Zobrazeno 1 - 10
of 179
pro vyhledávání: '"Aghaei, Alireza"'
Autor:
Aghaei, Alireza Afzal
In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explain how Gaussian quadrature can be employed to approximate the integral
Externí odkaz:
http://arxiv.org/abs/2409.06649
Autor:
Aghaei, Alireza Afzal
This paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. The core of this approach involves extending the support vector regression (SVR) algorithm
Externí odkaz:
http://arxiv.org/abs/2409.03507
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
Autor:
Aghaei, Alireza Afzal
The development of Kolmogorov-Arnold networks (KANs) marks a significant shift from traditional multi-layer perceptrons in deep learning. Initially, KANs employed B-spline curves as their primary basis function, but their inherent complexity posed im
Externí odkaz:
http://arxiv.org/abs/2406.14495
Autor:
Aghaei, Alireza Afzal
Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. This paper presents the Fractional Kolmogorov-Arnold Network (fKAN), a novel n
Externí odkaz:
http://arxiv.org/abs/2406.07456
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
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