Structured Machine Learning and Time–Stepping for Dynamical Systems (24w5301)

The Banff International Research Station will host the “Structured Machine Learning and Time–Stepping for Dynamical Systems” workshop in Banff from February 18 - 23, 2024.

Over the past decade, tremendous progress has been made at utilizing machine learning techniques to help us better understand and make predictions for dynamical systems arising from numerous areas of science and engineering. While traditional machine learning techniques have allowed us to successfully interpolate a wealth of domain knowledge and historical data, current machine learning approaches, however, possess significant limitations in their explainability and reproducibility in order to make new predictions accurately and reliably. On the other hand, over the past several decades, the numerical analysis community have established the benefits of utilizing structure-preserving time-stepping methods for dynamical systems. Specifically, by preserving the underlying geometrical structures of dynamical systems, such methods can make more accurate long-term predictions over traditional numerical methods, with diverse applications in areas such as celestial mechanics, weather forecasting, and computer graphics. More recently, structured machine learning approaches, which directly incorporate the inherent flow map and multi-resolution structures, have also been applied to solve many dynamical systems and multiscale problems, with a promising outlook on such approaches.

This workshop aims to bring together a diverse and multi-disciplinary group of researchers to cultivate exchange of ideas on structure-preserving time-stepping methods and structured machine learning techniques, with a common goal of achieving reliable, efficient and accurate predictions for data-driven dynamics. The key themes of this workshop are: i) structure-preserving discretizations; ii) structured machine learning; iii) applications of these methods. The participants of this workshop will foster new collaborations and a new community in sharing knowledge and working together at incorporating structures of dynamical systems within modern machine learning techniques. These exchanges and developments will no doubt result in long-lasting impacts at enabling more accurate and reliable machine learning techniques for forecasting dynamical systems and for their use in diverse applications.

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).