A Streaming Sparse Cholesky Method for Derivative-Informed Gaussian Process Surrogates Within Digital Twin Applications
This work addresses the need for real-time, accurate surrogate models in digital twin applications, such as fatigue crack growth in aerospace vehicles, though it is incremental as it extends existing sparse GP methods to include derivatives.
The paper tackled the high computational cost of including derivative data in Gaussian process surrogates for digital twins by developing a sparse GP approximation that incorporates derivatives, resulting in improved prediction accuracy upon dynamic data updates as demonstrated in numerical experiments.
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.