A Streaming Sparse Cholesky Method for Derivative-Informed Gaussian Process Surrogates Within Digital Twin Applications

TL;DR

This paper introduces a streaming sparse Gaussian process method that incorporates derivative data for real-time digital twin modeling, significantly improving accuracy while efficiently updating with new data.

Contribution

The paper develops a novel sparse GP extension to include derivatives and enables dynamic, real-time updates for digital twin applications.

Findings

Enhanced prediction accuracy with derivative data

Efficient dynamic updating of Gaussian process models

Successful application to aerospace fatigue crack growth

Abstract

Digital twins are developed to model the behavior of a specific physical asset (or twin), and they can consist of high-fidelity physics-based models or surrogates. A highly accurate surrogate is often preferred over multi-physics models as they enable forecasting the physical twin future state in real-time. To adapt to a specific physical twin, the digital twin model must be updated using in-service data from that physical twin. Here, we extend Gaussian process (GP) models to include derivative data, for improved accuracy, with dynamic updating to ingest physical twin data during service. Including derivative data, however, comes at a prohibitive cost of increased covariance matrix dimension. We circumvent this issue by using a sparse GP approximation, for which we develop extensions to incorporate derivatives. Numerical experiments demonstrate that the prediction accuracy of the derivative-enhanced sparse GP method produces improved models upon dynamic data additions. Lastly, we apply the developed algorithm within a DT framework to model fatigue crack growth in an aerospace vehicle.