Tensor-Based Forward-Backward Algorithms in Physics-Informed Coupled Hidden Markov Model

Imposing data-driven with physical laws for user activity prediction could effectively solve various physical problems such as smart care, surveillance and human-robot. In the growing field of artificial intelligence, the application of activity prediction based on physical Coupled Hidden Markov Model (CHMM) and tensor theory with physical properties has attracted increasing attentions. However, existing CHMMs usually only consider the time-series characteristic of data, while ignoring physical characteristics of user activity such as periodicity, timing and correlation. Moreover, they are all matrix-based models, which could not holistically analyze the dependencies among physical states. The above disadvantages lead to lower prediction accuracy of CHMM. To remove these disadvantages, three physics-informed tensor-based CHMMs are first constructed by incorporating prior physical knowledge. Then the corresponding forward-backward algorithms are designed for resolving the evaluation problem of CHMM. These algorithms could overall model multiple physical features by imposing physics and prior knowledge into CHMM during training to improve the precision of probabilistic computing. The algorithms reduce the dependence of the model on training data by adding physical features. Finally, the comparative experiments show that our algorithms have better performances than existing prediction methods in precision and efficiency. In addition, further selfcomparison experiments verify that our algorithms are effective and practical.