Reduced Order Modeling with Shallow Recurrent Decoder Networks

TL;DR

This paper introduces SHRED-ROM, a sensor-driven shallow recurrent decoder network for reduced order modeling that efficiently reconstructs complex high-dimensional systems from limited sensor data, handling nonlinear, chaotic, and parametric dependencies.

Contribution

The work presents a novel decoding-only approach combining LSTM and shallow decoders, improving robustness, efficiency, and flexibility over traditional methods for high-dimensional system reconstruction.

Findings

Accurately reconstructs state dynamics from limited sensors.

Handles various parametric dependencies and sensor placements.

Effective in estimating unknown parameters and integrating diverse data sources.

Abstract

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control. 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 sensor-driven SHallow REcurrent Decoder networks for Reduced Order Modeling (SHRED-ROM). Specifically, we consider the composition of a long short-term memory network, which encodes the temporal dynamics of limited sensor data in multiple scenarios, and a shallow decoder, which reconstructs the corresponding high-dimensional states. SHRED-ROM is a robust decoding-only strategy that circumvents the numerically unstable approximation of an inverse which is required by encoding-decoding schemes. To enhance computational efficiency and memory usage, the full-order state snapshots are reduced by, e.g., proper orthogonal decomposition, allowing for compressive training of the networks with minimal hyperparameter tuning. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED-ROM (i) accurately reconstructs the state dynamics for new parameter values starting from limited fixed or mobile sensors, independently on sensor placement, (ii) can cope with both physical, geometrical and time-dependent parametric dependencies, while being agnostic to their actual values, (iii) can accurately estimate unknown parameters, and (iv) can deal with different data sources, such as high-fidelity simulations, coupled fields and videos.