In this paper, a robot assistive Impedance and Admittance control methodology is proposed for a cooperative physical human-robot interaction (pHRI) task. In a pHRI task in which the human is the leader, the robot is a passive follower as the human intention of desired motion and force to be applied are unknown. It is generally difficult to predict the intention of the human leader. Recurrent Neural Networks (RNN) with Long Short-Term Memory (LSTM) units are employed to forecast the position,velocity and force anticipated to be applied by the human. The estimated parameters are integrated into the impedance and admittance controllers via a target impedance model which aids the robot in becoming a proactive partner of the human by sharing the physical load. The same methodology is also applied to the Minimum Jerk model which allows the robot to follow the Minimum Jerk trajectory without knowing the trajectory parameters in advance.