Variational autoencoders and transformers for multivariate time-series generative modeling and forecasting: Applications to vortex-induced vibrations

Abstract

This study employs a data-driven approach to studying physical system vibrations, focusing on two main aspects: using variational autoencoders (VAEs) to generate physical data (i.e. data “similar” to those obtained via real-world processes) and using transformers in order to continuously forecast flexible body nonstationary vibrations (2D time-series) in time–space using information from sparse sensors on the body (observers). A VAE is trained on vortex-induced vibrations (VIV) data collected from experiments conducted by the authors and is then tasked with generating synthetic VIV data similar to the experimental. The synthetic data are then used to train a transformer architecture whose objective is to continuously forecast the vibrations in time–space using sparse observations. The transformer (which has never seen real data) is tested against real experiments and its performance is compared to that of the same architecture trained on real data. In doing so, the ability of VAEs to generate data which preserve their training data’s intrinsic properties (i.e. physicality) is evaluated. Finally a comparison between the forecasting performance of the transformer architecture, an LSTM, and a DNN is presented.