Exchanging information across scales is one of the most significant challenges in multiscale modeling and simulation. By necessity, and naturally within a multiscale context, information is truncated as it is presented to a coarser scale, and is enriched as it traverses the opposite path. Information is lost and corrupted as it is, respectively, upscaled and downscaled. Mitigating these errors can be set on rigorous ground through a probabilistic description of information, whence finite-dimensional approximations of measures provides an analytical path for describing the coarsening and refining of information. Stochastic analysis, therefore, provides a rational context for the analysis of multiscale methods. This workshop on "Stochastic Multiscale Methods: Mathematical Analysis and Algorithms" will serve to define challenges and opportunities in the development of stochastic multiscale methods for various problems in science and engineering. Issues of uncertainty quantification, model validation, and optimization under uncertainty have taken center stage in many areas of science and engineering. Likewise, multiscale modeling and computing capabilities are becoming the standard against which model-based predictions are gauged. It thus behooves the scientific community, at this juncture, to elucidate the mathematical foundation of stochastic multiscale concepts so as to ensure a steady evolution of scientific capabilities as engines of economical growth societal well-being. This workshop will initiate a dialog between mathematicians, mechanicians, and computational scientists that will lay the foundation for an accelerated growth in stochastic multiscale methods.
Rapid growth in computational resources has heightened the expectation that scientific knowledge can indeed be a driver for societal well-being and betterment. At the same time, our ability to measure the natural and social world around has significantly increased, aided by technological development in sensors, the internet, and other modalities of communication. Science is thus faced, simultaneously, with a complex description of reality at an unprecendented resolution, and the possibility to describe this reality with mathematical models of increasing complexity. Multiscale descriptions of physical problems can be viewed as attempts to take advantage of these new oppotunities, while tackling the conceptual challenges they inevitably present. The communities of stochastic analysis and computational science have evolved essentially along separate paths. The path forward, however, in the direction of disruptive scientific impact, requires significant exchange and collaboration. It is the intent of this Workshop ``Stochastic Multiscale Methods: Mathematical Analysis and Algorithms'' to bring together leading researchers in these two fields with view to delineate new horizons and forge new synergies that will accelerate the evolution of multiscale capabilities to become an enabler of scientific and economic progress.
