Data-Driven Methods for Reduced-Order Modeling and Stochastic Partial Differential Equations (17w5140)


(University of Washington)

(University of British Columbia)

(Massachusetts Institute of Technology)


The Banff International Research Station will host the "Data-Driven Methods for Reduced-Order Modeling and Stochastic Partial Differential Equations" workshop from January 29th to February 3rd, 2017.

Complex dynamical systems are ubiquitous in characterizing the underlying behavior of almost any physical, biological and engineering system of the modern era. With few exceptions, underlying nonlinearities impair our ability to construct analytically tractable solutions, thus often forcing one to rely on experiments and modern high-performance computing for studying a given system. For such systems, numerical simulations can easily yield a million or billion (or more) degree of freedom system (i.e. the curse of dimensionality), thus greatly straining computational resources and jeopardizing one's understanding of the underlying mechanism driving the dynamics. Similarly, experiments can generate overwhelming amounts of data with sparse measurements being taken at a fixed number of spatial-temporal locations. However, many such high-dimensional systems often exhibit multi-scale dynamics that evolve on a slow-manifold and/or a low-dimensional attractor (e.g. pattern forming systems).

Moreover, it is also often the case that for large complex systems subject to vast spatial and time scales, the micro-scale dynamics are often advocated and parametrized through over-fitting of available data. Recent advances in data-driven methods, often under the aegis of machine learning, are transforming our mathematical strategies in the sciences. Indeed, innovative uses of machine learning, dimensionality reduction, sparse sensing, and/or network characterization techniques are allowing for significant advances in engineering designs for the prediction and control of highly complex, often networked, systems. This workshop proposes to bring together leading experts who are integrating one or more of the aforementioned methodologies with the goal of providing transformative analytic tools and computational algorithms for characterizing the underlying, low-dimensional, dynamics of complex systems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides
an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional
de Ciencia y Tecnología (CONACYT).