AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box
  Identification
Nazanin Ahmadi Daryakenari Mario De Florio Khemraj Shukla George Em Karniadakis
Discovering mathematical equations that govern physical and biological
systems from observed data is a fundamental challenge in scientific research.
We present a new physics-informed framework for parameter estimation and
missing physics identification (gray-box) in the field of Systems Biology. The
proposed framework -- named AI-Aristotle -- combines eXtreme Theory of
Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural
Networks (PINNs) with symbolic regression (SR) techniques for parameter
discovery and gray-box identification. We test the accuracy, speed, flexibility
and robustness of AI-Aristotle based on two benchmark problems in Systems
Biology: a pharmacokinetics drug absorption model, and an ultradian endocrine
model for glucose-insulin interactions. We compare the two machine learning
methods (X-TFC and PINNs), and moreover, we employ two different symbolic
regression techniques to cross-verify our results. While the current work
focuses on the performance of AI-Aristotle based on synthetic data, it can
equally handle noisy experimental data and can even be used for black-box
identification in just a few minutes on a laptop. More broadly, our work
provides insights into the accuracy, cost, scalability, and robustness of
integrating neural networks with symbolic regressors, offering a comprehensive
guide for researchers tackling gray-box identification challenges in complex
dynamical systems in biomedicine and beyond.