Abstract
We present the Mori–Zwanzig Mode Decomposition (MZMD), which extends Dynamic Mode Decomposition by embedding memory kernels derived from the Mori–Zwanzig formalism, providing a data-driven approximate closure for the dynamics that standard DMD leaves unresolved. By casting the evolution of chosen observables as a discrete-time Generalized Langevin Equation, MZMD extracts both modes and spectrum while explicitly modeling their memory-based coupling to unresolved degrees of freedom, a capability that distinguishes it from time-delay methods such as Higher-Order DMD. When applied to a Mach-6 flared-cone boundary-layer transition, MZMD resolves the leading coherent structures, especially the hypersonic "hot-streaks", with more fidelity than DMD, and less prone to overfitting than HODMD. Its memory kernels stabilize the reduced model, reveal higher-harmonic content that truncated DMD misses, and reduces short-time prediction error. Together, these benefits establish MZMD as a scalable, physically transparent extension of Koopman-based techniques for modal diagnosis, forecasting, and analysis.
*This work has been authored by employees of Triad National Security, LLC which operates Los Alamos National Laboratory (LANL) under Contract No. 89233218CNA000001 with the U.S. Department of Energy (DOE)/National Nuclear Security Administration. We acknowledge supports from LANL’s Laboratory Directed Research and development (LDRD) program, project number 20220104DR, %{\color{red} add MW's Agnew proposal if it has a number} and computational resources from LANL’s Institutional Computing (IC) program. This work was also partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research's Applied Mathematics Competitive Portfolios program.
