In recent years, machine learning has been extensively applied to data prediction during process ramp-up, with a particular focus on transistor characteristics for circuit design and manufacture. However, capturing the nonlinear current response across multiple operating regions remains a challenge for neural networks. To address such challenge, a novel machine learning framework, PRIME (Physics-Related Intelligent Mixture of Experts), is proposed to capture and integrate complex regional characteristics. In essence, our framework incorporates physics-based knowledge with data-driven intelligence. By leveraging a dynamic weighting mechanism in its gating network, PRIME adaptively activates the suitable expert model based on distinct input data features. Extensive evaluations are conducted on various gate-all-around (GAA) structures to examine the effectiveness of PRIME and considerable improvements (60\%-84\%) in prediction accuracy are shown over state-of-the-art models.