Strategic Package: Centre for Predictive Modelling in Science and Engineering

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Predictive modelling and uncertainty quantification are more than just another research direction relevant to science and engineering. They constitute a different way of thinking that impacts practically all aspects of scientific and engineering analysis and design. Rather than deriving deterministic answers to complex problems, distributions (error-bars) are obtained that account for our incomplete and often inaccurate information about the problems of interest. Modelling of uncertain physical and geometric properties in the large scales, intrinsic randomness in the small scales or incorporation of stochastic closures necessitate the use of stochastic simulations in many multiscale problems, heavily taxing computational resources. The emerging exascale computers will allow stochastic simulations of realistic systems but analysing petabyte data bases with existing methods can be too inefficient, and full-scale models cannot be used in optimisation, design or real-time control. To this end, the University of Warwick proposes to establish a new centre focused on Predictive Modelling and uncertainty quantification with the mission to develop computational, mathematical and statistical methodologies for uncertainty quantification (UQ) and predictive modelling applied to a broad range of applications. The new centre will emphasises a dynamic integration of several fundamental research areas including the following:1) Formulation, analysis and numerical solution of stochastic multiscale/multiphysics systems exploring synergies between mathematical, statistical and machine learning approaches.2) Data-driven development of certified stochastic reduced-order models. 3) Development of a probabilistic approach to systems synthesis, design, optimisation and control under uncertainty. This proposed work will develop methods for quantifying uncertainty in multiscale simulations driven by experimental data collected at different scales. In order to account for the high-dimensional nature of the input uncertainties and resulting stochastic outputs, it is proposed to develop reduced-order surrogate models both for the input uncertainties and for the output of multiscale systems. Topics (1)-(3) are unifying themes that are common to many disciplines. Bringing together existent strengths within the University of Warwick to address these problems would allow simultaneously to impact multiple applications and move forward the problem of resolving bottlenecks in uncertainty quantification (e.g. high-dimensionality, limited data, long term time integration, rare events).