87 citations · 196 across the 20 of their papers we have counts for
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Theoretical Guarantees for the Statistical Finite Element Method
Yanni Papandreou, Jon Cockayne, Mark Girolami +1
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a…
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
Junyang Wang, Jon Cockayne, Oksana Chkrebtii +2
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differe…
A probabilistic Taylor expansion with Gaussian processes
Toni Karvonen, Jon Cockayne, Filip Tronarp +1
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of deri…
Probabilistic Iterative Methods for Linear Systems
Jon Cockayne, Ilse C. F. Ipsen, Chris J. Oates +1
This paper presents a probabilistic perspective on iterative methods for approximating the solution of a nonsingular linear system $\mathbf{A} \math…