The primary objective of this study is to address the use of digital twins and neural networks to predict the mechanical behavior of liver tissue, a novel approach that could reduce the need for clinical trials and enhance the virtual simulation of complex systems. The existing bottlenecks in numerical methods and reduction models are exacerbated by the intricate mechanics of biological tissues. Here, neural networks offer a new pathway, enabling the modeling of viscoelastic behaviors with high robustness against changes in geometry or applied loads, while maintaining the high-performance characteristic of artificial intelligence. The proposed model employs a neural network architecture based on a multi-graph scheme [1], where the finite element mesh/graph interacts with an actuator graph representing the imposed displacement and energy input into the system. Additionally, it incorporates a physical bias that ensures the predictions comply with the laws of thermodynamics [2], thus enhancing the model's inference capabilities. The study demonstrates that neural networks, combined with digital twins, effectively simulate the viscoelastic behavior of liver tissue, achieving a prediction error margin of less than 1% for position and under 8% for stress and velocity. This approach outperforms traditional numerical methods, enhancing simulation accuracy and efficiency, and offers promising applications in precision medicine and realistic haptic environments.