A New Paradigm for Reduced-Order Modeling of Complex Dynamical System
DescriptionBayesian filtering is concerned with the time-sequential estimation of the hidden state of the underlying system, given noisy observations. For complex dynamical systems in high dimension, the straightforward implementation of the existing filtering algorithms is normally very expensive. The reduced-order model approach for filtering refers to the methodology of employing a simplified stochastic model which is low-dimensional and significantly cheaper to simulate than the original dynamics.The typical practice for obtaining a closed equation for the target system variable of a dynamical system is to replace the nonlinear coupling terms of the governing equation by the white-noise forcing and linear dissipation. The PI’s prior investigation using the Majda-McLaughlin-Tabak (MMT) prototypical model for nonlinear waves reveals that (i) for the case of slowly varying longwave, the resulting Ornstein-Uhlenbeck process is a good approximate model, but (ii) for the case of rapidly varying shortwave, this Markov model is highly inappropriate due to the non-Markov character of the true signal.In this project, we aim to provide a new paradigm for designing reduced-order models amenable to filtering. One advantage of our framework is the representation of the non-Markov process as a component of Markov system made by adding a so-called auxiliary variable. Our new formulation achieves high accuracy and eciency of the proposed model and, particularly for the case of shortwave turbulent signal, the new model will lead to a significantly improved filtering performance. The feasibility of this research is supported by the PI’s theoretical and numerical analysis on a simple test case.
|Effective start/end date||1/01/22 → 1/01/22|