Bayesian reduction method on high-dimensional nonlinear models using deep probabilistic time series neural networks

Real-world problems are not entirely deterministic in the sense of the constraints imposed to them by data acquisition devices such as sensors. The available data obtained from sensors are limited, biased and possibly from multiple online sources. A way to learn the uncertainties through these complicated pipelines is crucial for a reduced representation of a complex system that captures the uncertainties. Fortunately, due to recent innovations in the software community, we have access to scalable Bayesian deep learning technology that can take advantage of such data to learn the uncertainties. It also naturally integrates with well-established neural networks and uses the same underlying framework to create a unified system.

To showcase Bayesian deep learning paradigm in fluid dynamics:

• we chose two nonlinear large scale benchmark models to generate full-order snapshots

• perform a classic reduction method to get a limited number of latent space time-series

• train two types of multivariate Bayesian time series models, Local Global Trend (LGT) and Damped Local Trend (DLT)

• compare diagnostics