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

2025-10-31

AI Summary

Integrating derivative information into Gaussian process (GP) surrogate models enhances predictive accuracy in digital twin applications but incurs prohibitive computational cost due to exponential growth in covariance matrix dimensionality. To address this, we propose a derivative-aware sparse GP modeling framework: (i) we formally incorporate derivative constraints into sparse GP inference for the first time; (ii) we design a streaming sparse Cholesky decomposition algorithm enabling online incremental learning and dynamic data injection; and (iii) we introduce derivative-enhanced covariance modeling coupled with adaptive sparsification to jointly ensure real-time performance and high fidelity. Evaluated on aircraft fatigue crack propagation modeling under continuous data streams, our method achieves millisecond-scale model updates and maintains over 98.2% prediction accuracy, demonstrating superior precision, ultra-low latency, and strong scalability.

Technology Category

• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Developing streaming sparse Cholesky method for derivative-informed Gaussian processes
• Reducing computational cost of derivative-enhanced covariance matrices
• Enabling real-time digital twin updates with sparse derivative data

Innovation

• Streaming sparse Cholesky method for Gaussian processes
• Incorporates derivative data via sparse GP approximation
• Enables dynamic updating with physical twin data