Numerical Analysis and Approximation Theory meets Data Science (18w5172)

The Banff International Research Station will host the "Numerical Analysis and Approximation Theory meets Data Science " workshop from April 22nd to April 27th, 2018.

The central theme of the proposed workshop is to improve the scientific discovery process by fostering the interaction between numerical analysis, approximation theory, and continuous problems arising in data science. Realizing the future potential of international scientific facilities, including neutron and light sources, high-energy reactors, and extreme-scale computing requires scientists to address a fundamental question, namely "how many realizations of a nonlinear manifold are required to recover a complex phenomena, with optimal approximation guarantees and minimal computational cost?'' This grand challenge naturally arises in a large number of fields including neutron, tomographic and magnetic resonance image reconstruction, uncertainty quantification, optimal control and parameter identification for engineering and science applications, as well as many important energy, defense, and material science applications. Here constructing the solution map to these complex problems requires repeated measurements that are often expensive, high-dimensional, and stochastic, i.e., an ensemble of complex numerical simulations or time-consuming physical experiments. As such, this workshop aims to present the mathematical foundations for enabling next-generation computational methods for approximating and analyzing systems having a certain set of constraints, from a limited amount of sparse and noisy scientific data.

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 disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering 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).