The cold start problem is a challenging problem faced by most modern recommender systems. By leveraging knowledge from other domains, cross-domain recommendation can be an effective method to alleviate the cold start problem. However, the modelling distortion for long-tail data, which is widely present in recommender systems, is often overlooked in cross-domain recommendation. In this research, we propose a hyperbolic manifold based cross-domain collaborative filtering model using BiTGCF as the base model. We introduce the hyperbolic manifold and construct new propagation layer and transfer layer to address these challenges. The significant performance improvements across various datasets compared to the baseline models demonstrate the effectiveness of our proposed model.

Manufacturing complexities and uncertainties have impeded the transition from material prototypes to commercial batteries, making prototype verification critical to quality assessment. A fundamental challenge involves deciphering intertwined chemical processes to characterize degradation patterns and their quantitative relationship with battery performance. Here we show that a physics-informed machine learning approach can quantify and visualize temporally resolved losses concerning thermodynamics and kinetics only using electric signals. Our method enables non-destructive degradation pattern characterization, expediting temperature-adaptable predictions of entire lifetime trajectories, rather than end-of-life points. The verification speed is 25 times faster yet maintaining 95.1% accuracy across temperatures. Such advances facilitate more sustainable management of defective prototypes before massive production, establishing a 19.76 billion USD scrap material recycling market by 2060 in China. By incorporating stepwise charge acceptance as a measure of the initial manufacturing variability of normally identical batteries, we can immediately identify long-term degradation variations. We attribute the predictive power to interpreting machine learning insights using material-agnostic featurization taxonomy for degradation pattern decoupling. Our findings offer new possibilities for dynamic system analysis, such as battery prototype degradation, demonstrating that complex pattern evolutions can be accurately predicted in a non-destructive and data-driven fashion by integrating physics-informed machine learning.