Big Data: current computational models are capable of generating petabyte-sized databases providing insight into processes taking place at extremely fine spatio-temporal scales. Apart from the obvious difficulties in visualizing, storing and processing such data, the fundamental challenge lies in extracting knowledge about the salient features and understanding of the driving mechanisms. This is more pronounced in the context of multiscale simulations which can only be enabled by the ability to identify accurate but computationally-tractable reduced descriptions even in cases where physical insight is unavailable. Learning from data and identifying structural characteristics is a typical task in several computational statistics and machine learning applications. Coupling such tasks with physical models and enabling physical insight by leveraging computational statistics/machine-learning tools, will be one of the challenges addressed.

High-Dimension: Physical models are characterized by high-dimensional inputs and outputs. Dimensionality reduction is generally a necessary step in enabling the simulation of such systems. Overcoming the curse of dimensionality is a common objective within the Computational Mathematics UQ community and Computational Statistics machine learning community. This is tightly connected with the ability to identify salient input-output features that enable the construction of predictive models even when limited data is available.

Uncertainty: Predictive modeling 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. An important objective centers around the development of probabilistic frameworks for systems identification, model validation, analysis, design, optimization and control under uncertainty.