Koopman-informed recurrent neural networks

Abstract: Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems. In the context of dynamical systems, training with backpropagation through time can lead to challenges arising from exploding or vanishing gradients. Training such networks with backpropagation through time is a notoriously difficult problem because their loss gradients tend to explode or vanish. In this contribution, we introduce Koopman-informed recurrent neural networks, a computational approach to construct all weights and biases of a recurrent neural network without using gradient-based methods. The approach is based on a combination of random feature networks and Koopman operator theory for dynamical systems. The hidden parameters of a single recurrent block are sampled at random, while the outer weights are constructed using extended dynamic mode decomposition. This approach alleviates some problems with backpropagation commonly related to recurrent networks. The connection to Koopman operator theory also allows us to start using results in this area to analyze recurrent neural networks. In computational experiments on time series, forecasting for chaotic dynamical systems, and control problems, as well as on real-world data, we observe that the training time and forecasting accuracy of the Koopman-informed recurrent neural networks we construct are improved when compared to models trained with commonly used gradient-based methods.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Lijun_Wu1

Submission Number: 7802