  The dynamics of systems biological processes are usually modeled by a system
of ordinary differential equations (ODEs) with many unknown parameters that
need to be inferred from noisy and sparse measurements. Here, we introduce
systems-biology informed neural networks for parameter estimation by
incorporating the system of ODEs into the neural networks. To complete the
workflow of system identification, we also describe structural and practical
identifiability analysis to analyze the identifiability of parameters. We use
the ultridian endocrine model for glucose-insulin interaction as the example to
demonstrate all these methods and their implementation.
