Reduced order modeling with shallow recurrent decoder networks

Reduced order modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts. However, conventional dimensionality reduction techniques are typically limited to known and constant parameters, inefficient for nonlinear and chaotic dynamics, and uninformed to the actual system behavior. In this work, we propose a SHallow REcurrent Decoder-based Reduced Order Modeling technique (SHRED-ROM) capable of reconstructing high-dimensional state dynamics in multiple scenarios from the temporal history of limited sensor measurements. To enhance computational efficiency and memory usage, we reduce data dimensionality through data- or physics-driven basis expansions, allowing for compressive training of lightweight networks with minimal hyperparameter tuning. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED-ROM is a robust decoding-only strategy, capable of dealing with both fixed or mobile sensors, physical and geometrical (possibly time-dependent) parametric dependencies and different data sources, such as high-fidelity simulations, coupled fields and videos, while being agnostic to sensor placement and parameter values.