Sparse identification of nonlinear dynamics with Shallow Recurrent Decoder Networks

Liyao Gao, Jan P. Williams, J. Nathan Kutz

Keywords: Sata-driven modeling, scientific machine learning, sparse identification of nonlinear dynamics, AI in dynamic systems, spatiotemporal modeling, PDEs

TL;DR: We introduce SINDy-SHRED, an architecture that simultaneously solves the sensing and model identification problems, achieving state-of-the-art performance for accurate and stable long-term predictions.

Abstract: Spatio-temporal modeling of real-world data is a challenging problem as a result of inherent high-dimensionality, noisy observations, and expensive data collection procedures. In this paper, we present Sparse Identification of Nonlinear Dynamics with SHallow Recurrent Decoder networks (SINDy-SHRED) to jointly solve the sensing and model identification problems with simple implementation, efficient computation, and robust performance. SINDy-SHRED utilizes Gated Recurrent Units (GRUs) to model the temporal sequence of sensor measurements along with a shallow decoder network to reconstruct the full spatio-temporal field from the latent state space using only a few available sensors. Our proposed algorithm introduces a SINDy-based regularization. Beginning with an arbitrary latent state space, the dynamics of the latent space progressively converges to a SINDy-class functional, provided the projection remains within the set. We conduct a systematic experimental study including synthetic PDE data, real-world sensor measurements for sea surface temperature, and direct video data. With no explicit encoder, SINDy-SHRED allows for efficient training with minimal hyperparameter tuning and laptop-level computing. SINDy-SHRED demonstrates robust generalization in a variety of applications with minimal to no hyperparameter adjustments. Additionally, the interpretable SINDy model of latent state dynamics enables accurate long-term video predictions, achieving state-of-the-art performance and outperforming all baseline methods considered, including Convolutional LSTM, PredRNN, ResNet, and SimVP.

Primary Area: learning on time series and dynamical systems

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Submission Number: 554