Kinetic.jl: A portable finite volume toolbox for scientific and neural computing

Abstract

Kinetic.jl is a lightweight finite volume toolbox written in the Julia programming language for the study of computational physics and scientific machine learning. It is an open-source project hosted on GitHub and distributed under the MIT license. The main module consists of KitBase.jl for basic physics and KitML.jl for neural dynamics. The function library provides a rich set of numerical fluxes and source terms for differential and integral equations. Any advection-diffusion type mechanical or neural equation can be set up and solved within the framework. Machine learning methods can be seamlessly integrated to build data-driven closure models and accelerate the calculation of nonlinear terms. The package is designed to balance programming flexibility for scientific research, algorithmic efficiency for applications, the simplicity for educational usage.