Reduced Order Surrogate Modelling and Latent Assimilation for Dynamical Systems

Sibo Cheng, César Quilodrán Casas, Rossella Arcucci

Abstract: For high-dimensional dynamical systems, running high-fidelity physical simulations can be computationally expensive. Much research effort has been devoted to develop efficient algorithms which can predict the dynamics in a low-dimensional reduced space. In this paper, we developed a modular approach which makes use of different reduced-order modelling for data compression. Machine learning methods are then carried out in the reduced space to learn the dynamics of the physical systems. Furthermore, with the help of data assimilation, the proposed modular approach can also incorporate observations to perform real-time corrections with a low computational cost. In the present work, we applied this modular approach to the forecasting of wildfire, air pollution and fluid dynamics. Using the machine learning surrogate model instead of physics-based simulations will speed up the forecast process towards a real-time solution while keeping the prediction accuracy. The data-driven algorithm schemes introduced in this work can be easily applied/extended to other dynamical systems.