In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The main ...

この記事は ArXiv:2010.08895 “Fourier Neural Operator for Parametric Partial Differential Equations” をもとに、ChatGPT による要約と解説を含むものです。正確性を期すには原論文を参照してください。 背景と問題設定 多くの現象（流体の流れ、熱伝導、弾性体の応答など）は ...

The remarkable potentials of Artificial Intelligence (AI) and Deep Learning have paved the way for a variety of fields ranging from computer vision and language modeling to healthcare, biology, and ...

Mathematics Department, Texas A & M University Kingsville, Kingsville, USA. 1. Definitions and Example of Nonanticipative Operators An important feature of ordinary differential equations is that the ...

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various ...

Abstract: This paper presents the development of an operator algebra for differential systems which is useful in that it allows the transmittance methods commonly applied to linear stationary systems ...

Abstract: The sparrow search algorithm (SSA) represents a novel approach within swarm intelligence optimization, introduced in recent years. Renowned for its minimal control parameters and ...

To keep the global search capability and robustness for unmanned surface vessel (USV) path planning, an improved differential evolution particle swarm optimization algorithm (DePSO) is proposed in ...