16 citations · 37 across the 11 of their papers we have counts for
7 papers · 1 filter
KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems
Alireza Afzal Aghaei
In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explai…
A Physics-Informed Machine Learning Approach for Solving Distributed Order Fractional Differential Equations
Alireza Afzal Aghaei
This paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. The core of this appr…
PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problems
Alireza Afzal Aghaei, Mahdi Movahedian Moghaddam, Kourosh Parand
This paper introduces an efficient tensor-vector product technique for the rapid and accurate approximation of integral operators within physics-informed deep learning frameworks.…
rKAN: Rational Kolmogorov-Arnold Networks
Alireza Afzal Aghaei
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 a…
fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions
Alireza Afzal Aghaei
Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. This pap…
An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations
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. In this study, we ex…
Accelerating Fractional PINNs using Operational Matrices of Derivative
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). Our approach involves a non-uniform discre…