Data Assimilation with Deep Neural Nets Informed by Nudging

TL;DR

This paper introduces a machine learning approach using Deep Neural Networks trained to emulate the nudging data assimilation algorithm, achieving comparable accuracy with reduced computational cost demonstrated on Lorenz models.

Contribution

It presents a novel DNN-based data assimilation method that learns the nudging algorithm, offering a computationally cheaper alternative with proven approximation properties.

Findings

DNNs achieve accuracy comparable to traditional nudging.

The approach is validated on Lorenz 63 and Lorenz 96 models.

Theoretical approximation results support the method's effectiveness.

Abstract

The nudging data assimilation algorithm is a powerful tool used to forecast phenomena of interest given incomplete and noisy observations. Machine learning is becoming increasingly popular in data assimilation given its ease of computation and forecasting ability. This work proposes a new approach to data assimilation via machine learning where Deep Neural Networks (DNNs) are being taught the nudging algorithm. The accuracy of the proposed DNN based algorithm is comparable to the nudging algorithm and it is confirmed by the Lorenz 63 and Lorenz 96 numerical examples. The key advantage of the proposed approach is the fact that, once trained, DNNs are cheap to evaluate in comparison to nudging where typically differential equations are needed to be solved. Standard exponential type approximation results are established for the Lorenz 63 model for both the continuous and discrete in time models. These results can be directly coupled with estimates for DNNs (whenever available), to derive the overall approximation error estimates of the proposed algorithm.