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

2025-01-02

AI Summary

To address the challenge of inverting noisy observational data from high-dimensional dynamical systems—such as episodic slow-slip events in Earth’s crust—this paper proposes an efficient and scalable latent-variable factor modeling framework. Methodologically, it enforces orthogonal factor loadings to circumvent inversion of the posterior covariance matrix; integrates Kalman filtering with the Expectation-Maximization (EM) algorithm; and derives closed-form EM update equations, thereby substantially reducing computational complexity without approximation error. Validation on synthetic benchmarks and real Cascadia GPS data demonstrates that the method achieves higher inversion accuracy and superior scalability. Critically, the inferred slip distributions exhibit markedly improved spatiotemporal consistency with tectonic tremor activity, enabling real-time, quantitative hazard assessment under large-scale, noisy geodetic monitoring.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Inverse estimation of slow slip events from noisy geodetic data
• Scalable latent factor modeling for high-dimensional dynamical systems
• Reducing computational complexity in parameter estimation without approximation

Innovation

• Orthogonal factor loading matrix avoids inversion computation
• Closed-form EM algorithm reduces computational complexity
• Scalable approach for high-dimensional dynamical systems