Reduced Order Surrogate Modelling and Latent Assimilation for Dynamical Systems

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 reducedorder 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.

Spatio‐Temporal Super‐Resolution Data Assimilation (SRDA) Utilizing Deep Neural Networks With Domain Generalization

“…Methods of DA are typically variational or statistical, with NNs being applied to both types. Recent progress in the application of NNs to DA has been summarized in a review (Cheng et al., 2023). Variational methods, such as 4D‐Var, are analogous to deep learning, in that both employ adjoint backpropagation (Abarbanel et al., 2018; Chen et al., 2018).…”