scholarly journals Disparity Computation Through PDE and Data-Driven CeNN Technique

2021 ◽  
Vol 38 (4) ◽  
pp. 1051-1059
Author(s):  
Mahima Lakra ◽  
Sanjeev Kumar
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Experimental Study ◽  
Variational Approach ◽  
Cellular Neural Network ◽  
Energy Functional ◽  
Data Driven ◽  
Pde Model ◽  
Distance Regularization

This paper proposes a variational approach by minimizing the energy functional to compute the disparity from a given pair of consecutive images. The partial differential equation (PDE) is modeled from the energy function to address the minimization problem. We incorporate a distance regularization term in the PDE model to preserve the boundaries' discontinuities. The proposed PDE is numerically solved by a cellular neural network (CeNN) algorithm. This CeNN based scheme is stable and consistent. The effectiveness of the proposed algorithm is shown by a detailed experimental study along with its superiority over some of the existing algorithms.

GIẢI PHƯƠNG TRÌNH ĐẠO HÀM RIÊNG SỬ DỤNG MẠNG NEURAL NHÂN TẠO

2020 ◽  
Vol 45 (03) ◽  
Author(s):  
HO DAC QUAN ◽  
HUYNH TRUNG HIEU
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Neural Networks ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Neural Network Method ◽  
Network Method ◽  
Hidden Layer

Phương trình đạo hàm riêng đã được ứng dụng rộng rãi trong các lĩnh vực khác nhau của đời sống như vật lý, hóa học, kinh tế, xử lý ảnh vv. Trong bài báo này chúng tôi trình bày một phương pháp giải phương trình đạo hàm riêng (partial differential equation - PDE) thoả điều kiện biên Dirichlete sửdụng mạng neural truyền thẳng một lớp ẩn (single-hidden layer feedfordward neural networks - SLFN) gọi là phương pháp mạng neural (neural network method – NNM). Các tham số của mạng neural được xác định dựa trên thuật toán huấn luyện mạng lan truyền ngược (backpropagation - BP). Kết quả nghiệm PDE thu được bằng phương pháp NNM chính xác hơn so với nghiệm PDE giải bằng phương pháp sai phân hữu hạn.

scholarly journals A SEMI-LINEAR ELLIPTIC PDE MODEL FOR THE STATIC SOLUTION OF JOSEPHSON JUNCTIONS

1995 ◽  
Vol 06 (02) ◽  
pp. 241-262 ◽  
Author(s):  
JEAN-GUY CAPUTO ◽  
NIKOS FLYTZANIS ◽  
EMMANUEL VAVALIS
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Elliptic Partial Differential Equation ◽  
Static Solution ◽  
Elliptic Pde ◽  
Computational Results ◽  
Computer Implementation ◽  
Pde Model ◽  
Modeling Power ◽  
Zero Voltage

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window junction. Iterative methods for solving this problem are proposed and their computer implementation is discussed. The preliminary computational results that are given, show the modeling power of our approach and exhibit its computational efficiency.

scholarly journals On a nonlinear PDE involving weighted $p$-Laplacian

2019 ◽  
Vol 38 (5) ◽  
pp. 131-145
Author(s):  
A. El Khalil ◽  
M. D. Morchid Alaoui ◽  
Mohamed Laghzal ◽  
A. Touzani
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Method ◽  
Nonlinear Partial Differential Equation ◽  
Weighted Sobolev Spaces ◽  
Point Theory ◽  
Energy Functional ◽  
Nonlinear Pde ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions

In the present paper, we study the nonlinear partial differential equation with the weighted $p$-Laplacian operator\begin{gather*}- \operatorname{div}(w(x)|\nabla u|^{p-2}\nabla u) = \frac{ f(x)}{(1-u)^{2}},\end{gather*}on a ball ${B}_{r}\subset \mathbb{R}^{N}(N\geq 2)$. Under some appropriate conditionson the functions $f, w$ and the nonlinearity $\frac{1}{(1-u)^{2}}$, we prove the existence and the uniqueness of solutions of the above problem. Our analysis mainly combines the variational method and critical point theory. Such solution is obtained as a minimizer for the energy functional associated with our problem in the setting of the weighted Sobolev spaces.

scholarly journals Research on Odor Interaction between Aldehyde Compounds via a Partial Differential Equation (PDE) Model

Sensors ◽  
2015 ◽  
Vol 15 (2) ◽  
pp. 2888-2901 ◽  
Author(s):  
LuchunYan ◽  
Jiemin Liu ◽  
Chen Qu ◽  
Xingye Gu ◽  
Xia Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Pde Model

Dynamic Analysis of Nonlinear Oscillator Equation Arising in Double-Sided Driven Clamped Microbeam-Based Electromechanical Resonator

2012 ◽  
Vol 67 (8-9) ◽  
pp. 435-440 ◽  
Author(s):  
Yasir Khan ◽  
Mehdi Akbarzade
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Approach ◽  
Nonlinear Oscillator ◽  
Analytical Form ◽  
Angular Frequency ◽  
Initial Amplitude ◽  
Hamiltonian Approach ◽  
The Galerkin Method ◽  
The Relationship

In this paper, three different analytical methods have been successfully used to study a nonlinear oscillator equation arising in the microbeam-based electromechanical resonator. These methods are: variational approach, Hamiltonian approach, and amplitude-frequency formulation. The governing equation is based on the Euler-Bernoulli hypothesis and the partial differential equation (PDE) is simplified into an ordinary differential equartion (ODE) by using the Galerkin method. A frequency analysis is carried out, and the relationship between the angular frequency and the initial amplitude is obtained in closed analytical form. A comparison of the present solutions is made with the existing solutions and excellent agreement is noted.

scholarly journals Modification of Levenberg-Marquardt Algorithm for Solve Two Dimension Partial Differential Equation

2018 ◽  
Vol 26 (7) ◽  
pp. 107-117
Author(s):  
Khalid Mindeel M. Al-Abrahemee ◽  
Rana T. Shwayaa
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Partial Differential ◽  
Two Dimension ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
In The Beginning ◽  
Lm Algorithm

In this paper we presented a new way based on neural network has been developed for solutione of two dimension  partial differential equations . A modified neural network use to over passing the Disadvantages of LM algorithm, in the beginning we suggest signaler value decompositions of Jacobin matrix (J) and inverse of Jacobin matrix( J-1), if a matrix rectangular or singular  Secondly, we suggest new calculation of μk , that ismk=|| E (w)||2    look the nonlinear execution equations E(w) = 0 has not empty solution W* and we refer   to the second norm in all cases ,whereE(w):  is continuously differentiable and E(x) is Lipeschitz  continuous, that is=|| E(w 2)- E(w 1)||£ L|| w  2- w  1|| ,where L  is Lipeschitz  constant.

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