Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning

TL;DR

This paper demonstrates that reservoir computing, enhanced with transfer learning, can effectively predict the dynamics of shallow-water equations for unseen initial conditions, addressing previous limitations of trajectory-specific training.

Contribution

The study introduces a transfer learning method to reservoir computing, enabling it to generalize shallow-water dynamics predictions across different ambient conditions.

Findings

Reservoir computing can predict shallow-water trajectories with unseen initial conditions.

Transfer learning improves prediction accuracy for varying ambient conditions.

Performance deteriorates without transfer learning when ambient conditions differ.

Abstract

In this paper we demonstrate that reservoir computing can be used to learn the dynamics of the shallow-water equations. In particular, while most previous applications of reservoir computing have required training on a particular trajectory to further predict the evolution along that trajectory alone, we show the capability of reservoir computing to predict trajectories of the shallow-water equations with initial conditions not seen in the training process. However, in this setting, we find that the performance of the network deteriorates for initial conditions with ambient conditions (such as total water height and average velocity) that are different from those in the training dataset. To circumvent this deficiency, we introduce a transfer learning approach wherein a small additional training step with the relevant ambient conditions is used to improve the predictions.