# Probabilistic numerical analysis of differential equations

When? |
September 14, 2015 - September 18, 2015 |

Where? |
Potsdam, Germany |

Organizers |
Ben Calderhead |

Official Site |
http://scicade2015.math.uni-potsdam.de/scicade2015/index.html |

Classical approaches to solving Differential Equations approximate the true underlying infinite dimensional solution by providing a single discrete solution, whose accuracy is known up to a particular (user-defined) error tolerance. Recently there has been growing interest in considering such solutions from a statistical perspective, whereby the task is to characterise the epistemic uncertainty in the solution arising from the fact we cannot evaluate the solution of the differential equation at every point on the domain of interest. When considered as a statistical inference problem, we then seek a measure over functions that are consistent with the finite function evaluations that we observe. An early work on probabilistic methods for the solution of differential equations was offered by Skilling (Skilling, 1991), using a Bayesian extrapolation formulation, and more recently, (Chkrebtii, Campbell, Girolami & Calderhead, 2013) have provided further extensions and a more rigorous theoretical analysis. Some connections between Gaussian extrapolators and classic Runge-Kutta methods have also been highlighted (Schober, Duvenaud & Hennig, 2014). A very deep literature exists for any classical approaches such as the Runge-Kutta family of solvers, however probabilistic approaches are still in their infancy. The aim of this mini-symposium is to highlight the latest work in this new field, discuss theĆ many open questions that arise, and present these ideas to the wider mathematical community.