Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

TL;DR

This paper introduces RAFDA, a method combining neural networks and data assimilation to predict dynamical systems from noisy, partial data, outperforming traditional batch learning approaches.

Contribution

The paper proposes a novel framework that integrates random feature maps with data assimilation for efficient, online learning of dynamical systems from partial, noisy observations.

Findings

RAFDA outperforms standard random feature map methods.

The approach effectively learns from partial, noisy data.

Training on delay coordinates improves prediction accuracy.

Abstract

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens' embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.