SEARCH · Engineering Papers

Results for “Neural equations”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

10 records

All sources NASA NTRS DOE OSTI

NASA NTRS1988

Optimization with artificial neural network systems - A mapping principle and a comparison to gradient based methods

General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.

Leong, Harrison Monfook↗

NASA NTRSDate not supplied

Li-ion Battery Aging with Hybrid Physics-Informed Neural Networks and Fleet-wide Data

In this work, we propose a hybrid model for Li-ion battery discharge and aging prediction that leverages fleet-wide data to predict future capacity drops.The model is built upon an hybrid approach merging physics-based and empirical equations, as well as neural network models in a recurrent neural network cell. The hybrid physics-informed neural network can predict voltage discharge cycles given the loading profile, and estimate the used capacity of the battery under random-loading conditions by tracking aging parameters connected to the residual capacity of the battery. By merging information on the battery aging parameters with existing fleet-wide aging data, the model can predict the future residual capacity of the battery that is being monitored, and therefore enable predictions of voltage discharge curves far ahead in the battery life cycle. We validated the approach using the NASA Prognostics Data Repository Battery data-set, which contains experimental data on Li-ion batteries discharged at random loading conditions in a controlled environment. The approach also allows the identification of discrepancies between the battery aging trend and the trend observed at the fleet level, so that batteries behaving differently from the rest of the fleet can be subject to closer monitoring and further testing to refine predictions.

PINN↗

NASA NTRS1990

Application of adjoint operators to neural learning

A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.

Barhen, J.↗

NASA NTRS1990

Neurocomputing

The present work is intended to give technologists, research scientists, and mathematicians a graduate-level overview of the field of neurocomputing. After exploring the relationship of this field to general neuroscience, attention is given to neural network building blocks, the self-adaptation equations of learning laws, the data-transformation structures of associative networks, and the multilayer data-transformation structures of mapping networks. Also treated are the neurocomputing frontiers of spatiotemporal, stochastic, and hierarchical networks, 'neurosoftware', the creation of neural network-based computers, and neurocomputing applications in sensor processing, control, and data analysis.

Hecht-Nielsen, Robert↗

NASA NTRS1981

Benefits of detailed models of muscle activation and mechanics

Recent biophysical and physiological studies identified some of the detailed mechanisms involved in excitation-contraction coupling, muscle contraction, and deactivation. Mathematical models incorporating these mechanisms allow independent estimates of key parameters, direct interplay between basic muscle research and the study of motor control, and realistic model behaviors, some of which are not accessible to previous, simpler, models. The existence of previously unmodeled behaviors has important implications for strategies of motor control and identification of neural signals. New developments in the analysis of differential equations make the more detailed models feasible for simulation in realistic experimental situations.

Lehman, S. L.↗

NASA NTRS1973

Responses to rotating linear acceleration vectors considered in relation to a model of the otolith organs

Human subjects were exposed to a linear acceleration vector that rotated in the transverse plane of the skull without angular counterrotation. Lateral eye movements showed a sinusoidal change in slow phase velocity and an asymmetry or bias in the same direction as vector rotation. A model is developed that attributes the oculomotor response to otolithic mechanisms. It is suggested that the bias component is the manifestation of torsion of the statoconial plaque relative to the base of the utricular macula and that the sinusoidal component represents the translational oscillation of the statoconia. The model subsumes a hypothetical neural mechanism which allows x- and y-axis accelerations to be resolved. Derivation of equations of motion for the statoconial plaque in torsion and translation, which take into account forces acting in shear and normal to the macula, yield estimates of bias and sinusoidal components that are in qualitative agreement with the diverse experimental findings.

Benson, A. J.↗

NASA NTRSDate not supplied

Usage-based Lifing of Lithium-Ion Battery with HybridPhysics-Informed Neural Networks

Lithium-ion batteries are commonly used to power unmanned aircraft vehicles (UAVs).The ability to model and forecast the remaining useful life of these batteries enables UAV reliability assurance. Building accurate models for battery state of charge and state of health based on first principles is challenging due to the complex electrochemistry that governs battery operations and computational complexity required to solve them. Therefore, reduced order models are often used due to their ability to capture the overall battery discharge. Un-fortunately, these simplifications lead to residual discrepancy between model predictions and observed data. In this paper, we present a hybrid modeling approach merging reduced-order models and neural networks. In this approach, while most of the input-output relationship is captured by Nernst and Butler-Volmer equations, data-driven kernels reduce the gap between predictions and observations. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence repository. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with a limited number of observations.

Lithium-ion Battery↗

NASA NTRS1990

Application of the sine-Poisson equation in solar magnetostatics

Solutions of the sine-Poisson equations are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model (j) is directed along the x-axis, where x is the horizontal ignorable coordinate; (j) varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. Solutions for the magnetostatic potential A corresponding to the one-soliton, two-soliton, and breather solutions of the sine-Gordon equation are studied. Depending on the values of the free parameters in the soliton solutions, horizontally periodic magnetostatic structures are obtained possessing either a single X-type neutral point, multiple neural X-points, or solutions without X-points.

Webb, G. M.↗

NASA NTRS1988

How to cluster in parallel with neural networks

Partitioning a set of N patterns in a d-dimensional metric space into K clusters - in a way that those in a given cluster are more similar to each other than the rest - is a problem of interest in astrophysics, image analysis and other fields. As there are approximately K(N)/K (factorial) possible ways of partitioning the patterns among K clusters, finding the best solution is beyond exhaustive search when N is large. Researchers show that this problem can be formulated as an optimization problem for which very good, but not necessarily optimal solutions can be found by using a neural network. To do this the network must start from many randomly selected initial states. The network is simulated on the MPP (a 128 x 128 SIMD array machine), where researchers use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also by starting the network from many initial states at once, thus obtaining many solutions in one run. Researchers obtain speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of speedups comensurate with human perceptual abilities.

Kamgar-Parsi, Behzad↗

NASA NTRS1990

Non-Lipschitzian neural dynamics

A novel approach is presented which is motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks: their rigid behavior as compared with even the simplest biological systems. It is demonstrated that non-Lipschitzian dynamics, based on the faliure of the Lipschitz conditions at repellers, displays a new qualitative effect, i.e., a multichoice response to periodic external excitations. This makes it possible to construct unpredictable systems, represented in the form of coupled activation and learning dynamical equations. It is shown that unpredictable systems can be controlled by sign strings which uniquely define the system behavior by specifying the direction of the motions at the critical points. Unpredictable systems driven by sign strings are extremely flexible and can serve as a powerful tool for complex pattern recognition.

Barhen, Jacob↗