Fast data inversion for high-dimensional dynamical systems from noisy measurements

TL;DR

This paper introduces a scalable, efficient latent factor model for high-dimensional dynamical systems that improves computational speed and accuracy, demonstrated through geodetic data analysis of slow slip events.

Contribution

The authors develop a novel orthogonal factor loading approach with closed-form EM updates, significantly reducing computational complexity without sacrificing accuracy.

Findings

Higher accuracy and scalability compared to existing methods

Better agreement with seismic data in real-world geodetic application

Enables analysis of massive noisy datasets for geological hazard assessment

Abstract

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our study is motivated by inversely estimating slow slip events from geodetic data, such as continuous GPS measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. By applying our method to geodetic measurements in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications.