A research frontier has emerged in scientific computation, wherein discretisation error is
regarded as a source of epistemic uncertainty that can be modelled. This raises several …

Railway infrastructure monitoring is a vital task to ensure rail transportation safety. A rail
failure could result in not only a considerable impact on train delays and maintenance costs …

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 …

Direct illumination calculation is an important component of any physically-based Tenderer
with a substantial impact on the overall performance. We present a novel adaptive solution …

This work provides theoretical foundations for kernel methods in the hyperspherical context.
Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the …

Bayesian cubature provides a flexible framework for numerical integration, in which a priori
knowledge on the integrand can be encoded and exploited. This additional flexibility …

Efficient approximation of incident radiance functions from a set of samples is still an open
problem in physically based rendering. Indeed, most of the computing power required to …