AM Seminar: Linear Stochastic Emulators of the Ocean Circulation based on Balanced Truncation: A Caution, perhaps, for Machine Learning?

Presenter: Professor Andy Moore, UCSC Ocean Sciences

Description: Linear inverse models have enjoyed considerable popularity in the geosciences, particularly in the arena of climate research and climate prediction, for several decades as a straightforward approach to dimension reduction and streamlining computational efficiency. The most common approach is to truncate the system by retaining the leading Empirical Orthogonal Functions (EOFs) which represent the left singular vectors of the transition matrix. While singular value decomposition is the best low rank approximation of the transition matrix, ignoring information contained in the right singular vectors, as is commonly done in linear inverse models, has consequences for the dynamics that approximate the system. Dimension reduction based on balanced truncation simultaneously preserves information from the right and left singular vectors. This talk will review some of these ideas and present examples from the ocean. Since EOF decomposition is quite commonly used for dimension reduction in some machine learning approaches, there may be some lessons here for the machine learning community to consider.

Bio: Professor at UCSC since 2016.

Hosted by: Professor Julie Simons