Abstract
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 ultradian endocrine model for glucose-insulin interaction as the example to demonstrate all these methods and their implementation.
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Appendix
Appendix
1.1 A. Python
Python is the most common language for machine learning due to the plethora of libraries available for free. Learning python is fairly easy due to its popularity, and there are a number of free, high-quality videos and other tutorials on how to use python. We note that common software for installing Python is Anaconda, from which most common libraries have already been installed. The code we provide should remove the majority of the guesswork if solving similar problems to those stated in this tutorial; otherwise, the DeepXDE documentation https://deepxde.readthedocs.io should be of help.
1.2 B. Julia
Julia is another language used for machine learning. It is very similar to Python as far as the syntax is concerned. We recommend using the softwares Atom and the Juno IDE, though Jupiter notebook and similar programs will suffice. There are also a variety of online sources that provide free help for learning this language. If you understand the fundamentals of Python, you should be able to read our provided Julia code and use it for your own situation with only a few minor tweaks that do not involve a heavy amount of coding or even a thorough knowledge of Julia.
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Daneker, M., Zhang, Z., Karniadakis, G.E., Lu, L. (2023). Systems Biology: Identifiability Analysis and Parameter Identification via Systems-Biology-Informed Neural Networks. In: Nguyen, L.K. (eds) Computational Modeling of Signaling Networks. Methods in Molecular Biology, vol 2634. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-3008-2_4
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DOI: https://doi.org/10.1007/978-1-0716-3008-2_4
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Publisher Name: Humana, New York, NY
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