{Seminar} @ CDS: 06th January : “Learning physics-based data-driven reduced-order models and obtaining nonlinear systems’ stability limits.”

Obtaining data-driven nonlinear reduced-order models (ROMs) relies on projecting the high-dimensional system onto a linear subspace—also called a linear dimensionality reduction technique. However, intrinsically nonlinear systems seldom evolve on linear subspaces, so the ROMs obtained from linear dimensionality reduction techniques do not effectively generalize outside the training dataset. In the first part of this talk, I will present a data-driven nonlinear dimensionality reduction framework such that the resulting ROMs trajectories evolve on a quadratic (nonlinear) subspace. The proposed framework is non-intrusive, requiring only the system’s trajectory data, and does not need access or modification to the high-fidelity code. Additionally, the ROMs are obtained by solving a least-squares regression problem while retaining the linear-quadratic structure of the original high-dimensional system. The proposed quadratic manifold-based ROMs will enable a richer reconstruction of the system trajectories and enable accurate future-state predictions.

 

BIOGRAPHY