
arXiv: 2306.05224
<abstract><p>Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis. However, computing Koopman eigenpairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders(AE), a type of deep learning technique, to perform nonlinear geometric transformations on raw data before computing Koopman eigenvectors. The encoded data produced by the deep AE is diffeomorphic to a manifold of the dynamical system and has a significantly lower dimension than the raw data. To handle high-dimensional time series data, Takens' time delay embedding is presented as a preprocessing technique. The paper concludes by presenting examples of these techniques in action.</p></abstract>
FOS: Computer and information sciences, reduced order modelling, deep learning, data driven science, Computer Science - Neural and Evolutionary Computing, Dynamical Systems (math.DS), 37B05, autoencoders, koopman analysis, QA1-939, FOS: Mathematics, Neural and Evolutionary Computing (cs.NE), Mathematics - Dynamical Systems, Mathematics
FOS: Computer and information sciences, reduced order modelling, deep learning, data driven science, Computer Science - Neural and Evolutionary Computing, Dynamical Systems (math.DS), 37B05, autoencoders, koopman analysis, QA1-939, FOS: Mathematics, Neural and Evolutionary Computing (cs.NE), Mathematics - Dynamical Systems, Mathematics
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