  In this paper, we develop a machine learning-based Bayesian approach to
inversely quantify and reduce the uncertainties of the two-fluid model-based
multiphase computational fluid dynamics (MCFD) for bubbly flow simulations. The
proposed approach is supported by high-resolution two-phase flow measurement
techniques, including double-sensor conductivity probes, high-speed imaging,
and particle image velocimetry. Local distribution of key physical quantities
of interest (QoIs), including void fraction and phasic velocities, are obtained
to support the modular Bayesian inference. In the process, the epistemic
uncertainties of the closure relations are inversely quantified, the aleatory
uncertainties from stochastic fluctuation of the system are evaluated based on
experimental uncertainty analysis. The combined uncertainties are then
propagated through the MCFD solver to obtain uncertainties of QoIs, based on
which probability-boxes are constructed for validation. The proposed approach
relies on three machine learning methods: feedforward neural networks and
principal component analysis for surrogate modeling, and Gaussian processes for
model form uncertainty modeling. The whole process is implemented within the
framework of open-source deep learning library PyTorch with graphics processing
unit (GPU) acceleration, thus ensuring the efficiency of the computation. The
results demonstrate that with the support of high-resolution data, the
uncertainty of MCFD simulations can be significantly reduced.
