In this paper we study the problem of predicting dynamical systems from discrete-time measurements of the state variables. Our approach is based on the theory of Lie algebras and the Baker-Campbell-Hausdorff formula. We present the composition network which is a multilayer architecture which can use the a priori knowledge we have about the system. We also introduce the "MLP in dynamics space" which is a general implementation of the composition network having a universal approximation property. We demonstrate the efficiency of the proposed method on the task of predicting the Lorenz attractor.
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