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At least 235 records · Page 13

Categories of Neural Networks

We introduce new categories of neural networks that we hope will help us expose and explore their underlying structure and relationships. Our categories represent neural networks as objects and present structure for comparing neural networks with the same number of layers. In this paper we discuss the construction, properties, and currently known limitations – all with specific, illustrative examples. There are a number of directions this work can move towards, and we conclude with a section on future work summarizing several of these directions.

Category Theory↗

Neural Network Code MATLAB

SAND2022-12606 O Neural Network Code MATLAB reads in an excel file, processes the data, trains a neural network, and tests the neural network. The code generates predictions of diffusion constants based on the data in the excel file. 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.

Allers, Joshua↗

A unified and constructive framework for the universality of neural networks

Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is as follows: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.

97 MATHEMATICS AND COMPUTING↗

Quantum neural networks: Current status and prospects for development

The idea of quantum artificial neural networks, first formulated in [34], unites the artificial neural network concept with the quantum computation paradigm. Quantum artificial neural networks were first systematically considered in the PhD thesis by T. Menneer (1998). Based on the works of Menneer and Narayanan [42, 43], Kouda, Matsui, and Nishimura [35, 36], Altaisky [2, 68], Zhou [67], and others, quantum-inspired learning algorithms for neural networks were developed, and are now used in various training programs and computer games [29, 30]. The first practically realizable scaled hardware-implemented model of the quantum artificial neural network is obtained by D-Wave Systems, Inc. [33]. It is a quantum Hopfield network implemented on the basis of superconducting quantum interference devices (SQUIDs). In this work we analyze possibilities and underlying principles of an alternative way to implement quantum neural networks on the basis of quantum dots. A possibility of using quantum neural network algorithms in automated control systems, associative memory devices, and in modeling biological and social networks is examined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Application of deep neural networks to improve diagnostic accuracy of rheumatoid arthritis using diffuse optical tomography

A set of deep neural network models for rheumatoid arthritis (RA) classification using a highway network, a convolutional neural network and a residual network is proposed based on the data of diffuse optical tomography (DOT) utilising near-infrared light, which ensures early diagnosis of pathophysiological changes resulting from inflammation. A numerical model of the finger is used to generate images to overcome the inherent problem of insufficient clinical DOT images available. The proposed deep neural network models are applied to automatically classify simulated DOT images of inflamed and non-inflamed joints and transfer learning is also used to improve the performance of the classification. The results demonstrate that all three deep neural network methods improve the diagnostic accuracy as compared to the widely applied support vector machine (SVM), especially for high inter-subject variability databases. In cases of distinct modelled severity of disease, residual network achieved the highest accuracy (> 99 %), and both of highway and convolutional neural networks reached 99 %, respectively. However, as the severity of the modelled disease is reduced, this accuracy is reduced to 75.2 % for residual networks. The results indicate that transfer learning can improve the performance of deep neural network methods on RA classification from DOT data and highlight their potential as a computer aided tool in DOT diagnostic systems. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Nested Neural Networks

Report presents analysis of nested neural networks, consisting of interconnected subnetworks. Analysis based on simplified mathematical models more appropriate for artificial electronic neural networks, partly applicable to biological neural networks. Nested structure allows for retrieval of individual subpatterns. Requires fewer wires and connection devices than fully connected networks, and allows for local reconstruction of damaged subnetworks without rewiring entire network.

Baram, Yoram↗

Neural Network Machine Learning and Dimension Reduction for Data Visualization

Neural network machine learning in computer science is a continuously developing field of study. Although neural network models have been developed which can accurately predict a numeric value or nominal classification, a general purpose method for constructing neural network architecture has yet to be developed. Computer scientists are often forced to rely on a trial-and-error process of developing and improving accurate neural network models. In many cases, models are constructed from a large number of input parameters. Understanding which input parameters have the greatest impact on the prediction of the model is often difficult to surmise, especially when the number of input variables is very high. This challenge is often labeled the "curse of dimensionality" in scientific fields. However, techniques exist for reducing the dimensionality of problems to just two dimensions. Once a problem's dimensions have been mapped to two dimensions, it can be easily plotted and understood by humans. The ability to visualize a multi-dimensional dataset can provide a means of identifying which input variables have the highest effect on determining a nominal or numeric output. Identifying these variables can provide a better means of training neural network models; models can be more easily and quickly trained using only input variables which appear to affect the outcome variable. The purpose of this project is to explore varying means of training neural networks and to utilize dimensional reduction for visualizing and understanding complex datasets.

Liles, Charles A.↗

Neural networks for modeling and control of particle accelerators

Charged particle accelerators support a wide variety of scientific, industrial, and medical applications. They range in scale and complexity from systems with just a few components for beam acceleration and manipulation, to large scientific user facilities that span many kilometers and have hundreds-to-thousands of individually-controllable components. Specific operational requirements must be met by adjusting the many controllable variables of the accelerator. Meeting these requirements can be challenging, both in terms of the ability to achieve specific beam quality metrics in a reliable fashion and in terms of the time needed to set up and maintain the optimal operating conditions. One avenue toward addressing this challenge is to incorporate techniques from the fields of machine learning (ML) and artificial intelligence (AI) into the way particle accelerators are modeled and controlled. While many promising approaches within AI/ML could be used for particle accelerators, this dissertation focuses on approaches based on neural networks. Neural networks are particularly well-suited to modeling, control, and diagnostic analysis of nonlinear systems, as well as systems with large parameter spaces. They are also very appealing for their ability to process high-dimensional data types, such as images and time series (both of which are ubiquitous in particle accelerators). In this work, key studies that demonstrated the potential utility of modern neural network-based approaches to modeling and control of particle accelerators are presented. The context for this work is important: at the start of this work in 2012, there was little interest in AI/ML in the particle accelerator community, and many of the advances in neural networks and deep learning that enabled its present success had not yet been made at that time. As such, this work was both an exploration of possible application areas and a generator of proof-of-concept demonstrations in these areas.

43 PARTICLE ACCELERATORS↗

Neural Network Research on Tilt-Rotor Hover Performance

Results from a neural network study on XV-15 tilt-rotor hover performance are presented. Two XV-15 test data bases, acquired during separate tests conducted in the National Full-Scale Aerodynamics Complex at NASA Ames, were used in this study. The two XV-15 test data bases used were: the 1997 80- by 120-Foot Wind Tunnel test data base and the 1984 Outdoor Aerodynamic Research Facility (OARF) test data base. The objectives associated with the 80- by 120-Foot Wind Tunnel test data were to conduct data quality checks, obtain neural network representations, and demonstrate sensitivity to test conditions. The objectives associated with the OARF outdoor test data were to obtain a 'zero wind' neural network representation, and formulate and implement a neural network based wind correction procedure. An additional objective, common to both test data bases, was to conduct error comparisons. The conclusions from the present study were as follows: Compared to measured parameters (i.e., collective pitch angle), derived parameters (i.e., thrust coefficient) were found preferable as neural network inputs. For the 80- by 120-Foot Wind Tunnel test data base, the neural network based figure of merit representations did not extrapolate rotor stall. Using the OARF outdoor test database, a neural network based wind correction procedure was formulated and successfully implemented. Based on an error comparison, the present neural network based wind correction procedure was found to be more accurate compared to the existing, momentum-theory-based wind correction procedure. Also, a separate error comparison showed that the 80- by 120-Foot Wind Tunnel hover performance data were comparable to non-wind-corrected outdoor test data.

Kozapalli, S.↗

WSBP/NWBP small-world neural network and its performance for wind power forecasting

A small-world neural network has stronger generalization ability with high transfer efficiency than that of the regular neural networks. This paper presents two novel small-world neural networks, the Watts-Strogatz small-world based on a BP neural network (WSBP) and a Newman-Watts small-world neural network based on a BP neural network (NWBP), related to previous research of complex networks. The algorithms are developed separately by adopting WS and NW small-world networks as their topological structures, and their derivation and convergence criterion are progressively discussed. After that, the proposed models are subsequently tested by two typical nonlinear functions which confirm their significant improvement over the regular BP networks and other algorithms. Finally, a wind power prediction system is advanced to verify their generalization abilities, and show that the models are practically feasible and effective with improved accuracy and acceptable forecasting errors caused by wind fluctuation and randomness with a time scale up to 24 h.

17 WIND ENERGY↗

GAINN: The Galaxy Assembly and Interaction Neural Networks for High-redshift JWST Observations

We present the Galaxy Assembly and Interaction Neural Networks (Gainn), a series of artificial neural networks for predicting the redshift, stellar mass, halo mass, and mass-weighted age of simulated galaxies based on James Webb Space Telescope (JWST) photometry. Our goal is to determine the best neural network for predicting these variables at 11 < z < 15. The parameters of the optimal neural network can then be used to estimate these variables for real, observed galaxies. The inputs of the neural networks are JWST filter magnitudes of a subset of five broadband filters (F150W, F200W, F277W, F356W, and F444W) and two medium-band filters (F162M and F182M). We compare the performance of the neural networks using different combinations of these filters, as well as different activation functions and numbers of layers. The best neural network predicted redshift with a normalized rms error of $0.010^{+0.003}_{-0.001}$, stellar mass with rms = $0.089^{+0.044}_{-0.022}$, halo mass with a mean-squared error of $0.022^{+0.014}_{-0.008}$, and mass-weighted age with rms = $12.466^{+5.065}_{-2.408}$. We also test the performance of Gainn on real data from MACS0647JD, an object observed by JWST. Predictions from Gainn for the first projection of the object (JD1) have normalized bias $\langle$Δz$\rangle$ < 0.00228, which is significantly smaller than found with template-fitting methods. We find that the optimal filter combination is F277W, F356W, F162M, and F200W when considering both theoretical accuracy and observational resources from JWST.

97 MATHEMATICS AND COMPUTING↗

PHYGNN (Physics Guided Neural Networks)

This implementation of a Physics Guided Neural Network (PHYGNN) augments a traditional neural network loss function with a generic term that can be used to guide the neural network to learn physical or theoretical constraints.

Buster, Grant↗

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗

Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification

Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. Furthermore, the velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.

58 GEOSCIENCES↗

Neural networks for aircraft control

Current research in Artificial Neural Networks indicates that networks offer some potential advantages in adaptation and fault tolerance. This research is directed at determining the possible applicability of neural networks to aircraft control. The first application will be to aircraft trim. Neural network node characteristics, network topology and operation, neural network learning and example histories using neighboring optimal control with a neural net are discussed.

Linse, Dennis↗

Secure authentication using recurrent neural networks

A computer-implemented method of user authentication is provided. The method comprises combining, by a computer system, a user recurrent neural network with a system recurrent neural network to form a unique combined recurrent neural network. The user recurrent neural network is configured to generate a unique user key, and the system recurrent neural network is configured to generate a system key. The computer system inputs a predetermined input into the combined recurrent neural network, and the combined recurrent neural network generates a unique combined key from the input, wherein the combined key differs from both the user key and system key. The computer system then associates the combined key with a unique access authorization to authenticate a user.

Aimone, James Bradley↗

Artificial neural network implementation of a near-ideal error prediction controller

A theory has been developed at the University of Virginia which explains the effects of including an ideal predictor in the forward loop of a linear error-sampled system. It has been shown that the presence of this ideal predictor tends to stabilize the class of systems considered. A prediction controller is merely a system which anticipates a signal or part of a signal before it actually occurs. It is understood that an exact prediction controller is physically unrealizable. However, in systems where the input tends to be repetitive or limited, (i.e., not random) near ideal prediction is possible. In order for the controller to act as a stability compensator, the predictor must be designed in a way that allows it to learn the expected error response of the system. In this way, an unstable system will become stable by including the predicted error in the system transfer function. Previous and current prediction controller include pattern recognition developments and fast-time simulation which are applicable to the analysis of linear sampled data type systems. The use of pattern recognition techniques, along with a template matching scheme, has been proposed as one realizable type of near-ideal prediction. Since many, if not most, systems are repeatedly subjected to similar inputs, it was proposed that an adaptive mechanism be used to 'learn' the correct predicted error response. Once the system has learned the response of all the expected inputs, it is necessary only to recognize the type of input with a template matching mechanism and then to use the correct predicted error to drive the system. Suggested here is an alternate approach to the realization of a near-ideal error prediction controller, one designed using Neural Networks. Neural Networks are good at recognizing patterns such as system responses, and the back-propagation architecture makes use of a template matching scheme. In using this type of error prediction, it is assumed that the system error responses be known for a particular input and modeled plant. These responses are used in the error prediction controller. An analysis was done on the general dynamic behavior that results from including a digital error predictor in a control loop and these were compared to those including the near-ideal Neural Network error predictor. This analysis was done for a second and third order system.

Mcvey, Eugene S.↗

Pseudogradient Training For A Class Of Neural Networks

Developmental second-order recurrent neural networks of special type modified to enhance stability in face of inputs beyond range of inputs on which trained. Second-order recurrent neural networks contain product feedback units and can be trained, by use of example inputs and outputs, to act as finite-state automatons. Particular second-order recurrent neural networks in question learn grammars in sense they are trained to generate binary responses to input training sequences of ones and zeros, each sequence being marked "legal" or "illegal" according to grammar to be learned.

Zeng, Zheng↗