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 …

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 …

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

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

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 …

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 …