with partially complete isotopic lines by matching incoming measurements to the closest one of its memory-stored patterns. The testing database consisted of almost 10 000 1-s gamma spectra, including measurements of orphan isotopes 137 Cs, 241 Am, and 131 I, obtained during two urban search surveys with a NaI(Tl) detector. The performance of the HNN detection algorithm was evaluated using precision, recall, and F1 scores, and benchmarked with a multiple linear regression (MLR) identification algorithm. In conclusion, the test results demonstrate that HNN outperforms MLR in the detection of all the isotopes of interest.

Auto associative memory↗
DOE OSTI2022

Direct observation of a dynamical glass transition in a nanomagnetic artificial Hopfield network

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function, error-correcting codes5 or stock-market dynamics. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems. Here we present the experimental realization of an artificial spin glass consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network. Using cryogenic X-ray photoemission electron microscopy (XPEEM), we performed temperature-dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power-law trend predicted from theoretical models on two-dimensional spin glasses. As a result, we observe clear signatures of the hard-to-observe rugged spin glass free energy in the form of sub-aging, out-of-equilibrium autocorrelations and a transition from stable to unstable dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Identification of Distorted Gamma-Ray Signature Patterns Using Digital Filtering and Auto-Associative Memory Implemented with a Hopfield Neural Network

The detection and identification of radioactive sources in search applications involve analyzing passive gamma-ray emissions from high-level radioactive materials. This process uses a mobile detector-spectrometer in a complex field test environment. Recently, the use of artificial intelligence for gamma-ray spectrum analysis has shown promising results. However, challenges persist in identifying isotopic signatures from spectral measurements that may be distorted due to source shielding, random variations in natural radioactive background, or insufficient measurement time to obtain clear spectral lines. Here, this paper presents a novel intelligent signature recognition method that combines digital filtering techniques with an artificial Hopfield Neural Network (HNN). The HNN leverages auto-associative memory to store training sample patterns and match them with incoming gamma spectra from distorted sources. It restores the testing sources’ measurements by finding the closest matching signature patterns in the spectral library. Before HNN recognition, the measured spectrum undergoes preprocessing with a digital image filter to reduce fluctuations. Performance of the proposed method is evaluated using a set of gamma-ray spectra measured with a sodium iodide detector. The data collected include measurements from six pure samples: 241 Am, 60 Co, 137 Cs, 192 Ir, 239 Pu, and 235 U, which are used for training and validation (i.e. six cases). Additionally, the data set contains 24 distorted synthesized sources with various fluctuating backgrounds. Test results demonstrate the potential of the proposed method to accurately recognize the correct isotope with high precision, achieving an accuracy rate exceeding 85%. Furthermore, the proposed method exhibits superior performance compared to the conventional multiple regression fitting and simple feedforward neural network methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Exact quantisation of the relativistic Hopfield model

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Associative memories using complex-valued Hopfield networks based on spin-torque oscillator arrays

Abstract Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting the oscillatory output of the oscillators. Pseudo-inverse training suffices to store at least 12 images in a set of 192 oscillators, representing 16 × 12 pixel images. The energy required to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 5% root mean square deviations from the ideal image require approximately 5 μ s and consume roughly 130 nJ. Simulations show that the network functions well when the resonant frequency of the oscillators can be tuned to have a fractional spread less than 10 −3 , depending on the strength of the feedback.

Prasad, Nitin (ORCID:0000000180880164)↗
DOE OSTI2021

Detection of Anomalies in Environmental Gamma Radiation Background with Hopfield Artificial Neural Network - Consortium on Nuclear Security Technologies (CONNECT) Q3 Report

Environmental screening of gamma radiation consists of detecting weak nuisance and anomaly signal in the presence of strong and highly varying background. In a typical scenario, a mobile detector-spectrometer continuously measures gamma radiation spectra in short, e.g., one-second, signal acquisition intervals. The measurement data is a 2D matrix, where one dimension is gamma ray energy, and the other dimension is the number of measurements or total time. In principle, gamma radiation sources can be detected and identified from the measured data by their unique spectral lines. Detecting sources from data measured in a search scenario is difficult due to the highly varying background because of naturally occurring radioactive material (NORM), and low signal-to-noise ratio (S/N) of spectral signal measured during one-second acquisition intervals. The objective of this work is to investigate performance of a Hopfield Neural Network (HNN) in in detection and identification of weak nuisances and anomalies events in the presence of a highly fluctuating background. Performance of HNN algorithm is benchmarked using search data from an environmental screening campaign. One data set contained a 137 Cs source, and another dataset contained a 131 I source.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Development of Hopfield Artificial Neural Network for Anomaly Detection in Environmental Gamma Radiation Background: Consortium on Nuclear Security Technologies (CONNECT) (Q2 Report)

Environmental screening of gamma radiation consists of detecting weak nuisance and anomaly signal in the presence of strong and highly varying background. In a typical scenario, a mobile detector-spectrometer continuously measures gamma radiation spectra in short, e.g., one-second, signal acquisition intervals. The measurement data is a 2D matrix, where one dimension is gamma ray energy, and the other dimension is the number of measurements or total time. In principle, gamma radiation sources can be detected and identified from the measured data by their unique spectral lines. Detecting sources from data measured in a search scenario is difficult due to the highly varying background because of naturally occurring radioactive material (NORM), and low signal-to-noise ratio (S/N) of spectral signal measured during one-second acquisition intervals. The objective of this work is to explore supervised machine learning (ML) algorithms for development of a Hopfield Neural Network (HNN) in conjunction with an image processing algorithm for detection and identification of weak nuisances and anomalies events in the presence of a highly fluctuating background.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Anomaly Detection in Gamma Spectra Using Hopfield Neural Network with B-SAT and Grover’s Algorithm on a Quantum Computing Simulator

Environmental screening of gamma radiation consists of detecting weak nuisance and anomaly signal in the presence of strong and highly varying background. In a typical scenario, a mobile detector-spectrometer continuously measures gamma radiation spectra in short, e.g., one-second, signal acquisition intervals. In principle, gamma radiation sources can be detected and identified by their unique spectral lines. However, detecting sources from data measured in a search scenario is difficult due to the highly varying background because of naturally occurring radioactive material (NORM), and low signal-to-noise ratio (S/N) of spectral signal measured during one-second acquisition intervals. In recent prior work, we have developed a Hopfield Neural Network (HNN) in conjunction with an image processing algorithm to detect a weak signal anomaly hidden among the highly fluctuating background spectra. The objective of this work is to explore quantum computing methods to increase the speed of HNN. The approach is based on the Grover’s search algorithm in conjunction with a 3-SAT problem formalism. The Grover’s algorithm is implemented on a quantum computing simulator using Qiskit software. Performance of HNN algorithm is benchmarked using search data from an environmental screening campaign, where the anomaly is a subset of measurements containing a 137 Cs source. Results indicate that using Grover’s algorithm on a quantum simulator reduces runtime of HNN by two orders of magnitude.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Detection of Isotopes in Urban Source Search Gamma Spectra Using Hopfield Neural Network

Source search campaigns involve the measurement of consecutive background gamma-ray spectra obtained with a mobile detector-spectrometer, such as tellurium-doped sodium iodide NaI(Tl) scintillator detector-spectrometer. Counts are measured with NaI(Tl) detector in short acquisition intervals, such as one second. Detection of isotopes in search data is challenging because of the low signal-to-noise ratio (S/N) of the spectral lines and highly varying background due to naturally occurring radioactive material (NORM). In this work, we investigate the performance of the detection of orphan Cs-137, Am-241, and I-131 isotopes in a gamma ray data set obtained in a search survey. Isotopic detection is performed with a Hopfield Neural Network (HNN), which implements an auto-associative memory by matching incoming measurements to the closest one of its memory-stored signature patterns. HNN is trained on examples of spectra of calibrated isotopic sources with well-resolved spectral lines. During testing, HNN processes spectra with partially complete or distorted isotopic lines. The performance of the HNN detection algorithm is benchmarked with Precision, Recall, and F1 scores. Test results demonstrate the potential of HNN to detect the isotope of interest with high accuracy (F1 > 90%) for all isotopes in this study.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗