# Reduced Order Modeling with Shallow Recurrent Decoder Networks

**Authors:** Matteo Tomasetto, Jan P. Williams, Francesco Braghin, Andrea Manzoni, J. Nathan Kutz  
**arXiv:** [2502.10930](https://arxiv.org/abs/2502.10930)  
**Date:** 2025-02-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2502.10930v1/

## Key points

- Reduced Order Modeling (ROM) is essential for efficiently inferring high-dimensional spatio-temporal fields within parametric contexts
- Traditional dimensionality reduction techniques struggle with nonlinear and chaotic dynamics, as well as unknown and varying parameters
- SHRED-ROM combines a long short-term memory network with a shallow decoder to capture temporal dynamics from limited sensor data across multiple scenarios
- Unlike traditional encoding-decoding schemes, SHRED-ROM adopts a robust decoding-only strategy to enhance computational efficiency and memory usage
- The framework demonstrates capabilities in accurately reconstructing state dynamics for new parameter values based on limited fixed or mobile sensors, handling various parametric dependencies without prior knowledge of their actual values, and accommodating different data sources such as high-fidelity simulations, coupled fields, and videos

## Summary

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Reduced Order Modeling (ROM) is essential for efficiently inferring high-dimensional spatio-temporal fields within parametric contexts. It enables computationally tractable parametric analyses, uncertainty quantification, and control. However, traditional dimensionality reduction techniques struggle with nonlinear and chaotic dynamics, as well as unknown and varying parameters, limiting their effectiveness in capturing the true system behavior. To address these challenges, this study introduces sensor-driven SHallow REcurrent Decoder networks for Reduced Order Modeling (SHRED-ROM). The proposed SHRED-ROM framework combines a long short-term memory network to capture temporal dynamics from limited sensor data across multiple scenarios with a shallow decoder that reconstructs the corresponding high-dimensional states. Unlike traditional encoding-decoding schemes that rely on numerically unstable approximations of inverses, SHRED-ROM adopts a robust decoding-only strategy to enhance computational efficiency and memory usage. By reducing full-order state snapshots through methods like proper orthogonal decomposition, the networks can be trained compressively with minimal hyperparameter tuning. Through applications in chaotic and nonlinear fluid dynamics, this study demonstrates the capabilities of SHRED-ROM. It accurately reconstructs state dynamics for new parameter values based on limited fixed or mobile sensors regardless of sensor placement. Moreover, SHRED-ROM can handle physical, geometrical, and time-dependent parametric dependencies without prior knowledge of their actual values. The framework also shows promise in accurately estimating unknown parameters and accommodating various data sources such as high-fidelity simulations, coupled fields, and videos. Overall, the sensor-driven SHRED-ROM approach presents a novel solution for efficient Reduced Order Modeling that overcomes limitations of conventional techniques by leveraging deep learning architectures tailored for capturing complex system behaviors in diverse parametric settings.