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Physics-Informed Neural Networks with Unknown Partial Differential Equations: An Application in Multivariate Time Series [PDF]

Entropy
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: How can models utilize physics or mathematical principles to enhance ...
Seyedeh Azadeh Fallah Mortezanejad, Ruochen Wang, Ali Mohammad-Djafari   +2 more
doaj   +2 more sources

The solutions of nonlinear fractional partial differential equations by using a novel technique

Open Physics, 2022
In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately.
Alderremy Aisha Abdullah, Khan Hassan, Khan Qasim, Kumam Poom, Aly Shaban, Ahmad Said, Sitthithakerngkiet Kanokwan   +6 more
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Mathematical modelling of unsteady Oldroyd-B fluid flow due to stretchable cylindrical surface with energy transport

Ain Shams Engineering Journal, 2023
The unsteady boundary layer flow and thermal transportation analysis of an incompressible Oldroyd-B nanofluid driven by stretching cylinder is scrutinized with analytically approach in this study.
Muhammad Yasir, Awais Ahmed, Masood Khan, Abdullah Khamis Alzahrani, Zaka Ullah Malik, Ahmed Mohammad Alshehri   +5 more
doaj   +1 more source

A novel analytical Aboodh residual power series method for solving linear and nonlinear time-fractional partial differential equations with variable coefficients

AIMS Mathematics, 2022
The goal of this research is to develop a novel analytic technique for obtaining the approximate and exact solutions of the Caputo time-fractional partial differential equations (PDEs) with variable coefficients.
Muhammad Imran Liaqat, Sina Etemad, Shahram Rezapour , Choonkil Park   +3 more
doaj   +1 more source

A Chebyshev Spectral Collocation Method-Based Series Approach for Boundary Layer Flow and Heat Transfer in a Micropolar Fluid past a Permeable Flat Plate

Journal of Applied Mathematics, 2022
This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly.
T. M. Agbaje, G. Makanda
doaj   +1 more source

Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems

Advanced Modeling and Simulation in Engineering Sciences, 2023
Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and ...
Pratyush Bhatt, Yash Kumar, Azzeddine Soulaïmani   +2 more
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Approximate analytical solutions for multispecies convection-dispersion transport equation with variable parameters

Frontiers in Earth Science, 2023
Multispecies pollutant migration often occurs in polluted groundwater systems. Most of the multispecies problems that have been dealt in the literature assume constant transport parameters, primarily because analytical solutions for varying parameters ...
Manotosh Kumbhakar, Vijay P. Singh
doaj   +1 more source

The Analytic Solutions of the Fractional-Order Model for the Spatial Epidemiology of the COVID-19 Infection

Advances in Mathematical Physics, 2023
This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of ...
Benedict Barnes, Martin Anokye, Mohammed Muniru Iddrisu, Bismark Gawu, Emmanuel Afrifa   +4 more
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Superconvergence Analysis of Discontinuous Galerkin Methods for Systems of Second-Order Boundary Value Problems

Computation, 2023
In this paper, we present an innovative approach to solve a system of boundary value problems (BVPs), using the newly developed discontinuous Galerkin (DG) method, which eliminates the need for auxiliary variables.
Helmi Temimi
doaj   +1 more source

Wave Effects of the Fractional Shallow Water Equation and the Fractional Optical Fiber Equation

Frontiers in Applied Mathematics and Statistics, 2022
The non-linear space-time fractional Estevez-Mansfield-Clarkson (EMC) equation and the non-linear space-time fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation showed the motion of waves in the shallow water equation and the optical fiber equation ...
Sirasrete Phoosree, Weerachai Thadee
doaj   +1 more source