Shape deviation modeling and compensation in additive manufacturing (AM) are pivotal for achieving high geometric accuracy and enabling industrial-scale production. While traditional analytical and statistical methods laid the foundation, recent advancements in machine learning (ML) have improved prediction and compensation precision. However, 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 generative adversarial network (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%) 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. This work bridges critical gaps in AM process control, paving the way for high-precision, automated, and industrial-scale design and manufacturing systems.