We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near fast subsystem bifurcation points can be computed to leading order. This leading order approximation shows that the MMD depends intricately on the fast-slow systems parameters, which can influence the detection of potential early-warning signs before critical transitions. However, the MMD turns out to be an excellent binary classifier to detect the change-point location induced by the critical transition. We cross-validate our results by numerical simulations for a van der Pol-type model.
KEYWORDSbifurcation, critical transition, kernel methods, maximum mean discrepancy, multiscale system, time series, tipping point• Change-point detection: In a time series generated by a fast-slow SODE, there could be many different types and sizes of drastic jumps. Hence, it would not only be useful to develop an automatic and generic classifiers, 10-12 when we actually observe a critical transition, but also to cross validate a classifier against explicit low-dimensional models.Math Meth Appl Sci. 2019;42:907-917. wileyonlinelibrary.com/journal/mma
This work treats the physical one-dimensional (1D) and two-dimensional (2D) modelling of a chemical process of filtration of slurry, which is the second step of phosphoric acid manufacture. This work focuses on the different physical laws involved in the filtration stage in order to obtain a simulator of the filter. In this work, we are interested in the 1D modelling of a rotary filter using all parameters and physical phenomena established in the filtration phase. Then, a 2D model emerged from the previous model by choosing both a temporal and a spatial variable. These two parameters are quite necessary for the construction of a 2D model based on the method of Fornasini–Marchesini (FM-II) to describe the dynamics of the system.
This work deals with a physical one-and two-dimensional (1D and 2D) parameters estimation of a filtration process of slurry, the second stage of phosphoric acid manufacture. This study focuses on recursive least square and instrumental variable techniques applied to the (1D) and (2D) models. The model of the rotary drum filter is based on different physical laws involved in the filtration phase in order to get a simulator of the filtration process. Besides, many physical parameters rise in the system model and effect enormously the efficiency which should be modelled with precision such as permeability, porosity and viscosity. We use a constructive realization procedure for (2D) systems which may lead to a Fornasini-Marchesini local state-space model to describe the dynamic of the system states.
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