This paper addresses graph topology identification for applications where the underlying structure of systems like brain and social networks is not directly observable. Traditional approaches based on signal matching and spectral templates have limitations, particularly in handling scale issues and sparsity assumptions. We introduce a novel covariance matching methodology that efficiently reconstructs the graph topology using observable data. For the structural equation model (SEM) using an undirected graph, we demonstrate that our method can converge to the correct result under relatively soft conditions. Furthermore, we extend our methodology to polynomial models and any known distribution of latent variables, broadening its applicability and utility in diverse graph-based systems.

This paper presents an efficient approach to battery cycle life prediction through few-shot transfer learning, addressing the challenges of costly and limited battery aging data. Leveraging freely available datasets, a multi-layer perceptron (MLP) model was pretrained on diverse battery aging datasets to adapt to new prediction tasks with minimal training samples through few-shot fine-tuning techniques on the target data. The proposed fine-tuning strategy was validated using a heterogeneous aging dataset of 347 batteries, with cycle lives ranging from 144 to 4,052 cycles, incorporating batteries with lithium iron phosphate (LFP), lithium cobalt oxide (LCO), nickel cobalt aluminum oxide (NCA), and nickel manganese cobalt oxide (NMC) chemistries, which ensures robust validation of our methods. The results show that even with few samples of data from a target task, a comparable generalization performance to training from scratch with 100% data can be achieved, thus demonstrating its effectiveness in utilizing available resources for accurate cycle life prediction.