Cell migration is a necessary function in organisms. It is relevant to wound healing, immune reaction, cancer expansion. One example is durotaxis: Cells exhibit qualitatively different behaviors on substrates with different rigidities. The fact that cells are more polarized on the stiffer substrate motivates us to construct a two-dimensional cell with the distribution of focal adhesions dependent on substrate rigidities. This distribution affects the forces exerted by the cell and thereby determines its motion. Our model reproduces the experimental observation that the persistence time is higher on the stiffer substrate. This stiffness-dependent persistence will lead to durotaxis, the preference in moving towards stiffer substrates. We derive and validate a two-dimensional corresponding Fokker-Planck equation associated with our model. Another example is the chemotaxis: Leukotriene B4 is secreted as exosomes by neutrophils, serving as a secondary gradient to amplify the chemical attraction of primary chemoattractants. We introduce a model to compare the enhancement effect between directly releasing Leukotriene B4 and generating as exosomes. We attribute this advantage to the longer lifetime of exosomes which leads to a larger range of attraction. The third example is in the immune system: The infiltrations of T are different in patients, which could be a tool for the prognosis. High CD8+ T cell counts (both overall and inside cancer-cell islands) is associated with better patient outcome. However, a cut-off of the T-cell count has to be selected manually to separate groups of patients. In this work, we propose a method to classify the small patch of triple-negative breast cancer (TNBC) tumor and use the overall percentage of good patches as a marker to predict the prognosis, which is an automatic method of prognosis and could also be used for other cancers. The result shows that the machine learns the importance of cell count and cell infiltration and use the combination as an indicator for prognosis. We also applied the machine learning method on sperm classification and quantum many body problem. In sperm classification, we could get around 70% accuracy with balanced good and poor example. In quantum many body problem, we proposed a deep neural network to calculate the ground-state energies and it shows excellent agreement with the Bethe-Ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained.