Steve Brunton: Machine Learning for Scientific Discovery, with Examples in Fluid Mechanics

Abstract

Accurate and efficient nonlinear dynamical systems models are essential understand, predict, estimate, and control complex natural and engineered systems. In this talk, I will explore how machine learning may be used to develop these models purely from measurement data. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system. We also discuss the importance of learning effective coordinate systems in which the dynamics may be expected to be sparse. This sparse modeling approach will be demonstrated on a range of challenging modeling problems, for example in fluid dynamics. Because fluid dynamics is central to transportation, health, and defense systems, we will emphasize the importance of machine learning solutions that are interpretable, explainable, generalizable, and that respect known physics.