PHSCS 580
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Theory of Predictive Modeling
Physics and AstronomyCollege of Computational, Mathematical, & Physical Sciences
Course Description
Mathematical, computational, and philosophical foundations of machine learning and its dual problem, control. Introduction to system identification, causality, uncertainty, model. approximation, and information geometry
When Taught
Fall
Fixed/Max
3
Fixed
3
No Prerequisites
Title
Problem Formulation
Learning Outcome
Precisely formulate, and understand the distinction between, mathematical learning and control problems. This outcome is Intellectually Enlarging because it requires the rigorous mental discipline and logical clarity necessary to define and categorize complex systems.
Title
Solution Techniques
Learning Outcome
Be familiar with common methods for solving learning problems. Note the role of optimization as a method for separating solution design from specific computational methods, and understand the role of key ideas like gradient descent and convexity. This fulfills the Intellectually Enlarging aim by helping students master the technical depth of gradient descent and convexity within their professional practice.
Title
System Identification
Learning Outcome
Apply learning techniques to model classes of controlled dynamical systems. Understand notions of data informativity, model identifiability, and the spectrum of model classes linking phenomenological (black box) and mechanistic (white box) models.
Title
Limitations
Learning Outcome
Understand how uncertainty is modeled and its role in learning and control problems. Be familiar with ways in which machine learning fails. This builds Character by fostering the integrity and responsibility required to acknowledge the boundaries of technical solutions and manage the risks of failure.
Title
Model Approximation
Learning Outcome
Understand the ideas of coarse-graining, universality classes, the renormalization group, and other methods for approaching model approximation. Understand information geometry and be able to apply the model boundary approximation method for a class of models.
Title
Application
Learning Outcome
Be familiar with a rich collection of model classes used in a wide variety of disciplines. Explore one area deeply in the construction of a specific, predictive model as part of a semester-long project. This supports Lifelong Learning and Service by training students to "go forth to serve" as they apply their predictive expertise to solve meaningful problems in the broader community.
