Abstract: The properties of nuclear matter at various densities is of great interest, as it is crucial for the understanding of the structure of nuclei and neutron stars, the dynamics of heavy ion collision (HIC), and neutron star mergers. HIC provides a unique opportunity to create nuclear matter with density away from the normal nuclear density (ρ₀) in the terrestrial laboratory, however, the created nuclear matter only exists for a very short period and its properties cannot be measured directly. Usually, the properties of nuclear matter are deduced from the comparison of the event-average quantities between experimental measurements and transport model simulations. However, quantities in HIC can be obtained event-by-event both in experiments and in transport model simulations. These event-by-event data usually comprise a huge amount of data which encodes rich physical information, and at the same time, large fluctuations which can be taken as noises. Machine learning (ML) has been proven very powerful for the extraction of information from complex data in many branches of science. In this work, event-by-event observables from Au+Au and Sn+Sn collisions at intermediate energies are generated with the ultrarelativistic quantum molecular dynamics (UrQMD) model. Model parameters with different nuclear incompressibility K0 of isospin symmetric nuclear matter, the slope parameter L of nuclear symmetry energy, and the in-medium correction factor F of nucleon-nucleon cross section were used to generate labeled dataset. The light gradient boosting machine (LightGBM) which is a decision-tree-based algorithm was used to learn the labeled dataset. The advantages of LightGBM include faster training efficiency, low memory usage, higher accuracy, and ability to tackle large-scale data. It is found that the trained machine learning algorithm is able to infer K0 and L, and F from the event-by-event data. The mean absolute errors (MAE) which measure the average magnitude of the absolute differences between the predicted and true values of K0 and L, and F are 52 MeV, 29.6 MeV, and 0.08, respectively. These MAE values can be further reduced by using event-averaged data instead of event-by-event data, as fluctuations in the event-averaged data are largely suppressed. Furthermore, by using the feature_importance technology and shapley additive explanations (SHAP) which are two popular feature attribution methods to identify the most important features that drive predictions, features that have the greatest effect on the extraction of K₀ and L, and F are found out. This work suggests that, with the help of ML, physical information can be extracted on the event-by-event basis, and it may offer a new paradigm to study the underlying physics in heavy ion collisions.