Compression of the Koopman matrix for nonlinear physical models via hierarchical clustering
This work addresses a domain-specific problem in computational physics and machine learning for more efficient predictions of nonlinear systems, but it is incremental as it builds on existing Koopman operator approximations.
The paper tackles the problem of compressing the Koopman matrix for nonlinear dynamical systems by proposing a hierarchical clustering method, which outperforms conventional singular value decomposition in numerical demonstrations on the cart-pole model.
Machine learning methods allow the prediction of nonlinear dynamical systems from data alone. The Koopman operator is one of them, which enables us to employ linear analysis for nonlinear dynamical systems. The linear characteristics of the Koopman operator are hopeful to understand the nonlinear dynamics and perform rapid predictions. The extended dynamic mode decomposition (EDMD) is one of the methods to approximate the Koopman operator as a finite-dimensional matrix. In this work, we propose a method to compress the Koopman matrix using hierarchical clustering. Numerical demonstrations for the cart-pole model and comparisons with the conventional singular value decomposition (SVD) are shown; the results indicate that the hierarchical clustering performs better than the naive SVD compressions.