This work aims to explore the use of neural networks as a driver for real-time simulation, opening new avenues for the implementation of digital twins in computational biomechanics and overcoming the inherent limitations of traditional numerical simulations. The proposed methodology focuses on predicting the behavior of a hepatic digital twin, accurately describing its evolution in terms of stress, velocity, and position under various loading conditions. Moreover, the approach demonstrates robustness to unseen geometries and adaptability to different spatial discretizations. The proposed framework combines the potential of graph neural networks [1] as the main geometric bias with a physical bias derived from the imposition of the metriplectic structure related to the GENERIC formalism [2,3], ensuring the convergence while preserving the thermodynamic consistency of the system. Numerically, the results demonstrate relative errors below 1% for position and below 7% for stress and velocity across 190 unseen simulations, being also able to compensate the recurrent error accumulation during time-step integration and generating a natural behavior of the soft tissue. These results demonstrate a deep understanding of the tissue’s hyper-viscoelastic behavior, showcasing a high capacity for generalization to unseen geometries and conditions, with faster response times than standard numerical solvers. This highlights a promising potential for applications in precision medicine and haptic environments, while underscoring the value of graph neural networks in mechanical computation.