• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.4
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• pp.501-507
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• 2021

Neural networks with differentiable activation functions are differentiable with respect to input variables. We improve the approximation capability of neural networks by using the gradient and Hessian of neural networks to satisfy the differential equations of the problems of interest. We apply differential neural networks to the pricing of financial options, where stochastic differential equations and the Black-Scholes partial differential equation represent the differential relation of price of option and underlying assets, and the first and second derivatives of option price play an important role in financial engineering. The proposed neural network learns - (a) the sample paths of option prices generated by stochastic differential equations and (b) the Black-Scholes equation at each time and asset price. Experimental results show that the proposed method gives accurate option values and the first and second derivatives.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.8
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• pp.777-782
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• 2011

Neural network technique is widely employed in the fields of signal processing, control systems, pattern recognition, etc. Learning of neural networks is an important procedure to accomplish dynamic system modeling. This paper presents a novel learning approach for differential neural network models based on the Kalman-Bucy filter theory. We construct an augmented state vector including original neural state and parameter vectors and derive a state estimation rule avoiding gradient function terms which involve to the conventional neural learning methods such as a back-propagation approach. We carry out numerical simulation to evaluate the proposed learning approach in nonlinear system modeling. By comparing to the well-known back-propagation approach and Kalman-Bucy filtering, its superiority is additionally proved under stochastic system environments.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.221-234
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• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.39-52
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• 2022

We introduce Clifford-valued neural networks with leakage delays. Furthermore, we study the uniqueness and existence of Clifford-valued Hopfield artificial neural networks having the Stepanov weighted pseudo almost periodic forcing terms on leakage delay terms. However the noncommutativity of the Clifford numbers' multiplication made our investigation diffcult, so our results are obtained by decomposing Clifford-valued neural networks into real-valued neural networks. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Journal of Industrial Technology
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• v.21 no.B
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• pp.91-98
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• 2001

In this paper, center detection and motion analysis of a moving object are studied. Kohonen's self-organizing neural network models are used for the moving objects tracking and time delay neural networks are used for dynamic characteristic analysis. Instead of objects brightness, neuron projections by Kohonen Networks are used. The motion of target objects can be analyzed by using the differential neuron image between the two projections. The differential neuron image which is made by two consecutive neuron projections is used for center detection and moving objects tracking. The two differential neuron images which are made by three consecutive neuron projections are used for the moving trajectory estimation. It is possible to distinguish 8 directions of a moving trajectory with two frames and 16 directions with three frames.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.6
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• pp.638-648
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• 1990

An effective resolved motion control method of redundant manipulators is proposed to minimize the energy consumption and to increase the dexterity while satisfying the physical actuator constraints. The method employs the neural optimization networks, where the computation of Jacobian matrix is not required. Specifically, end effector movement resulting from each joint differential motion is first separated into orthogonal and tangential components with respect to a given desired trajectory. Then the resolved motion is obtained by neural optimization networks in such a way that 1) linear combination of the orthogonal components should be null 2) linear combination of the tangential components should be the differential length of the desired trajectory, 3) differential joint motion limit is not violated, and 4) weighted sum of the square of each differential joint motion is minimized. Here the weighting factors are controlled by a newly defined joint dexterity measure as the ratio of the tangential and orthogonal components.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.63.5-63
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• 2001

In this paper, moving objects tracking and dynamic characteristic analysis are studied. Kohonen´s self-organizing neural network models are used for moving objects tracking and time delay neural networks are used for dynamic characteristic analysis. Instead of objects brightness, neuron projections by Kohonen Networks are used. The motion of target objects can be analyzed by using the differential neuron image between the two projections. The differential neuron image which is made by two consecutive neuron projections is used for center detection and moving objects tracking. The two differential neuron images which are made by three consecutive neuron projections are used for the moving trajectory estimation.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1165-1181
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• 2013

In this paper, we consider a class of periodic It$\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\hat{o}$ et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.3
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• pp.134-142
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• 2002

This paper presents a new method for the protective relaying scheme in power transformer using wavelet based neural networks. This approach is as fellows. After approximation and detail information is extracted by daub wavelet transform from differential current of power transformer, the former is used for obtaining the rate of differential currents and restrain currents, the latter used as the input of artificial neural networks to avoid the Hiss-operation in over-exciting state and magnetizing inrush state of power transformer. The simulation of EMTP with respect to different faults, inrush conditions and over-exciting conditions in power transformer have been conducted, and the results preyed that the proposed method is able to discriminate magnetizing inrush states, over-exciting stales and internal faults.