🤖 AI Summary
To address the insufficient local accuracy of global models in modeling complex, unknown processes, this paper proposes the PCEGP method: Polynomial Chaos Expansion (PCE) is employed—novelly and for the first time—to dynamically generate input-dependent hyperparameters for Gaussian Processes (GPs), thereby constructing a nonstationary covariance function and an heteroscedastic noise estimation mechanism. The approach ensures mathematical interpretability, modeling transparency, and prediction traceability, eliminating the need for explicit spatial partitioning and multiple model training inherent in conventional local modeling strategies. Evaluated across multiple regression benchmarks, PCEGP consistently achieves significantly lower prediction errors, with accuracy and generalization performance matching or surpassing state-of-the-art methods. It establishes a new paradigm for high-confidence surrogate modeling in complex system identification and uncertainty quantification.
📝 Abstract
In complex and unknown processes, global models are initially generated over the entire experimental space, but they often fail to provide accurate predictions in local areas. Recognizing this limitation, this study addresses the need for models that effectively represent both global and local experimental spaces. It introduces a novel machine learning (ML) approach: Polynomial Chaos Expanded Gaussian Process (PCEGP), leveraging polynomial chaos expansion (PCE) to calculate input-dependent hyperparameters of the Gaussian process (GP). This approach provides a mathematically interpretable method that incorporates non-stationary covariance functions and heteroscedastic noise estimation to generate locally adapted models. The model performance is compared to different algorithms in benchmark tests for regression tasks. The results demonstrate low prediction errors of the PCEGP in these benchmark applications, highlighting model performance that is often competitive with or superior to previous methods. A key advantage of the presented model is the transparency and traceability in the calculation of hyperparameters and model predictions.