Our group aims to develop and broaden the understanding of numerical algorithms in terms of probabilistic inference. That is, we try to phrase the computations performed by a numerical method as the actions taken by an agent equipped with a notion of uncertainty about its task, captured by a probability measure. Exact computations performed on a chip provide information about the (normally not analytically solvable) task, yielding a posterior probability measure whose location and width should ideally provide a point estimate and meaningful surrounding uncertainty over the true solution.
We study numerical problems across a broad spectrum of areas, including linear algebra, nonlinear optimization, integration, and the solution of differential equations. In all these areas, we study both the theory and practical applications of probabilistic numerical methods. More information on individual areas can be found in the project pages linked on the left.