Under-Sampled Data-Based Reduced Order Models for Periodic Dynamical Systems*

The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm requires accurate data time derivatives. Hence, under-sampled data sets essentially prevents the use of SINDy due to time derivative inaccuracy. This issue is overcome here for periodic dynamical systems though a novel topological data analysis (TDA). It consists on a technique that folds data, originally available over many periods, into a single period based on its phase portrait analysis. Doing so enables the accurate reconstruction of the data temporal behavior. Under-sampled data from the Lorenz equations is used to demonstrate that the technique works. It is then applied to generate reduced order models (ROMs) for methane-air laminar jet diffusion flame dynamics under acoustic excitation. This sustained oscillatory combustion data consists of proper orthogonal decomposition (POD) coefficients over time obtained from high speed visible imaging using a sampling rate whose frequency is not high enough to satisfy the Nyquist theorem. Under-sampled data from single and triple jet injection systems are analyzed and highly accurate ROMs can be generated.

Supported by Grants FA9550-19-1-0096 and FA9550-22-1-0190 (PO: Mitat Birkan – AFOSR), and FA9550-18-1-0419 (PO: Roger Greenwood – SOARD & Sarah Popkin – AFOSR).