John Harlim, Thesis Supervisor Aissa Wade, Thesis Honors Advisor
Keywords:
Mori-Zwanzig
Abstract:
In this thesis, we investigate theoretical and numerical methods of Mori-Zwanzig Formalism, a formulation that allows us to estimate the solutions of nonlinear time-dependent problems when the full dynamics are too complex to be fully resolved or when part of the dynamics are unknown. We began by introducing the general goal and background knowledge for this thesis. At the heart of this thesis, we
investigate the solutions of the Mori-Zwanzig projection using various choices of bases of L2 space, including the analytical basis functions that can be derived in special circumstances and the data-driven basis functions obtained via the diffusion map algorithm. We found that the quality of the solutions is sensitive to the choice of basis functions.
