We present a learnable physics-based predictive model that provides accurate motion and force-torque prediction of the robot end effector in contact-rich manipulation. The proposed model extends the state-of-the-art GNN-based simulator (FIGNet) with novel node and edge types, enabling action-conditional predictions for control and state estimation in the context of robotic peg insertion. Our model learns in a self-supervised manner, using only joint encoder and force-torque data while the robot is touching the environment. In simulation, the MPC agent using our model matches the performance of the same controller with the ground truth dynamics model in a challenging peg-in-hole task, while in the real-world experiment, our model achieves a 50$\%$ improvement in motion prediction accuracy and 3$\times$ increase in force-torque prediction precision over the baseline physics simulator. Finally, we apply the model to track the robot end effector with a particle filter during real-world peg insertion, demonstrating a practical application of its predictive accuracy.

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