Reduced-order modeling of unsteady fluid flow using neural network
  ensembles
Rakesh Halder Mohammadmehdi Ataei Hesam Salehipour Krzysztof Fidkowski Kevin Maki
The use of deep learning has become increasingly popular in reduced-order
models (ROMs) to obtain low-dimensional representations of full-order models.
Convolutional autoencoders (CAEs) are often used to this end as they are adept
at handling data that are spatially distributed, including solutions to partial
differential equations. When applied to unsteady physics problems, ROMs also
require a model for time-series prediction of the low-dimensional latent
variables. Long short-term memory (LSTM) networks, a type of recurrent neural
network useful for modeling sequential data, are frequently employed in
data-driven ROMs for autoregressive time-series prediction. When making
predictions at unseen design points over long time horizons, error propagation
is a frequently encountered issue, where errors made early on can compound over
time and lead to large inaccuracies. In this work, we propose using bagging, a
commonly used ensemble learning technique, to develop a fully data-driven ROM
framework referred to as the CAE-eLSTM ROM that uses CAEs for spatial
reconstruction of the full-order model and LSTM ensembles for time-series
prediction. When applied to two unsteady fluid dynamics problems, our results
show that the presented framework effectively reduces error propagation and
leads to more accurate time-series prediction of latent variables at unseen
points.