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At least 55 records · Page 3

Layer-Parallel Training of Deep Residual Neural Networks

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be interpreted as forward Euler discretizations of a nonlinear initial value problem whose time-dependent control variables represent the weights of the neural network. Hence, training a ResNet can be cast as an optimal control problem of the associated dynamical system. For similar time-dependent optimal control problems arising in engineering applications, parallel-in-time methods have shown notable improvements in scalability. This paper demonstrates the use of those techniques for efficient and effective training of ResNets. The proposed algorithms replace the classical (sequential) forward and backward propagation through the network layers with a parallel nonlinear multigrid iteration applied to the layer domain. This adds a new dimension of parallelism across layers that is attractive when training very deep networks. From this basic idea, we derive multiple layer-parallel methods. The most efficient version employs a simultaneous optimization approach where updates to the network parameters are based on inexact gradient information in order to speed up the training process. Finally, using numerical examples from supervised classification, we demonstrate that the new approach achieves a training performance similar to that of traditional methods, but enables layer-parallelism and thus provides speedup over layer-serial methods through greater concurrency.

97 MATHEMATICS AND COMPUTING↗

Case Study: Analysis of Autonomous Center line Tracking Neural Networks

Deep neural networks have gained widespread usage in a number of applications. However, limitations such as lack of explainability and robustness inhibit building trust in their behavior, which is crucial in safety critical applications such as autonomous driving. Therefore, techniques which aid in understanding and providing guarantees for neural network behavior are the need of the hour. In this paper, we present a case study applying a recently proposed technique, Prophecy, to analyze the behavior of a neural network model, provided by our industry partner and used for autonomous guiding of airplanes on taxi runways. This regression model takes as input an image of the runway and produces two outputs, cross-track error and heading error, which represent the position of the plane relative to the center line. We use the Prophecy tool to extract neuron activation patterns for the correctness and safety properties of the model. We show the use of these patterns to identify features of the input that explain correct and incorrect behavior. We also use the patterns to provide guarantees of consistent behavior. We explore a novel idea of using sequences of images (instead of single images) to obtain good explanations and identify regions of consistent behavior.

Deep Neural Networks↗

Inversion of surface parameters using fast learning neural networks

A neural network approach to the inversion of surface scattering parameters is presented. Simulated data sets based on a surface scattering model are used so that the data may be viewed as taken from a completely known randomly rough surface. The fast learning (FL) neural network and a multilayer perceptron (MLP) trained with backpropagation learning (BP network) are tested on the simulated backscattering data. The RMS error of training the FL network is found to be less than one half the error of the BP network while requiring one to two orders of magnitude less CPU time. When applied to inversion of parameters from a statistically rough surface, the FL method is successful at recovering the surface permittivity, the surface correlation length, and the RMS surface height in less time and with less error than the BP network. Further applications of the FL neural network to the inversion of parameters from backscatter measurements of an inhomogeneous layer above a half space are shown.

Dawson, M. S.↗

Automation of Some Operations of a Wind Tunnel Using Artificial Neural Networks

Artificial neural networks were used successfully to sequence operations in a small, recently modernized, supersonic wind tunnel at NASA-Lewis Research Center. The neural nets generated correct estimates of shadowgraph patterns, pressure sensor readings and mach numbers for conditions occurring shortly after startup and extending to fully developed flow. Artificial neural networks were trained and tested for estimating: sensor readings from shadowgraph patterns, shadowgraph patterns from shadowgraph patterns and sensor readings from sensor readings. The 3.81 by 10 in. (0.0968 by 0.254 m) tunnel was operated with its mach 2.0 nozzle, and shadowgraph was recorded near the nozzle exit. These results support the thesis that artificial neural networks can be combined with current workstation technology to automate wind tunnel operations.

Decker, Arthur J.↗

Predicting cloud-to-ground lightning with neural networks

A neural network is being trained to predict lightning at Cape Canaveral for periods up to two hours in advance. Inputs consist of ground based field mill data, meteorological tower data, lightning location data, and radiosonde data. High values of the field mill data and rapid changes in the field mill data, offset in time, provide the forecasts or desired output values used to train the neural network through backpropagation. Examples of input data are shown and an example of data compression using a hidden layer in the neural network is discussed.

Barnes, Arnold A., Jr.↗

Parametric motion control of robotic arms: A biologically based approach using neural networks

A neural network based system is presented which is able to generate point-to-point movements of robotic manipulators. The foundation of this approach is the use of prototypical control torque signals which are defined by a set of parameters. The parameter set is used for scaling and shaping of these prototypical torque signals to effect a desired outcome of the system. This approach is based on neurophysiological findings that the central nervous system stores generalized cognitive representations of movements called synergies, schemas, or motor programs. It has been proposed that these motor programs may be stored as torque-time functions in central pattern generators which can be scaled with appropriate time and magnitude parameters. The central pattern generators use these parameters to generate stereotypical torque-time profiles, which are then sent to the joint actuators. Hence, only a small number of parameters need to be determined for each point-to-point movement instead of the entire torque-time trajectory. This same principle is implemented for controlling the joint torques of robotic manipulators where a neural network is used to identify the relationship between the task requirements and the torque parameters. Movements are specified by the initial robot position in joint coordinates and the desired final end-effector position in Cartesian coordinates. This information is provided to the neural network which calculates six torque parameters for a two-link system. The prototypical torque profiles (one per joint) are then scaled by those parameters. After appropriate training of the network, our parametric control design allowed the reproduction of a trained set of movements with relatively high accuracy, and the production of previously untrained movements with comparable accuracy. We conclude that our approach was successful in discriminating between trained movements and in generalizing to untrained movements.

Bock, O.↗

Sharing leaky-integrate-and-fire neurons for memory-efficient spiking neural networks

Spiking Neural Networks (SNNs) have gained increasing attention as energy-efficient neural networks owing to their binary and asynchronous computation. However, their non-linear activation, that is Leaky-Integrate-and-Fire (LIF) neuron, requires additional memory to store a membrane voltage to capture the temporal dynamics of spikes. Although the required memory cost for LIF neurons significantly increases as the input dimension goes larger, a technique to reduce memory for LIF neurons has not been explored so far. To address this, we propose a simple and effective solution, EfficientLIF-Net, which shares the LIF neurons across different layers and channels. Our EfficientLIF-Net achieves comparable accuracy with the standard SNNs while bringing up to ~4.3× forward memory efficiency and ~21.9× backward memory efficiency for LIF neurons. We conduct experiments on various datasets including CIFAR10, CIFAR100, TinyImageNet, ImageNet-100, and N-Caltech101. Furthermore, we show that our approach also offers advantages on Human Activity Recognition (HAR) datasets, which heavily rely on temporal information. The code has been released at https://github.com/Intelligent-Computing-Lab-Yale/EfficientLIF-Net.

60 APPLIED LIFE SCIENCES↗

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗

Co-training of multiple neural networks for simultaneous optimization and training of physics-informed neural networks for composite curing

This paper introduces a Physics-Informed Neural Network (PINN) technique that co-trains neural networks (NNs) that represent each function in a system of equations to simultaneously solve equations representing an out-of-autoclave (OOA) cure process while conducting optimization in adherence to process requirements. Specifically, this co-training approach benefits from using NNs to represent OOA inputs (air temperature profile) and outputs (part and tool temperature profiles and degree of cure). Production requirements can then be levied on the inputs, such as maximum air temperature and minimum cure cycle, and simultaneously on the outputs, such as degree of cure, maximum part temperature, and part temperature rate limits. The technique is validated with finite element (FE) simulations and physical experiments for curing a Toray T830H-6 K/3900-2D composite panel. Furthermore, this novel approach efficiently models and optimizes the OOA cure process.

Composite curing↗

BitGNN: Unlocking the Performance Potential of Binary Graph Neural Networks on GPUs

Graph Neural Networks (GNNs) have shown compelling results in many graph-based learning tasks. They are, however, time-consuming. Recent work has shown a promising direction in improving GNN speed and shrinking the size — network binarization, which binarizes network values and operations. Prior work, however, mainly focused on algorithm designs, leaving it open on how to fully materialize the performance potential. This work fills the gap by proposing techniques to best map binary GNNs and their computations to fit the nature of bit manipulations, optimizations and algorithms to maximize BSpMM kernel efficiency, and solutions to other factors influencing the end-to-end time on GPUs. Results on real-world graphs show that the proposed techniques outperform state of-the-art binary GNN implementations by 21-67× with little accuracy loss.

Chen, Jou-An↗

Scaling kinetic Monte-Carlo simulations of grain growth with combined convolutional and graph neural networks

Graph neural networks (GNN) have emerged as a promising machine learning method for microstructure simulations such as grain growth. However, accurate modeling of realistic grain boundary networks requires large simulation cells, which GNN has difficulty scaling up to. To alleviate the computational costs and memory footprint of GNN, we suggest a hybrid architecture combining a convolutional neural network (CNN) based bijective autoencoder to compress the spatial dimensions, and a GNN that evolves the microstructure in the latent space of reduced spatial sizes. Our results demonstrate that the new design significantly reduces computational costs with using fewer message passing layer (from 12 down to 3) compared with GNN alone. The reduction in computational cost becomes more pronounced as the spatial size increases, indicating strong computational scalability. For the largest mesh evaluated (160 3 ), our method reduces memory usage and runtime in inference by 117× and 115×, respectively, compared with GNN-only baseline. More importantly, it shows higher accuracy and stronger spatiotemporal capability than the GNN-only baseline, especially in long-term testing. Such combination of scalability and accuracy is essential for simulating realistic material microstructures over extended time scales. The improvements can be attributed to the bijective autoencoder’s ability to compress information losslessly from spatial domain into a high dimensional feature space, thereby producing more expressive latent features for the GNN to learn from, while also contributing its own spatiotemporal modeling capability. Training data are generated from stochastic grain growth simulations, providing realistic variability for learning robust microstructure evolution. Comprehensive system validation confirms that the model is accurate, robust, and scalable.

36 MATERIALS SCIENCE↗

Accelerated version of NUBEAM capabilities in DIII-D using neural networks

A neural network model of the effects of neutral beam injection on DIII-D has been developed. The training and testing data used by the model have been generated by the NUBEAM module of TRANSP for experimental discharges from the 2018 DIII-D campaign. Using a principle component analysis to reduce the dimensionality of profile data, the model has been shown to reproduce the results of the Monte Carlo code NUBEAM with a high level of accuracy and an execution time orders of magnitude faster than the execution time of NUBEAM. Furthermore, this makes the neural network model uniquely suited to applications in model-based scenario planning (off-line) and active control (on-line), where a large number of simulation runs are required by the associated optimization tasks that need to be performed before and during the discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Source shape estimation for neutron imaging systems using convolutional neural networks

Neutron imaging systems are important diagnostic tools for characterizing the physics of inertial confinement fusion reactions at the National Ignition Facility (NIF). In particular, neutron images give diagnostic information on the size, symmetry, and shape of the fusion hot spot and surrounding cold fuel. Images are formed via collection of neutron flux from the source using a system of aperture arrays and scintillator-based detectors. Currently, reconstruction of fusion source geometry from the collected neutron images is accomplished by solving a computationally intensive maximum likelihood estimation problem via expectation maximization. In contrast, it is often useful to have simple representations of the overall source geometry that can be computed quickly. In this work, we develop convolutional neural networks (CNNs) to reconstruct the outer contours of simple source geometries. We compare the performance of the CNN for penumbral and pinhole data and provide experimental demonstrations of our methods on both non-noisy and noisy data.

Machine learning, neutron imaging, source reconstr↗

B-PINNs: Bayesian Physics-informal Neural Networks for Forward and Inverse PDE Problems with Noisy Data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINNs posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI with mean field Gaussian approximation for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Loève (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.

Non linear PDEs, Noisy data, Bysian physics inform↗

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↗

Classification of remotely sensed data using OCR-inspired neural network techniques

Neural networks have been applied to classifications of remotely sensed data with some success. To improve the performance of this approach, an examination was made of how neural networks are applied to the optical character recognition (OCR) of handwritten digits and letters. A three-layer, feedforward network, along with techniques adopted from OCR, was used to classify Landsat-4 Thematic Mapper data. Good results were obtained. To overcome the difficulties that are characteristic of remote sensing applications and to attain significant improvements in classification accuracy, a special network architecture may be required.

Kiang, Richard K.↗

Adjoint-Operator Learning For A Neural Network

Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

Barhen, Jacob↗

Model metamers reveal divergent invariances between biological and artificial neural networks

Deep neural network models of sensory systems are often proposed to learn representational transformations with invariances like those in the brain. To reveal these invariances, we generated ‘model metamers’, stimuli whose activations within a model stage are matched to those of a natural stimulus. Metamers for state-of-the-art supervised and unsupervised neural network models of vision and audition were often completely unrecognizable to humans when generated from late model stages, suggesting differences between model and human invariances. Targeted model changes improved human recognizability of model metamers but did not eliminate the overall human–model discrepancy. The human recognizability of a model’s metamers was well predicted by their recognizability by other models, suggesting that models contain idiosyncratic invariances in addition to those required by the task. Metamer recognizability dissociated from both traditional brain-based benchmarks and adversarial vulnerability, revealing a distinct failure mode of existing sensory models and providing a complementary benchmark for model assessment.

59 BASIC BIOLOGICAL SCIENCES↗