Scoliosis, an abnormal curvature of the human spinal column, is characterized by a lateral deviation of the spine, accompanied by axial rotation of the vertebrae. Adolescent Idiopathic Scoliosis (AIS) is the most common type, affecting children between ages 8 to 18 when bone growth is at its maximum rate. We propose a mechanistic machine learning algorithm in order to study patient-specific AIS curve progression, which is associated with the bone growth and other genetic and environmental factors. Two different frameworks are used to analyse and predict curve progression, one with implementing clinical data extracted from 2D X-ray images and the other one with incorporating both clinical data and physical equations governing the non-uniform bone growth. The physical equations governing bone growth are affiliated with calculating all stress components at each region. The stress values are evaluated through a surrogate finite element simulation and a bone growth model on a detailed patient-specific geometry of the human spine. We also propose a patient-specific framework to generate the volumetric model of human spine which is partitioned into different tissues for both vertebra and intervertebral disc. It is shown that implementing physical equations governing bone growth into the prediction framework will notably improve the prediction results as compared to only using clinical data for prediction. In addition, we can predict curve progression at ages outside the range of training samples.