Jacob Price

Numerical and analytical simulation methods that capitalize on multiscale structures, both spatial and temporal, have often been used to reduce the dimensionality of high dimensional systems. The Mori-Zwanzig formalism is the general framework for multiscale methods that incorporates a memory term. In this talk, I present a novel approach for constructing a closed reduced order model by approximating the memory term using a renormalization-inspired method. This new approach uses fewer assumptions than other popular models based on the Mori-Zwanzig formalism. This model is applied to the Korteweg-de Vries equation with small dispersion. The renormalization process reveals startling structure including algebraic time dependence and incomplete similarity in the renormalization coefficients. Furthermore, the results are suggestive of a comprehensive understanding of the role memory plays in reduced order models.