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

• Autores: Alonso Ogueda Oliva, Padmanabhan Seshaiyer
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 55, Nº. 2, 2024, págs. 509-542
• Idioma: inglés
• DOI: 10.1080/0020739X.2023.2249901
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• Resumen

  • In 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.