AI-Aristotle: A physics-informed framework for systems biology gray-box identification

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 the 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. To test the performance of AI-Aristotle, we use sparse synthetic data perturbed by uniformly distributed noise. 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.Author summary: Our study addresses the fundamental challenge of uncovering mathematical rules governing physical and biological systems from real-world data. We introduce a novel framework, AI-Aristotle, designed for parameter estimation and identifying hidden physics (gray-box) in Systems Biology. AI-Aristotle combines the powerful eXtreme Theory of Functional Connections (X-TFC), Physics-Informed Neural Networks (PINNs), and symbolic regression (SR) techniques to discover parameters and uncover hidden relationships. Our work offers guidance to researchers addressing gray-box identification challenges in complex dynamic systems, including applications in biomedicine and beyond.