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Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional…

This paper proposes fractional order graph neural networks (FGNNs), optimized by the approximation strategy to address the challenges of local optimum of classic and fractional graph neural networks which are specialised at aggregating…

Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…

In the present paper a newer application of Artificial Neural Network (ANN) has been developed i.e., predicting response-function results of electrical-mechanical system through ANN. This method is specially useful to complex systems for…

This paper investigates typical behaviors like damped oscillations in fractional order (FO) dynamical systems. Such response occurs due to the presence of, what is conceived as, pseudo-damping and meta-damping in some special class of FO…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…

In this paper we present a method to solve initial value problems for fractional growth models, such as generalizations of the exponential and logistic with periodic harvesting models. Using a discretization of the Caputo derivative we…

In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a…

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…

The paper investigates nonlinear system identification using system output data at various linearized operating points. A feed-forward multi-layer Artificial Neural Network (ANN) based approach is used for this purpose and tested for two…

The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…

We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…

Uncertain fractional differential equation (UFDE) is a kind of differential equation about uncertain process. As an significant mathematical tool to describe the evolution process of dynamic system, UFDE is better than the ordinary…

Fractional differential equations (FDEs) describe subdiffusion behavior of dynamical systems. Its non-local structure requires taking into account the whole evolution history during the time integration, which then possibly causes…

Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

With the increasing use of nonlinear devices in both generation and consumption of power, it is essential that we develop accurate and quick control for active filters to suppress harmonics. Time delays between input and output are…

Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive algorithm: the adaptive network enhancement (ANE) method,…