Uncertainty quantification for complex systems: theory and methodologies

In areas as diverse as climate modelling, manufacturing, energy, life sciences, finance, geosciences and medicine, mathematical models and their discretisations into computer models are routinely used to inform decisions, assess risk and formulate policies. How accurate are the predictions made using such models? This crucial question lies at the heart of uncertainty quantification (UQ).

UQ is a broad phrase used to describe methodologies for taking account of uncertainties when mathematical and computer models are used to describe real-world phenomena. This includes propagating uncertainty from unknown model inputs to model outputs, the study of uncertainty in the models themselves, developing approximation schemes that result in tractable and accurate computer models, robust design, model calibration and other inverse problems, model bias and discrepancy etc. This programme focuses on UQ for complex systems which have complicated mathematical descriptions such as systems of partial differential equations for which even a single deterministic inversion of an associated computer model is very costly.

The scientific challenges of modern life, the recent rapid growth in computing power and the demand for more accurate and precise predictions in areas affecting improved infrastructures, public safety and economic well-being have spawned a recent surge in UQ activity. New UQ methodologies have and are continuing to be developed by statisticians and applied mathematicians independently.

The main aim of the programme is to bring applied mathematicians and statisticians together to formulate a common mathematical foundation for UQ and to establish long-lasting interactions that will lead to significant advances in UQ theory and methodologies for complex systems. Participants will work together to develop theories and methodologies for reducing the cost of model inversion, increasing the level of tractable complexity in modelling, and enabling efficient risk assessment and decision making. Five core themes of common interest to statisticians and applied mathematicians will provide the focus. These are:

Surrogate models Multilevel, multi-scale, and multi-fidelity methods Dimension reduction methods Inverse UQ methods Careful and fair comparisons