Work

New efficient data-driven reduced order models for oscillatory dynamics

Year: 2025

Type: article

Abstract: A new methodology is presented to construct data-driven reduced order models able to efficiently approximate periodic attractors of dynamical systems depending on one or more parameters. In an offline stage, some sets of temporally equidistant snapshots are computed for a limited number of parameter values. Such computation is performed using a standard numerical solver when the problem is governed by a low-dimensional system of ordinary differential equations. If, instead, the underlying dynamical system is high-dimensional (i.e., governed by partial differential equations), the snapshots are computed relying on a physics-based reduced order model obtained via proper orthogonal decomposition plus Galerkin projection. The snapshot sets are then treated using a recent, very robust data processing method, the higher order dynamic mode decomposition, which permits describing the periodic attractors as synchronized expansions in terms of spatial modes and associated temporal frequencies. Modes and frequencies are effectively interpolated at new parameter values, different from those involved in the offline stage. The online operation of the resulting data-driven reduced order model is very fast, since it requires carrying out only a small number of algebraic computations. The performance of the new method is tested for two representative dynamical systems, namely the three-dimensional Lorenz system and a high-dimensional system describing the electron transport in a semiconductor superlattice. • Data-driven ROMs simulating periodic attractors of multi-parameter dynamical systems in real time. • Snapshots computed using a standard numerical solver for low-dimensional systems and a model-based ROM for extended systems. • Approach combining HODMD, synchronization, and SVD/HOSVD plus interpolation. • Methodology applied to the three-dimensional Lorenz system and an extended model for the electron transport in a semiconductor superlattice.

Source: Journal of Computational Physics

DOI: 10.1016/j.jcp.2025.113997

Authors: Filippo Terragni, Jose M. Vega

Institutions: Universidad Carlos III de Madrid, Universidad Politécnica de Madrid

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,980

Funders: Ministerio de Ciencia, Innovación y Universidades, European Regional Development Fund, Agencia Estatal de Investigación