Artificial growth systems help in addressing the challenges associated with the population growth, urbanization, and climate change. In this work, we apply the Dynamic Mode Decomposition (DMD) method for a plant growth dynamics and artificial growing system modelling. For modelling we collect the data using a custom-made experimental testbed. The dataset of the time-sequenced top-down images of the plant growth (3168 images) and growth conditions is available online. The proposed data-driven system identification results in a markovian model of growth dynamics. We extend DMD with the features based on classic Fishman and Genard model of fruit growth and consider several combinations of those. Then we select a small number of the features providing best fit to the observed data. Our results demonstrate that the proposed approach provides an opportunity for making the accurate long-term dynamics predictions. This outcome is vital for designing control systems for precision agriculture.