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

arXiv: https://arxiv.org/abs/2511.00366 · HTML: https://mlsanity.com/paper/2511.00366/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 13 of 13)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Solving and Learning Nonlinear PDEs with Gaussian Processes](https://mlsanity.com/paper/2103.12959/) (2021)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations](https://mlsanity.com/paper/2207.06503/) (2022)
- [Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes](https://mlsanity.com/paper/2304.01294/) (2023)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Scaling Gaussian Processes with Derivative Information Using Variational Inference](https://mlsanity.com/paper/2107.04061/) (2021)
- [Solving High Frequency and Multi-Scale PDEs with Gaussian Processes](https://mlsanity.com/paper/2311.04465/) (2023)
- [Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference](https://mlsanity.com/paper/2112.14591/) (2021)
- [DGP-LVM: Derivative Gaussian process latent variable models](https://mlsanity.com/paper/2404.04074/) (2024)

## Abstract (arXiv)

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. In this paper, we combine and extend several previous surrogate-related advancements with the goal of demonstrating an end-to-end digital twin (DT) solution for predicting performance of an aircraft structure (the physical asset). To this end, 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 through our modified dynamic sparse Cholesky linear system solver. Numerical experiments demonstrate that the prediction accuracy of the derivative-enhanced sparse Cholesky GP method produces improved models upon dynamic data additions. Lastly, we demonstrate the developed algorithm within a DT framework to model fatigue crack growth in an aerospace vehicle, thereby exhibiting through our assembled engineered system how digital twin technologies can be combined in practice.