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.

Some of our work can also be directly accessed as code packages on our github page.

Bayesian Optimization is an increasingly popular approach to industrial and scientific prototyping problems. The basic premise in this setting is that one is looking for a location $x$ in some domain where a fitness function $f(x)$ is (globally) minimized. The additional, sometimes implicit, assumption is t... Read More

Linear algebra methods form the basis for the majority of numerical computations. Because they perform a positively elementary task, they have to satisfy strict requirements on computational efficiency and numerical robustness. Our work has added to a growing understanding that many, widely used, linear solvers c... Read More

Optimization problems arising in intelligent systems are similar to those studied in other fields (such as operations research, control, and computational physics). But they also have a few prominent features that are not addressed particularly well by classic optimization methods. One big issue is that classic optimi... Read More

Solvers for ordinary differential equations (ODEs) are one of the basic algorithm classes of numerical mathematics. An ODE is an implicit statement about the relationship of a curve $x:\mathbb{R}\to\mathbb{R}^N$ to its derivative, in the form $x'(t) = f(x(t),t)$, where $x'$ is the derivative of curve, and $f$ ... Read More