Before deploying autonomous decision-making systems in high-stakes applications, it is important to ensure that they will operate as intended. This course presents a variety of mathematical concepts and algorithms that can be used to validate their performance in simulation. The course first introduces a framework for setting up validation problems using topics from model fitting, model validation, and property specification. The course then covers sampling-based validation techniques for tasks such as falsification and probability of failure estimation. The course concludes with an overview of formal methods for tasks such as reachability analysis. Topics include but are not limited to: mathematical modeling, temporal logic specifications, optimization-based falsification, Markov chain Monte Carlo, importance sampling, reachability analysis, model checking, satisfiability, and explainability. Applications are drawn from air traffic control, autonomous systems, and self-driving cars. Prerequisites: basic probability theory, multivariable calculus, and fluency in a high-level programming language
3-4 units · Letter or Credit/No Credit
Before deploying autonomous decision-making systems in high-stakes applications, it is important to ensure that they will operate as intended. This course presents a variety of mathematical concepts and algorithms that can be used to validate their performance in simulation. The course first introduces a framework for setting up validation problems using topics from model fitting, model validation, and property specification. The course then covers sampling-based validation techniques for tasks such as falsification and probability of failure estimation. The course concludes with an overview of formal methods for tasks such as reachability analysis. Topics include but are not limited to: mathematical modeling, temporal logic specifications, optimization-based falsification, Markov chain Monte Carlo, importance sampling, reachability analysis, model checking, satisfiability, and explainability. Applications are drawn from air traffic control, autonomous systems, and self-driving cars. Prerequisites: basic probability theory, multivariable calculus, and fluency in a high-level programming language
Offered in Winter 2026 at Stanford University.