Machine Learning, Modeling, and Simulation Principles is a 5-week course that will introduce the conceptual underpinnings of machine learning from the ground up.
This course teaches the foundations and principles of machine learning as a tool for modeling and prediction that builds on other tools from modeling simulation and prediction that learners already have some exposure to. It reviews how complex physical processes can be simulated by discretizing differential equations and explores how optimization techniques are foundational to machine learning, and at the heart of parameter estimation, regression, and classification—the building blocks of machine learning methods.
The course is well-suited for scientists, researchers, engineers, and others looking to expand their ability to model and simulate systems to produce and refine data and make better decisions.
While many machine learning courses focus on how machine learning can predict consumer behavior, analyze human preferences, remodel huge repositories of text, speech, or images, this course focuses specifically on engineering and science applications, which often have very different demands.
The technical nature of the course requires that learners be proficient in several areas of undergraduate-level mathematics, and makes heavy use of MATLAB to present a guided environment to explore the foundations of machine learning within. Prior experience with MATLAB and computer programming will be helpful, but is not necessary! Please refer to this FAQ article for more information.
The coursework features practice activities with immediate feedback as well as graded assignments that use guided MATLAB code, permitting learners to experiment with and develop an intuition for the methods, their strengths, and weaknesses. Learners are presented with case studies from Schlumberger, Aurora Flight Sciences, and BASF—companies applying machine learning methods to practical problems—in order to refine their understanding of real-world challenges and solutions and to apply their knowledge.
You will explore the historical trajectory and broader context in which machine learning methods exist in science and engineering, identifying the major modeling paradigms: experimentation, theory-based models, model-based computation and simulation, and the new computational paradigm of modeling and simulation built on machine learning ideas. Throughout the course, visual aids and practice environments within MATLAB will be presented to develop intuition and refine understanding.
The week will focus on modeling and simulation fundamentals with ordinary differential equations (ODEs), reviewing explicit and implicit methods and approximation, including higher-order methods.
The second and third weeks will continue with partial differential equations (PDEs), reviewing numerical methods for approximation, including explicit and implicit solutions and boundary conditions. You will also explore how choices of discretization stencil-like finite difference formulas—require careful consideration of the properties of functions being approximated.
Next, you will be introduced to optimization problems, and numerical methods for solving them, beginning with direct solution methods for least squares problems and progressing to more general problems using iterative optimization methods like gradient descent and Newton’s method. Finally, you will begin to be introduced to parameter estimation.
Following that, you will explore regression problems and methods—including linear and logistic regression—, regularization for solving underdetermined systems, classification to make predictions for discrete or non-continuous outputs, and stochastic gradient descent for working with very large datasets. You will begin to pull together these numerical methods to cross over into machine learning methods, investigating model training and the validation methods required to assess model fit, error, and over-fitting considerations.
Week four with focus on probabilistic methods, exploring the role of uncertainty in modeling, specifically exploring how to use Monte Carlo methods for probabilistic forecasting, sensitivity analysis, and risk assessment.
Week five will present several real-world case studies, looking at how companies are applying machine learning methods to practical problems. You will analyze the problems and solutions, and practice applying methods via interactive MATLAB simulations.
The course will introduce you to the foundational principles of machine learning, reviewing the underlying numerical methods to realize machine learning as a core component of the latest computational paradigm of modeling and simulation.
Because this first course primarily covers the foundations and principles of machine learning, and the second course in the program, Applying Machine Learning to Engineering and Science, primarily explores applications of machine learning, the Course Team strongly recommends that most learners take the Machine Learning program's courses in sequential order. Prospective learners who hold a master’s or higher degree in Engineering, are comfortable with the math pre-requisite, Linear Algebra, and have work experience in this or a related field within the last 5 years are likely to find that they are able to take course 2 first, but others should take course 1 first.