Physics-Aware Deep Learning for Reduced Order Modeling

Recently, deep neural networks have been widely used for learning the underlying dynamics of complex physical systems from the spatiotemporal patterns in experimental and/or simulation data. In the context of reduced order modeling (ROM), the deep learning-based auto-encoders are a popular candidate for compression of the full-order physical model. However, the classical purely data-driven auto-encoders ignore the fundamental underlying physical laws in the system. In this work, we explore several model reduction strategies to bridge the gap between the state-of-the-art data science algorithms and the physics-aware deep learning-based ROM. We focus on importance of preserving the shape and geometry of the space of data points during the data compression step in order to capture the essential features of the corresponding time-evolving physical system. It is shown that, by incorporating the underlying physical laws into the reduced order model, its prediction accuracy and generalizability to unseen scenarios improves considerably.