Shape deviation modeling and compensation in additive manufacturing are pivotal for achieving high geometric accuracy and enabling industrial-scale production. Critical challenges persist, including generalizability across complex geometries and adaptability to position-dependent variations in batch production. Traditional methods of controlling geometric deviations often rely on complex parameterized models and repetitive metrology, which can be time-consuming yet not applicable for batch production. In this paper, we present a novel, process-agnostic approach to address the challenge of ensuring geometric precision and accuracy in position-dependent AM production. The proposed GraphCompNet presents a novel computational framework integrating graph-based neural networks with a GAN inspired training paradigm. The framework leverages point cloud representations and dynamic graph convolutional neural networks (DGCNNs) to model intricate geometries while incorporating position-specific thermal and mechanical variations. A two-stage adversarial training process iteratively refines compensated designs using a compensator-predictor architecture, enabling real-time feedback and optimization. Experimental validation across various shapes and positions demonstrates the framework's ability to predict deviations in freeform geometries and adapt to position-dependent batch production conditions, significantly improving compensation accuracy (35 to 65 percent) across the entire printing space, addressing position-dependent variabilities within the print chamber. The proposed method advances the development of a Digital Twin for AM, offering scalable, real-time monitoring and compensation capabilities.