Physical structure-preservation & advanced computational techniques for scientific machine…

Catalog description

This course serves as a foundation in advanced topics in scientific machine learning, providing a foundational overview of conventional principles in variational mechanics and the numerical discretization of PDEs to develop machine learning architectures able to construct predictive simulators from observational data. While physics-agnostics techniques dominate much of the literature, we focus on how to embed symmetries, topological structures, variational principles, and stochastic dynamics into models. These concepts provide guarantees necessary to deploy data-driven models in realistic, high-consequence engineering settings. The course will introduce advanced discretizations of finite elements, dynamical systems, and stochastic dynamics and illustrate how modern transformer-based architectures may be integrated alongside these conventional frameworks. We highlight how these frameworks admit analysis and allow us to provide theoretical guarantees, and also show how physics-inspired architectures may be used to define non-scientific machine learning algorithms with guaranteed performance and stability. While the course is best taken in a sequence with ENGR5310, it is designed to be self-contained and accessible to anyone with a background in linear algebra and modern machine learning libraries, with no required previous training in scientific computing or mechanics.