Zobrazeno 1 - 10
of 243
pro vyhledávání: '"PARAND, KOUROSH"'
This paper introduces an efficient tensor-vector product technique for the rapid and accurate approximation of integral operators within physics-informed deep learning frameworks. Our approach leverages neural network architectures to evaluate proble
Externí odkaz:
http://arxiv.org/abs/2409.01899
Cognitive decision-making processes are crucial aspects of human behavior, influencing various personal and professional domains. This research delves into the application of differential equations in analyzing decision-making accuracy by leveraging
Externí odkaz:
http://arxiv.org/abs/2402.13027
Autor:
Parand, Kourosh, Pakniyat, Aida
The Schrodinger equation is a mathematical equation describing the wave function's behavior in a quantum-mechanical system. It is a partial differential equation that provides valuable insights into the fundamental principles of quantum mechanics. In
Externí odkaz:
http://arxiv.org/abs/2402.10649
This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs). Our approach involves a non-uniform discretization of the fractional Caputo operator, facilitating swift computa
Externí odkaz:
http://arxiv.org/abs/2401.14081
The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of different
Externí odkaz:
http://arxiv.org/abs/2401.14382
Publikováno v:
International Journal of Computer Science and Information Technology 2022
A brain tumor consists of cells showing abnormal brain growth. The area of the brain tumor significantly affects choosing the type of treatment and following the course of the disease during the treatment. At the same time, pictures of Brain MRIs are
Externí odkaz:
http://arxiv.org/abs/2401.02537
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the proposed desi
Externí odkaz:
http://arxiv.org/abs/2309.07684
In this paper, a new deep-learning architecture for solving the non-linear Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks, this approach shows how orthogonal polynomials can be used in neural networks to increase the ap
Externí odkaz:
http://arxiv.org/abs/2308.03337
Autor:
Aghaei, Alireza Afzal, Parand, Kourosh
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm manner, are
Externí odkaz:
http://arxiv.org/abs/2304.14088
In this article, a new deep learning architecture, named JDNN, has been proposed to approximate a numerical solution to Partial Differential Equations (PDEs). The JDNN is capable of solving high-dimensional equations. Here, Jacobi Deep Neural Network
Externí odkaz:
http://arxiv.org/abs/2212.12700