Physics-informed machine learning for system reliability analysis and design with partially observed information

Constructing a high-fidelity predictive model is crucial for analyzing complex systems, optimizing system design, and enhancing system reliability. Although Gaussian Process (GP) models are well-known for their capability to quantify uncertainty, they rely heavily on data and necessitate a large representative dataset to establish a high-fidelity predictive model. Physics-informed Machine Learning (PIML) has emerged as a way to integrate prior physics knowledge and machine learning models. However, current PIML methods are generally based on fully observed datasets and mainly suffer from two challenges: (1) effectively utilize partially available information from multiple sources of varying dimensions and fidelity; (2) incorporate physics knowledge while maintaining the mathematical properties of the GP-based model and uncertainty quantification capability of the predictive model. To overcome these limitations, this paper proposes a novel physics-informed machine learning method that incorporates physics prior knowledge and multi-source data by leveraging latent variables through the Bayesian framework. This method effectively utilizes partially available limited information, significantly reduces the need for costly fully observed data, and improves prediction accuracy while maintaining the model property of uncertainty quantification. The developed approach has been demonstrated with two case studies: the vehicle design problem and the battery capacity loss prediction. The case study results demonstrate the effectiveness of the proposed model in complex system design and optimization while propagating uncertainty with limited fully observed data.