🤖 AI Summary
Machine learning (ML) surrogate models in engineering simulation suffer from unreliable predictions due to the coupling of model uncertainty and input variability. To address this, we propose a unified uncertainty quantification framework based on polynomial chaos expansion (PCE). This method jointly maps the predictive distribution of Gaussian process regression and the input random variables onto a standard orthogonal polynomial basis, enabling synergistic modeling of both sources of uncertainty. The framework enables efficient computation of output statistical moments (e.g., mean and variance) and global sensitivity analysis, allowing quantitative decomposition of the individual contributions of each input variable and model uncertainty to the total output variability. Compared with conventional Monte Carlo methods, our approach achieves comparable accuracy while drastically reducing computational cost. As a result, it enhances the reliability and interpretability of ML surrogates in engineering design applications.
📝 Abstract
Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes. However, ML predictions contain inherent errors, often estimated as model uncertainty, which is coupled with variability in model inputs. Accurately quantifying and propagating these combined uncertainties is essential for generating reliable engineering predictions. This paper presents a robust framework based on Polynomial Chaos Expansion (PCE) to handle joint input and model uncertainty propagation. While the approach applies broadly to general ML surrogates, we focus on Gaussian Process regression models, which provide explicit predictive distributions for model uncertainty. By transforming all random inputs into a unified standard space, a PCE surrogate model is constructed, allowing efficient and accurate calculation of the mean and standard deviation of the output. The proposed methodology also offers a mechanism for global sensitivity analysis, enabling the accurate quantification of the individual contributions of input variables and ML model uncertainty to the overall output variability. This approach provides a computationally efficient and interpretable framework for comprehensive uncertainty quantification, supporting trustworthy ML predictions in downstream engineering applications.