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Particle identification (PID) is one of the main strengths of the ALICE experiment at the LHC. It is a crucial ingredient for detailed studies of the strongly interacting matter formed in ultrarelativistic heavy-ion collisions. ALICE provides PID information via various experimental techniques, allowing for the identification of particles over a broad momentum range (from around 100 MeV/$c$ to around 50 GeV/$c$). The main challenge is how to combine the information from various detectors effectively. Therefore, PID represents a model classification problem, which can be addressed using Machine Learning (ML) solutions. Moreover, the complexity of the detector and richness of the detection techniques make PID an interesting area of research also for the computer science community. In this work, we show the current status of the ML approach to PID in ALICE. We discuss the preliminary work with the Random Forest approach for the LHC Run 2 and a more advanced solution based on Domain Adaptation Neural Networks, including a proposal for its future implementation within the ALICE computing software for the upcoming LHC Run 3.