Introduction to neural networks for engineering and computational science

These notes are part of the pedagogical material I have prepared for the 3-hour tutorial in Physics-aware machine learning, 16-17 January 2023, Isaac Newton Institute, “The mathematical and statistical foundation of future data-driven engineering” programme. This short tutorial is meant to introduce the key ideas of feedforward neural networks and convolutional neural networks in which the physics of the problem is constrained in hard and soft ways. The approach combines theory and hands-on coding with applications in wave equations for acoustic propagation (aeronautical propulsion), and incompressible turbulent flows. These notes contain data-only neural networks.

The notes are inspired by the notes I wrote for my MSc course “Artifi- cial Intelligence for Aerospace Engineers” at Imperial College London, Aeronautics Department. The course is open to a variety of students: 3rd- and 4th-year MEng students, as well as MSc students.