Abstract: The equation of state (EOS) of nuclear matter is essential for studying the properties of nuclei and the evolution of universe and astro-objects. Heavy-ion collisions at intermediate energies permit creating nuclear matter with high density and temperature, by comparing transport model simulations with the corresponding experimental data offers one of the most important way to study the nuclear EOS. Unfortunately, different models do not always give the same results. In this work, a deep convolutional neural network (CNN) is used to identify the nuclear EOS from the spectra in transverse momentum and rapidity of protons. It is found that the network can be taken as a useful decoder to extract the nuclear EOS from the transverse momentum and rapidity distribution of protons. By using the Prediction Difference Analysis method, the most sensitive region of the transverse momentum and rapidity distribution to the nuclear EOS can be found out, which may offer an alternative strategy for experimental and theoretical studies of heavy-ion collisions. In addition, a gradient boosting framework (LightGBM) that uses tree based learning algorithms is also applied, and it is found that the accuracy obtained with the LightGBM is similar to that with CNN.