Foldable, origami-inspired, and laminate mechanisms are highly susceptible to deformation under external loading, which can lead to position or orientation errors if idealized kinematic models are used. According to dimensional scaling laws, laminate devices can often be treated as rigid bodies at millimeter and smaller scale deformations. However, foldable mechanisms enter the territory of soft robots at larger scales. In this paper, we show the effect of external loads applied to a laminate, 2-DOF parallel robot and the corresponding errors during a pointing task. We then present two control methods, based on deep learning, that compensates for errors caused by the material deformation in foldable robots. For each proposed control method, a Deep Neural Network (DeepNN) is trained to learn the end-effector's deformation model in no-load and loaded conditions. A DeepNN called an updating network is trained and applied in real-time using measured sensor data, in order to transfer updated weights into another DeepNN called the target network. The target network generates control signals with the aim of compensating for the end-effector's error in tracking a desired trajectory. We evaluate our proposed control methods when applied to a laminate robotic end-effector under different external loading conditions in tracking spiral paths. The experimental results show the effectiveness of our proposed control methods in compensating for material deformation in foldable robots.