Data-driven modelling of nonlinear dynamics by polytope projections and memory

• URL: http://arxiv.org/abs/2112.06742v1
• Date: Mon, 13 Dec 2021 15:49:36 GMT
• Title: Data-driven modelling of nonlinear dynamics by polytope projections and memory
• Authors: Niklas Wulkow, P\'eter Koltai, Vikram Sunkara, Christof Sch\"utte
• Abstract summary: We present a numerical method to model dynamical systems from data. We project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples.

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