Probalistic numerics is a new field that aims to bring a principled Bayesian framework to the computational bottlenecks common to all AI systems: numerical optimisation, quadrature and ODE solving. This framework allows the numerical errors that emerge from the use of numerical procedures to be correctly accommodated and propagated. It also permits a finite computational budget to be optimally and automatically allocated amongst a pipeline of numerics procedures: the numerics procedures where error is most severe can be assigned more computation. Probabilistic numerics has found great success in its introduction to global optimisation, under the name of Bayesian optimisation. Bayesian optimisation has found use in automated machine learning, neural architecture search, interactive user-interfaces, robotics, environmental monitoring, sensor networks and many other applications.
