245 citations · 562 across the 35 of their papers we have counts for
39 papers
IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs
Sima Naraghi, Kourosh Parand, Amirhossein Sadr +1
Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accura…
LyAm: Robust Non-Convex Optimization for Stable Learning in Noisy Environments
Elmira Mirzabeigi, Sepehr Rezaee, Kourosh Parand
Training deep neural networks, particularly in computer vision tasks, often suffers from noisy gradients and unstable convergence, which hinder performance and generalization. In t…
BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equations
Elmira Mirzabeigi, Rezvan Salehi, Kourosh Parand
BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-P…
Advanced Physics-Informed Neural Network with Residuals for Solving Complex Integral Equations
Mahdi Movahedian Moghaddam, Kourosh Parand, Saeed Reza Kheradpisheh
In this paper, we present the Residual Integral Solver Network (RISN), a novel neural network architecture designed to solve a wide range of integral and integro-differential equat…
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.…
Solving the decision-making differential equations from eye fixation data in Unity software by using Hermite Long-Short-Term Memory neural network
Kourosh Parand, Saeed Setayeshi, Mir Mohsen Pedram +2
Cognitive decision-making processes are crucial aspects of human behavior, influencing various personal and professional domains. This research delves into the application of diffe…
Hermite Neural Network Simulation for Solving the 2D Schrodinger Equation
Kourosh Parand, Aida Pakniyat
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 valu…
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…
Using Singular Value Decomposition in a Convolutional Neural Network to Improve Brain Tumor Segmentation Accuracy
Pegah Ahadian, Maryam Babaei, Kourosh Parand
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 dise…
deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations
Ali Nosrati Firoozsalari, Hassan Dana Mazraeh, Alireza Afzal Aghaei +1
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 r…
Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks
Alireza Afzal Aghaei, Kourosh Parand, Ali Nikkhah +1
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 or…
Hyperparameter optimization of orthogonal functions in the numerical solution of differential equations
Alireza Afzal Aghaei, Kourosh Parand
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known…
JDNN: Jacobi Deep Neural Network for Solving Telegraph Equation
Maryam Babaei, Kimia Mohammadi Mohammadi, Zeinab Hajimohammadi +1
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 o…
A least squares support vector regression for anisotropic diffusion filtering
Arsham Gholamzadeh Khoee, Kimia Mohammadi Mohammadi, Mostafa Jani +1
Anisotropic diffusion filtering for signal smoothing as a low-pass filter has the advantage of the edge-preserving, i.e., it does not affect the edges that contain more critical da…
Legendre Deep Neural Network (LDNN) and its application for approximation of nonlinear Volterra Fredholm Hammerstein integral equations
Zeinab Hajimohammadi, Kourosh Parand, Ali Ghodsi
Various phenomena in biology, physics, and engineering are modeled by differential equations. These differential equations including partial differential equations and ordinary dif…
Symbolically Solving Partial Differential Equations using Deep Learning
Maysum Panju, Kourosh Parand, Ali Ghodsi
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our…
A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval
Amir Hosein Hadian-Rasanan, Mehran Nikarya, Arman Bahramnezhad +2
In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation…
A development of Lagrange interpolation, Part I: Theory
Mehdi Delkhosh, Kourosh Parand, Amir H. Hadian-Rasanan
In this work, we introduce the new class of functions which can use to solve the nonlinear/linear multi-dimensional differential equations. Based on these functions, a numerical me…
Solving the Boundary Layer Flow of an Eyring-Powell Non-Newtonian Fluid
K. Parand, S. Latifi, M. M. Moayeri
In this paper, the Rational Jacobi (RJ) collocation method is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. Thi…
Generalized Lagrangian Jacobi-Gauss-Radau collocation method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation
Kourosh Parand, Sobhan Latifi, Mehdi Delkhosh +1
In this paper, a nonlinear 2D Optimal Control Problem (2DOCP) is considered. The quadratic performance index of a nonlinear cost function is endowed with the state and control func…
A Comparison Between Laguerre, Hermite, and Sinc Orthogonal Functions
Fattaneh Bayatbabolghani, Kourosh Parand
A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations…
Two efficient computational algorithms to solve the singularly perturbed Lane-Emden problem
Kourosh Parand, Amin Ghaderi
In this paper, we decide to compare two new approaches based on Rational and Exponential Bessel functions (RBs and EBs) to solve several well-known class of Lane-Emden type models.…
A matrix formulation of the Tau method for the numerical solution of non-linear problems
Kourosh Parand, Amin Ghaderi, Mehdi Delkhosh +1
The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational…