Abstract: In recent years, physics-informed neural networks (PINNs) have shown remarkable potential in modeling conservative systems of rigid-body dynamics. However, when applied to practical interaction tasks of manipulators (e.g., part assembly and medical operations), existing PINN frameworks lack e ective external force modeling mechanisms, resulting in signi cantly degraded prediction accuracy in dynamic interaction scenarios. Additionally, because industrial robots (including UR5 and UR10e robots) are generally not equipped with joint torque sensors, obtaining precise dynamics training data remains challenging. To address these issues, this study proposes two enhanced PINNs that integrate motor dynamics and external force modeling. First, two data-driven Jacobian matrix estimation methods are introduced to incorporate external forces: one method learns the mapping between end-e ector velocity and joint velocity to approximate the Jacobian matrix, while the other rst learns the system's kinematic behavior and then derives the Jacobian matrix through analytical di erentiation of the forward kinematics model. Second, current-to-torque mapping is embedded as physical prior knowledge to establish direct correlations between system motion states and motor currents. Experimental results on two di erent manipulators demonstrate that both models achieve high-precision torque estimation in complex external force scenarios without requiring joint torque sensors. Compared with state-of-the-art methods, the proposed models improve overall modeling accuracy by 31.12% and 37.07% on average across various complex scenarios, while reducing joint trajectory tracking errors by 40.31% and 51.79%, respectively.