GIFR: A Graph-Informed Functional Regression Model for Process- Structure-Property Relationships Discovery

High Temperature Superconductors (HTS) have demonstrated profound applications in capital-intensive industries. These high-field applications of superconductors have led to high demand for cost-effective superconducting tapes on a large scale. However, challenges arise from the instability in the growth conditions during the HTS manufacturing process, leading to nonuniform tape performance. This nonuniformity has, in turn, hindered the broad commercialization of HTS. To address this issue, it is critical to understand the Process-Structure-Property (PSP) relationships in the HTS manufacturing process and develop appropriate monitoring tools with enhanced interpretability and reproducibility. In this study, we present a novel approach, a graph-informed functional regression (GIFR) model, to achieve two primary objectives. The first objective is to unearth the intricate interactions among multivariate time series data, allowing for the systematic investigation and visualization of the underlying PSP relationships. The second objective is to leverage these PSP relationships to real-time predict and monitor the uniformity of tape performance in the HTS manufacturing process. The proposed GIFR model seamlessly integrates the discovered PSP relationships from a functional graphical model, with a functional regression model for real-time uniformity prediction and monitoring. The evaluation of our model using real data from HTS tapes demonstrates that the GIFR model can effectively discover PSP relationships and enable improved prediction of HTS tapes' uniformity compared to other benchmark models.