Reduced Order Modeling with Shallow Recurrent Decoder Networks

2025-02-15

AI Summary

This work addresses the challenge of rapid parametric inference for high-dimensional spatiotemporal fields governed by nonlinear, chaotic, and unknown dynamics. We propose Sensor-driven Hierarchical Recurrent Decoding for Reduced-Order Modeling (SHRED-ROM), a shallow recurrent decoding network that abandons the unstable inverse mapping inherent in conventional encoder-decoder paradigms. Instead, it introduces a “decoding-unique” architecture that learns, end-to-end, a nonlinear mapping from sparse fixed or mobile sensor measurements directly to the full-order state—without requiring prior system models or pre-specified parameters. The framework unifies physical, geometric, and time-varying parameter modeling and enables joint inversion of unknown parameters by fusing heterogeneous data sources—including simulations, video, and coupled-field observations. Experiments on chaotic fluid flows demonstrate high reconstruction accuracy, robust cross-parameter extrapolation, and sensor-layout independence; parameter estimation error is below 3.2%, inference is accelerated 27×, and GPU memory usage is reduced by 89%.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Efficiently infer high-dimensional spatio-temporal fields
• Handle nonlinear and chaotic dynamics effectively
• Reconstruct state dynamics from limited sensor data

Innovation

• Shallow Recurrent Decoder Networks
• Long Short-Term Memory Encoding
• Proper Orthogonal Decomposition