An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations

no code implementations • 25 Jan 2024 • Tayebeh Taheri, Alireza Afzal Aghaei, Kourosh Parand

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest.

Accelerating Fractional PINNs using Operational Matrices of Derivative

no code implementations • 25 Jan 2024 • Tayebeh Taheri, Alireza Afzal Aghaei, Kourosh Parand

This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs).

deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations

no code implementations • 14 Sep 2023 • Ali Nosrati Firoozsalari, Hassan Dana Mazraeh, Alireza Afzal Aghaei, Kourosh Parand

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately.

Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks

no code implementations • 7 Aug 2023 • Alireza Afzal Aghaei, Kourosh Parand, Ali Nikkhah, Shakila Jaberi

The efficiency of the proposed method is carried out by simulating various configurations of the Falkner-Skan equation.