EPSRC Centre for Doctoral Training Cloud Computing for Big Data


Matthew Fisher

I completed my BSc in Mathematics from Newcastle University in 2017. 

PhD title

Toward an Adaptive Probabilistic Numerical Method

My research project is within the field of probabilistic numerics. Probabilistic numerics is a relatively new field. It involves the study of probabilistic numerical methods:

  • algorithms for solving numerical tasks, such as numerical integration
  • solving differential equations and optimisation, that return uncertainties in their calculation.

The uncertainty that arises can be interpreted as the uncertainty due to the incomplete or finite information about the continuous mathematical problem that is being approximated.

There is a gulf in sophistication between existing probabilistic numerical methods and the numerical methods that are used as standard.

In particular the Gaussian process model on which almost all probabilistic numerical methods are based does not yet allow for genuine adaptation. This is a necessary requirement for a general purpose numerical method. An adaptive numerical method usually exploits a local error indicator in order tosequentially refine an estimate until a prescribed tolerance is met.

The goal of my project is then to work towards and investigate how classical adaptive routines can be suitably modified to become adaptive probabilistic numerical methods.


Chris Oates, Aretha Teckentrup, Catherine Powell