Topological Approach for Data Assimilation

TL;DR

This paper introduces a novel topological data analysis-based data assimilation method that optimizes model predictions without requiring noise statistics, demonstrated on Lorenz systems.

Contribution

The paper presents a new topological approach for data assimilation that does not depend on measurement noise statistics, enhancing model accuracy in chaotic systems.

Findings

Effective in Lorenz 63 system

Works on higher-dimensional Lorenz 96 system

Does not require noise information

Abstract

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data, machine learning models often deviate from the true system states over time and need to be continually updated as new measurements are taken using data assimilation. Classical data assimilation algorithms typically require knowledge of the measurement noise statistics which may be unknown. In this paper, we introduce a new data assimilation algorithm with a foundation in topological data analysis. By leveraging the differentiability of functions of persistence, gradient descent optimization is used to minimize topological differences between measurements and forecast predictions by tuning data driven model coefficients without using noise information from the measurements. We describe the method and focus on its capabilities performance using the chaotic Lorenz 63 system as an example and we also show that the method works on a higher dimensional example with the Lorenz 96 system.