  The identification of nonlinear dynamics from observations is essential for
the alignment of the theoretical ideas and experimental data. The last, in
turn, is often corrupted by the side effects and noise of different natures, so
probabilistic approaches could give a more general picture of the process. At
the same time, high-dimensional probabilities modeling is a challenging and
data-intensive task. In this paper, we establish a parallel between the
dynamical systems modeling and language modeling tasks. We propose a
transformer-based model that incorporates geometrical properties of the data
and provide an iterative training algorithm allowing the fine-grid
approximation of the conditional probabilities of high-dimensional dynamical
systems.
