Advances in data-driven reduced order models using two-stage dimension reduction for coupled viscous flow and transport

This study presents advances in non-intrusive data-driven reduced order model techniques for parametric partial differential equations based on a two-stage machine learning method, using a feedforward neural network and an autoencoder after a linear dimensionality reduction. Reduced order models are important tools for enabling many query tasks, typical of uncertainty quantification, optimization, and control, which are essential ingredients in digital twins and digital shadows. We exemplify the use of the proposed technique with two examples: the Rayleigh–Bénard problem, modeling convective heat flow, and a 2D lock-exchange setup, modeling gravity currents. Both cases are described by parametric systems of nonlinear partial differential equations governing coupled viscous flow and transport, showing complex dynamics. The models’ performances are rigorously assessed on data within and outside the interval of parameters used for training. We observe that the results yield values within acceptable limits for unseen scenarios and a substantial increase in runtime efficiency.