Probabilistic numerical computation formalises the connection between machine learning
and applied mathematics. Numerical algorithms approximate intractable quantities from …

There is a growing interest in probabilistic numerical solutions to ordinary differential
equations. In this paper, the maximum a posteriori estimate is studied under the class of ν ν …

Probabilistic solvers for ordinary differential equations assign a posterior measure to the
solution of an initial value problem. The joint covariance of this distribution provides an …

Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient
framework for uncertainty quantification and inference on dynamical systems. In this work …

We propose a fast, simple and robust algorithm for computing shortest paths and distances
on Riemannian manifolds learned from data. This amounts to solving a system of ordinary …

Mechanistic models with differential equations are a key component of scientific applications
of machine learning. Inference in such models is usually computationally demanding …

The numerical solution of differential equations can be formulated as an inference problem
to which formal statistical approaches can be applied. However, nonlinear partial differential …

Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical
simulation of dynamical systems as problems of Bayesian state estimation. Aside from …

We show how probabilistic numerics can be used to convert an initial value problem into a
Gauss–Markov process parametrised by the dynamics of the initial value problem …

This work develops a class of probabilistic algorithms for the numerical solution of nonlinear,
time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers …