A machine learning assisted modal power analyzing scheme designed for optical modes in integrated multi-mode waveguides is proposed and studied in this work. Convolutional neural networks (CNNs) are successfully trained to correlate the far-field diffraction intensity patterns of a superposition of multiple waveguide modes with its modal power distribution. In particular, a specialized CNN is trained to analyze thin optical waveguides, which are single-moded along one axis and multi-moded along the other axis. A full-scale CNN is also trained to cross-validate the results obtained from this specialized CNN model. Prediction accuracy for modal power is benchmarked statistically with square error and absolute error distribution. It is found that the overall accuracy of our trained specialized CNN is very satisfactory for thin optical waveguides while that of our trained full-scale CNN remains nearly unchanged but the training time doubles. This approach is further generalized and applied to a waveguide that is multi-moded along both horizontal and vertical axes and the influence of noise on our trained network is studied. Overall, we find that the performance in this general condition keeps nearly unchanged. This new concept of analyzing modal power may open the door for high fidelity information recovery in far field and holds great promise for potential applications in both integrated and fiber-based spatial-division demultiplexing.