Fig. 1. Demonstration of difficulty encountered when extracting the nuclear equation of state (EoS) through model-data comparison in heavy-ion collisions^[4]

Fig. 2. Demonstration of the sign problem in lattice QCD

Fig. 3. Extraction of nuclear EoS at a high temperature and zero baryon chemical potential region using Bayesian analysis^[19]

Fig. 4. A single layer artificial neural network transforms the input data by a linear matrix operation z=xW+b, in combination with a non-linear operation on each element of the output z using a non-linear activation function

Fig. 5. Identification of the nuclear EoS and types of phase transition from the final state particle spectra using deep convolutional neural network^[24]

Fig. 6. Identification of the nuclear EoS from the final state particle cloud in momentum space using point cloud neural network^[28]

Fig. 7. Search for self-similarity in momentum space using dynamical edge convolution network and identification of correlated particles^[39]

Fig. 8. Framework of the deep neural network when constructing three temperature-dependent mass functions and calculating the QCD EoS using DNN learned masses^[42]

Fig. 9. Flow chart illustrating active learning^[43]

Fig. 10. Classification of nuclear liquid gas phase transition using an auto encoder, which learns from the experimental data of heavy-ion collisions^[46]

Fig. 11. Distribution of the slope L parameters predicted by LightGBM^[55]

Fig. 12. Deep learning assisted jet tomography used to locate the initial jet production positions and aid in searching the Mach cone in nuclear liquid^[58]

Fig. 13. Flow chart illustrating active learning^[61]