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  3. Sparse Identification Of Nonlinear Dynamics And Koopman Operators With Shallow Recurrent Decoder Networks.

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

Mars Liyao Gao1, Jan P Williams2, J Nathan Kutz3,4

  • 1Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, WA 98195.

Proceedings of the National Academy of Sciences of the United States of America
|April 17, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces SINDy-SHRED, a novel method for modeling complex spatiotemporal data by learning interpretable dynamics and discovering governing equations. It achieves superior accuracy and data efficiency compared to existing deep learning models.

Keywords:
deep learningdynamical systemsmachine learningmodel discoveryreduced order models

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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.