A coupled Variational Encoder-Decoder - DeepONet surrogate model for the Rayleigh-Bénard convection problem

Fluid mechanics continues to advance quickly in the age of artificial intelligence, mainly due to the abundance of experimental data, field data assimilation, and high-fidelity multiscale simulations. Among the many data-driven approaches recently applied to such a discipline, ML-based reduced-order models (ROMs) have received particular attention because of their algorithmic simplicity, explainability, and computational efficiency. In this work, we have devised and implemented an ML-based ROM which combines dimensionality reduction via an Encoder-Decoder (ED) neural network with forecasting capabilities in latent space using Deep Neural Operators (DeepONets). We assessed the proposed architecture with a spatiotemporal dataset generated by the numerical solution of the Rayleigh-Bénard convection (RBC) problem. The reconstruction error of the model over the unseen datasets was lower than 10 %, demonstrating the ED technique's accurate spatial representation and the neural operators' robustness in estimating future system states. This work represents a solid contribution to the fluid dynamics community with an accurate and efficient ML-based model to tackle the challenging well-known RBC problem.