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

2025-10-21 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

A novel Streaming Sparse Cholesky Method enhances Derivative-Informed Gaussian Process (GP) surrogates for Digital Twin (DT) applications, specifically demonstrated for fatigue crack growth in aerospace vehicles. This approach extends GP models to integrate derivative data, significantly improving prediction accuracy while mitigating the computational burden of larger covariance matrices through a sparse GP approximation. The method incorporates derivatives up to the 4th order and features a dynamic update algorithm designed for sequential sensor data, enabling real-time model adaptation without full retraining. Numerical experiments on Griewank and Rosenbrock functions confirm that derivative enhancement and dynamic data additions reduce prediction error, with the "point-wise ordering algorithm 1" and "SU-Approach1" showing superior performance. The framework includes criteria for model retraining based on outliers, unused data budget, or continuous prediction divergence.

Key takeaway

For Machine Learning Engineers developing real-time digital twin surrogates, you should consider integrating derivative-informed sparse Gaussian Processes. This method significantly boosts prediction accuracy and computational efficiency, crucial for dynamic systems like aerospace crack growth monitoring. Implement the dynamic update algorithm with retraining triggers to ensure your models adapt smoothly to new sensor data, maintaining high fidelity and enabling proactive maintenance decisions.

Key insights

Derivative-informed sparse Gaussian Processes enable accurate, dynamically updated digital twin surrogates for real-time system prognostics.

Principles

• Incorporating derivatives improves GP accuracy for smooth functions.
• Sparse Cholesky factorization maintains computational tractability for large datasets.
• Dynamic updates allow real-time model adaptation in DTs.

Method

The method extends sparse Cholesky factorization to derivative-enhanced GPs, using point-wise ordering and dynamic supernodes. It updates or retrains based on outlier detection, unused data budget, or continuous prediction divergence.

In practice

• Use derivative data to boost GP surrogate accuracy.
• Employ sparse Cholesky for scalable GP inference.
• Implement dynamic updates for real-time DT adaptation.

Topics

• Digital Twin
• Gaussian Process Surrogates
• Sparse Cholesky Factorization
• Derivative-Informed Models
• Dynamic Model Update
• Fatigue Crack Growth

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.