Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

This article attempts to place the emergence of probabilistic numerics as a mathematical–
statistical research field within its historical context and to explore how its gradual …

We formulate probabilistic numerical approximations to solutions of ordinary differential
equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear …

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 …

A recently introduced class of probabilistic (uncertainty-aware) solvers for ordinary
differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems …

A novel probabilistic numerical method for quantifying the uncertainty induced by the time
integration of ordinary differential equations (ODEs) is introduced. Departing from the …

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty
quantification of elliptic partial differential equations based on random meshes, which we …

Likelihood-free (aka simulation-based) inference problems are inverse problems with
expensive, or intractable, forward models. ODE inverse problems are commonly treated as …