Multitask Modeling for Reliability Analysis and Design with Partial Information

Accurate predictive modeling plays a pivotal role in enhancing system performance, mitigating failures, and optimizing maintenance strategies. However, traditional modeling techniques often face challenges when dealing with partially labeled datasets, leading to inaccuracies and unreliable results. In this study, we propose a multi-task surrogate modeling framework with conformal prediction to tackle these challenges effectively. The proposed model utilizes latent variables to recover unlabeled observations and reconstruct missing dimensions through latent variables. Moreover, our method leverages partially observed/labeled information from diverse sources, encompassing varying observed labels, to mitigate the computational cost associated with collecting and evaluating expensive high-dimensional complex systems. To ensure that the model is not misspecified, we employ conformal prediction to calibrate the Bayesian prediction interval and provide accurate uncertainty quantification for engineering systems. This step enhances the model's reliability and aids in making informed decisions. To validate the effectiveness of our proposed method, we demonstrate its application to a vehicle design problem. The results highlight its ability to accommodate the inherent intricacies of partially labeled datasets, propelling the field towards more robust and accurate uncertainty quantification.