Blending machine learning and sequential data assimilation over latent spaces for surrogate modeling of Boussinesq systems

One outcome of rapid digital transformation is the emergence of technologies like reduced order models. This growth has resulted in a major challenge in many scientific applications. It is computationally demanding to train an end-to-end data-driven machine learning model that can be trustworthily used in future predictions. To address this challenge, our main innovation in this paper is a construction of a hybrid analysis and modeling framework, which is designed to combine non-intrusive surrogate models and sequential data assimilation practices seamlessly. Specifically, we first utilize proper orthogonal decomposition to generate a linear latent space. Second, we build a recurrent neural network model in simulating temporal dynamics. The key aspect of our approach comes next, where we use a deterministic Kalman filter to perform our analysis for the surrogate model over the latent space. Our findings for simulating Rayleigh–Bénard convection, a prototype spatiotemporal transport problem for Boussinesq flows, show that the proposed approach reduces the uncertainty of the predictive model significantly over a wide range of parameters. •A latent space data assimilation framework is proposed to generate non-intrusive reduced order models.•It presents an equation-free surrogate model that blends machine learning and data assimilation approaches.•The robustness of the model has been tested by considering the Rayleigh–Bénard convection.