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Objectives of WCPM

WCPM is an inderdisciplinary centre addressing the mathematical, statistical and scientific computing challenges necessary for predictice modelling in science and engineering. Our fundamental approach is in exploring synergies between Uncertainty Quantification (UQ), Machine Learning (ML) and Scientific Computing. The broad objectives of the Centre are:

1 To develop rigorous mathematical theory, algorithms and software to enable the quantification, analsys and subsequent control of complex multiscale systems in the presence of uncertainties, in a computationally scalable way
2 To demonstate how a mathematical framework that addresses stochastic multiscale system can be driven by limited and gappy information, leading to a completely new approach to capture and exploit uncertainty in engineered systems
3 To demonstrate the physical relevanance and broad applicability of our multiscale framework through the consideration of a number of application themes

The emphasis of the Centre is on common themes linking the UQ, ML and Scientific Computing communities and identifying innovative research directions that can accelerate the impact of uncertainty modeling in engineering and the sciences as well as demonstrate the capabilities of computational uncertainty quantification methods and tools in various problems.

Methodological Themes

The Centre focuses on a number of fundamental themes common to many scientific applications, including:

  • Resolving the curse of stochastic dimenstionality for multiscale problems
  • Developing data-driven hierachical model reduction schemes for high-dimensional property fields
  • Developing an information-theoretic framework for coarse-graining
  • Modelling of rare events in random media
  • Developing scalable uncertainty quantification models for multiscale and multiphysics problems
  • Exploring high dimensional relations between process, structure and properties for design and decision making
  • Multiscale inverse problems
  • Machine Learning approaches such as Bayesian Statistics, Probabilisitic Graphical Models, Kernel methods
  • Model reduction
  • Non-parametric methods
  • Making effective and efficient use of Big Data

Application Themes

Current application themes at WCPM include:

  • Materials science, with a particular focus on mechanical failure and device design
  • Subsusrface flows and reservoir engineering
  • Fluid/structure interaction
  • Energy and the environment
  • Developing improved batteries for automative engineering
  • Modelling biological systems
  • Bioinformatics
  • Inference and rare event modelling in complex networks