Reduced Order Modeling Using Advection-Aware Autoencoders

Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They known pose severe challenges both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations learning efficient, physics-informed, nonlinear embeddings the high-fidelity system snapshots. A fully model is developed mapping snapshots a latent space defined AA autoencoder, followed dynamics using long-short-term memory (LSTM) network. This framework also extended parametric problems explicitly incorporating parameter information into encoded space. Numerical results obtained with advection indicate proposed reproduce dominant flow features even for unseen values.