Comments on "Bayesian Solution Uncertainty Quantification for Differential Equations" by Chkrebtii, Campbell, Calderhead & Girolami

TL;DR

This paper comments on a recent work in probabilistic numerics, highlighting the importance of prior modeling considerations for future research in Bayesian differential equation solvers.

Contribution

It provides a critical discussion on prior modeling aspects in Bayesian solution uncertainty quantification for differential equations.

Findings

Highlights the need for thorough prior modeling in probabilistic numerics

Emphasizes future research directions in Bayesian differential equation methods

Acknowledges the original paper's contribution to probabilistic numerics

Abstract

We commend the authors for an exciting paper which provides a strong contribution to the emerging field of probabilistic numerics (PN). Below, we discuss aspects of prior modelling which need to be considered thoroughly in future work.