Multivariate Identification via Linear Projection of Eigenvectors

A data-driven system identification algorithm which utilizes eigenvector is presented. The eigenvectors are extracted from an unified solution space comprising both input and output subspaces. To expand the input subspace, a higher-order subspace out of input subspaces are augmented with the measured input subspace; this higher-order subspace exhibit additional cross-correlations with both the input and output subspaces, thus producing more informative eigenvectors and linearizing the system. The extracted eigenvectors are then deployed to sequentially project new input snapshots first onto the input subspace and subsequently onto the output subspace to predict the output. The algorithm effectively reconstructs the original governing equations of a dynamic system, providing an inference that the original system is a series of data projection via eigenvectors, and also implying the possibility of reconstructing the low-rank governing equation with limited number of eigenvectors thus yielding a linearized representation of the system from the data. Notably, identifying the system from the well expanded, high-dimensional nonlinear solution space requires only a limited duration of data snapshots, indicating that the essential spatial features manifested by the governing equation are determined rapidly.