E260A: Models in Engineering

The first session begins with foundational concepts and an overview of the use of models in engineering. What is a model? What is the role of data and measurements? What are mechanistic, data-based, and mixed models? What are static and dynamical models? Where do optimization theory and control theory fit in? The second session will be devoted to mechanistic models: those that are built on prior physical principles. We will classify these into static and dynamical models. For static models we will introduce finite differences as a fundamental numerical technique, as well as give a glimpse of more advanced approaches such as FEM. For dynamical models we will review the role of ordinary differential equations, and run numerical experiments with PID feedback control. The third session will focus on data-based models, culminating with the modern techniques of deep learning. In the process we will learn the basic techniques of linear regression and logistic regression, as well as practical considerations such as training versus testing data sets and over-fitting.