Probabilistic numerics is an emerging field that develops randomized algorithms for core problems in numerical linear algebra, optimization, and related areas. This talk introduces some basic methods from randomized linear algebra. As an example of these techniques, we develop an algorithm that can compute an accurate truncated singular value decomposition (SVD) of a huge matrix after a single pass over the data.
This algorithm was designed for on-the-fly compression of matrices that arise from large-scale scientific simulations and data collection. Among other things, it allows us to compute the proper orthogonal decomposition of a direct Navier--Stokes simulation of vortex shedding. We also show how the SVD of a high-resolution sea surface temperature dataset exposes some features of the global climate.
Joint work with Volkan Cevher (EPFL), Madeleine Udell (Cornell), and Alp Yurtsever (EPFL).