Robust Design Under Machine Learning Model Uncertainty

Abstract Robust design ensures consistent product performance in the presence of uncertainty arising from randomness in manufacturing, materials, and user environments. This type of uncertainty, known as aleatory uncertainty, is typically addressed using models derived from domain physics principles. However, many physics models are computationally expensive, leading to the growing use of statistical and machine learning techniques to construct surrogate models. While surrogate models significantly reduce computational cost, they introduce epistemic (model) uncertainty, which is used to estimate prediction errors. This study presents a robust design methodology for managing mixed uncertainty—aleatory and epistemic—without requiring retraining of the surrogate model. The expected quality loss function under mixed uncertainty serves as the objective function, while the constraints are expressed as reliability constraints based on the probability distribution or the first two moments of the corresponding performance functions. By incorporating the first-order second-moment method, this approach quantifies and optimizes robustness in the presence of mixed uncertainty. The methodology is demonstrated with three design problems, and results show that accounting for model (epistemic) uncertainty yields more conservative designs or robust designs compared to traditional robust design methods.