Literate programming for motivating and teaching neural network-based approaches to solve differential equations

Abstract

AbstractIn this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook environments during real-time instruction. Each of these teaching modules employs a literate programming approach that uses the notebook environment to explain the concepts in a natural language, such as English, interspersed with snippets of macros and traditional source code on a web browser. The pedagogical approach employed is reproducible and leads to openaccess material for students to motivate and teach differential equations efficiently. We will share examples of this framework applied to teaching advanced concepts such as machine learning and neural network approaches for solving ordinary and partial differential equations as well as estimating parameters in these equations for given datasets. More details of the work can be accessed from https://aoguedao.github.io/teaching-ml-diffeq.Keywords: Literate programmingdifferential equationsmachine learning AcknowledgmentsThe authors are also very grateful to the anonymous reviewers whose feedback was very useful.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThis work is partially supported by the National Science Foundation [grant numbers DMS-2031029 and DMS-2230117].