In this paper, a solver is developed to obtain accurate analytical solutions for fractional partial differential equations based on artificial neural networks. By leveraging the powerful function ...

$$U({\boldsymbol{\theta }})={V}_{m}{U}_{m}\left({\theta }_{m}\right)\cdots {V}_{1}{U}_{1}\left({\theta }_{1}\right),$$ In this work, we observe that all existing ...

⚠️ A thorough tutorial and explanation of Lie groups, Lie algebras, and geometric priors for deep learning models is beyond the scope of this article. Instead, the following sections concentrate on ...

This package implements numerical solvers for Hamilton-Jacobi (HJ) Partial Differential Equations (PDEs) which, in the context of optimal control, may be used to represent the continuous-time ...

The study of the geometric organization of biological tissues has a rich history in the literature. However, the geometry and architecture of individual cells within tissues has traditionally relied ...

This review aims to provide a comprehensive evaluation of the dynamics of the double pendulum, with a particular emphasis on its chaotic behavior. It examines the complicated and unpredictable ...

Kohn–Sham density functional theory (KS-DFT) is a powerful method to obtain key materials’ properties, but the iterative solution of the KS equations is a numerically intensive task, which limits its ...

1 Physical/Theoretical Chemistry Research Group, Department of Pure and Applied Chemistry, University of Calabar, CRS, Calabar, Nigeria. 2 CAS Key Laboratory for Nanosystem and Hierarchical ...

The given task was to implement the Jacobi method in several versions: a serial CPU function, an un-optimized CUDA kernel, and an optimized version of the CUDA kernel. The Jacobi method was ...