Data-driven Discovery of Biological Time-delay System by Parameterized Dictionary Learning

This work deals with the equation discovery problem of a biological bacterial zinc response system from real-world observed data. The system represents the gene expression procedure of bacterium Pseudomonas aeruginosa under zinc concentrations, which is important in bacterial zinc regularization. Governing equations of the system dynamics are not clear but supposed to perform time-delay effects. With published data, a parameterized dictionary learning method is employed to identify such system. The identification experiment is carried out and the result shows that the underlying delay differential equations are successfully discovered with biological consistency. The result is further compared with that produced with SINDy-delay method. The comparison shows that our model is more reasonable than the other from the perspective of mathematical modeling.