Studies on object rearrangement planning typically consider known objects. Some learning-based methods can predict the movement of an unknown object after single-step interaction, but require intermediate targets, which are generated manually, to achieve the rearrangement task. In this work, we propose a framework for unknown object rearrangement. Our system first models an object through a small-amount of identification actions and adjust the model parameters during task execution. We implement the proposed framework based on a low-cost tabletop robot (under 180 USD) to demonstrate the advantages of using a physics engine to assist action prediction. Experimental results reveal that after running our adaptive learning procedure, the robot can successfully arrange a novel object using an average of five discrete pushes on our tabletop environment and satisfy a precise 3.5 cm translation and 5° rotation criterion.