Stability Preserving Data-driven Models With Latent Dynamics

TL;DR

This paper presents a data-driven modeling framework incorporating latent variables and stability constraints, demonstrated through fluid-structure interaction problems and benchmark tests, enhancing predictive accuracy and stability.

Contribution

The paper introduces a novel stability-preserving data-driven modeling approach with latent variables and recurrent cells, applicable to complex dynamics problems.

Findings

Model enforces stability in coupled dynamics

Efficient recurrent cell implementation demonstrated

Accurate predictions in fluid-structure interaction applications

Abstract

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a given data set. We present a model framework where the stability of the coupled dynamics can be easily enforced. The model is implemented by recurrent cells and trained using backpropagation through time. Numerical examples using benchmark tests from order reduction problems demonstrate the stability of the model and the efficiency of the recurrent cell implementation. As applications, two fluid-structure interaction problems are considered to illustrate the accuracy and predictive capability of the model.