Unifying state spaces of a dynamical system via multilinear mapping

Unifying state spaces of a dynamical system via multilinear mapping

Tikhonov D.M. (Forecsys, Moscow, Russia)
Strijov V.V. (Forecsys, Moscow, Russia)

Abstract

The problem of the state space reconstruction is being considered. In the one-dimensional case, the phase space is reconstructed using the method of delays. In multivariate case the resulting state spaces are combined either by direct union or by union the obtained subspaces. This article proposes an approach for combining state spaces via a multilinear map. The mapping tensor is decomposed using a canonical decomposition to reduce the number of model parameters. This approach preserves model accuracy while significantly simplifying it. The results are tested on mobile device accelerometer data from several individuals engaged in two types of activity.

Keywords

multivariate time series; dynamical systems; delay embedding; tensor map; neural network models.

Edition

Proceedings of the Institute for System Programming, vol. 38, issue 6, part 1, 2026, pp. 63-72

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2026-38(6)-4

For citation

Tikhonov D.M., Strijov V.V. Unifying state spaces of a dynamical system via multilinear mapping. Proceedings of the Institute for System Programming, vol. 38, issue 6, part 1, 2026, pp. 63-72 DOI: 10.15514/ISPRAS-2026-38(6)-4.

Full text of the paper in pdf (in Russian) Back to the contents of the volume