{"product_id":"latent-modes-of-nonlinear-flows","title":"Latent Modes of Nonlinear Flows","description":"\u003cp\u003eExtracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this Element the authors attempt to provide a consistent framework through Koopman theory and its related popular discrete approximation - dynamic mode decomposition (DMD). They investigate the conditions to perform appropriate linearization, dimensionality reduction and representation of flows in a highly general setting. The essential elements of this framework are Koopman eigenfunctions (KEFs) for which existence conditions are formulated. This is done by viewing the dynamic as a curve in state-space. These conditions lay the foundations for system reconstruction, global controllability, and observability for nonlinear dynamics. They examine the limitations of DMD through the analysis of Koopman theory and propose a new mode decomposition technique based on the typical time profile of the dynamics.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":56668781838722,"sku":"9781009323857","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781009323857i.jpg?v=1779631226","url":"https:\/\/www.cambridgebookshop.co.uk\/products\/latent-modes-of-nonlinear-flows","provider":"Cambridge University Press Bookshop","version":"1.0","type":"link"}