Optimization under Uncertainty Using Physics-Based Label-Free Machine Learning

Machine learning is increasingly employed in engineering, with one of its primary applications being the construction of surrogate models to replace computationally expensive physical models for analysis and design, especially control co-design which integrates physical and control system design. In cases where generating labels for training through physical models is computationally intensive, label-free machine learning offers a viable alternative. However, surrogate models built from label-free machine learning typically have prediction errors, which can be characterized and quantified through epistemic uncertainty, representing model-form uncertainty. Moreover, when these surrogate models are used in optimization design for real-world applications, inherent random variables introduce aleatory uncertainty. This study introduces a robust design optimization method that addresses the intertwined epistemic and aleatory uncertainty. By optimizing both the average product performance and reducing uncertainty stemming from the coupled uncertainty, the method achieves improved robustness. A four-bar linkage mechanism design serves as a demonstration of this approach. The surrogate model for the design is constructed using label-free neural network, accommodating a system of physical equations. The error of the surrogate model is assessed through Gaussian Process regression, using existing training points and derivatives of the physical equations at these points. The design of the four-bar linkage aims to minimize both its average motion error and the variability of the error attributed to coupled uncertainty.