Multidimensional approximation of nonlinear dynamical systems

TL;DR

This paper introduces MANDy, a method that combines data-driven techniques with tensor network decompositions to efficiently approximate high-dimensional nonlinear dynamical systems from measurement data.

Contribution

The paper presents MANDy, a novel approach that reduces computational costs in modeling high-dimensional nonlinear systems by integrating tensor network decompositions with data-driven methods.

Findings

Successfully applied to several high-dimensional systems

Significantly reduces computational costs

Maintains accuracy in system identification

Abstract

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method MANDy which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.