Uncertainty quantification for black box models

Developing methods for the quantification of uncertainty in complex numerical models

Project status



Most numerical models used in science and industry are so computationally expensive that we cannot use naive methods such as Monte Carlo to estimate the uncertainty in their outputs. In this project we are developing methods that will extend the range of numerical models.

Explaining the science

Increasingly real world decisions are made using the output of often complex numerical models. If decision makers are to evaluate possibly conflicting advice from different sources they need some measure of uncertain. In general we know how to estimate uncertainty in data but it is much harder to estimate for a complex numerical model, for example a model of the climate or the human heart. In this project we are investigating new statistical methodology that will allow us to extend uncertainty quantification to a broader class of numerical simulators and to improve our existing methods.

Project aims

Our aim is to extend the methodology for uncertainty quantification in complex numerical models. One major part of our work is the development of a new library for computer programmes that will bring the most modern methods of computation, exploiting GPUs and such like, in an easy to use set of computer code. if at the end of the project we have a well validated computer code that is easy to use and is being used in a variety of applications we will regard that as a success. On the methodological side we have four workpackages. The first aims to improve the quantification in cases where we have a hierarchy of models at different resolutions/fidelities. Such models are common across all application areas. The second  investigates whether we can improve on the calibration of models (estimate the model parameters using data on the outputs), taking into account the fact that ‘all our models are wrong’, so called model discrepancy. The third concentrates on models whose properties change as we move around parameter space, so called non-stationary models. The final workpackage will investigate the relationship between uncertainty quantification and machine learning and deep learning. In particular can we use our methods for understanding how numerical models based on partial differential equations to investigate deep learning models and bring some transparency to such models.


Our work has application across any sector that uses numerical modelling to make predictions and take decisions. Examples include climate, ecology, healthcare and engineering. But there are many areas which could benefit but don’t currently. Part of our work is to reach out to new applications.

Recent updates

March 2020 - We have the first version of the software package released


Researchers and collaborators

Contact info

Peter Challenor - [email protected]