Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks.

Area of Science:

• Computational Physics
• Machine Learning
• Data Science

Background:

• Modeling complex spatiotemporal data is challenging due to high dimensionality, noise, and partial observations.
• Existing methods often require extensive data and computational resources.

Purpose of the Study:

• To present Sparse Identification of Nonlinear Dynamics with SHallow REcurrent Decoder networks (SINDy-SHRED), a method for joint sensing and model identification.
• To develop a computationally efficient and robust approach for spatiotemporal data analysis.

Main Methods:

• Utilizes Gated Recurrent Units for temporal sequence modeling of sparse sensor measurements.
• Employs a shallow decoder network to reconstruct spatiotemporal fields from latent states.
• Introduces SINDy-based regularization for latent space convergence to a SINDy-class functional.

Main Results:

• Learns a symbolic, interpretable, low-dimensional latent space for complex dynamics.
• Discovers governing equations for physical systems and achieves a convex loss landscape.
• Demonstrates superior accuracy, data efficiency, and reduced training cost over state-of-the-art methods.

Conclusions:

• SINDy-SHRED provides a powerful tool for understanding and predicting complex spatiotemporal phenomena.
• The method enables stable and accurate long-term video predictions, outperforming deep learning baselines.
• Offers a parsimonious and interpretable model with fewer parameters than competing approaches.