  We demonstrate high prediction accuracy of three important properties that
determine the initial geometry of the heavy-ion collision (HIC) experiments by
using supervised Machine Learning (ML) methods. These properties are the impact
parameter, the eccentricity and the participant eccentricity. Though ML
techniques have been used previously to determine the impact parameter of these
collisions, we study multiple ML algorithms, their error spectrum, and sampling
methods using exhaustive parameter scans and ablation studies to determine a
combination of efficient algorithm and tuned training set that gives multi-fold
improvement in accuracy for all three different heavy-ion collision models. The
three models chosen are a transport model, a hydrodynamic model and a hybrid
model. The motivation of using three different heavy-ion collision models was
to show that even if the model is trained using a transport model, it gives
accurate results for a hydrodynamic model as well as a hybrid model. We show
that the accuracy of the impact parameter prediction depends on the centrality
of the collision. With the standard application of ML training methods,
prediction accuracy is considerable low for central collisions. Our method
increases this accuracy by multiple folds. We also show that the eccentricity
prediction accuracy can be improved by inclusion of the impact parameter as a
feature in all these algorithms. We discuss how the errors can be minimized and
the accuracy can be improved to a great extent in all the ranges of impact
parameter and eccentricity predictions.
