With the increasing global attention to climate change and energy crisis, as well as the gradual shift from traditional energy to renewable energy, the demand for lithium-ion batteries (LIBs) has surged. Accurately estimating the State of Health (SOH) of these batteries is crucial for ensuring their safety and performance. In battery management systems, model driven and data-driven methods are commonly used to estimate SOH, but the model driven method using white box models is limited by its fixed model structure and has poor adaptability. Data driven methods typically provide higher accuracy, but often rely on large datasets and are more susceptible to data interference. In this study, we introduce a new neural network architecture, Physical Enhanced Neural Network (PENN), which combines a long shot term memory neural network with a specially designed structure based on Arrhenius equation to improve performance. The experimental results show that in the case of insufficient training data, the PENN model is significantly better than existing methods, with root mean square error and other error indicators consistently below 1%, and also below 2% in multiple cross battery generalization tests. These findings provide valuable insights for the future development of advanced battery management systems and emphasize the potential of integrating physics and chemistry knowledge into data-driven models to achieve more efficient energy storage solutions.