Using Physics-Informed Neural Networks for Modeling Biological and Epidemiological Dynamical Systems

Amer Farea, Olli Yli-Harja and Frank Emmert-Streib ()
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Amer Farea: Predictive Society and Data Analytics Laboratory, Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland
Olli Yli-Harja: Predictive Society and Data Analytics Laboratory, Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland
Frank Emmert-Streib: Predictive Society and Data Analytics Laboratory, Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland

Mathematics, 2025, vol. 13, issue 10, 1-23

Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a powerful approach for integrating physical laws into a deep learning framework, offering enhanced capabilities for solving complex problems. Despite their potential, the practical implementation of PINNs presents significant challenges. This paper explores the application of PINNs to systems of ordinary differential equations (ODEs), focusing on two key challenges: the forward problem of solution approximation and the inverse problem of parameter estimation. We present three detailed case studies involving dynamical systems for tumor growth, gene expression, and the SIR (Susceptible, Infected, Recovered) model for disease spread. This paper outlines the core principles of PINNs and their integration with physical laws during neural network training. It details the steps involved in implementing PINNs, emphasizing the critical role of network architecture and hyperparameter tuning in achieving optimal performance. Additionally, we provide a Python package, ODE-PINN, to reproduce results for ODE-based systems. Our findings demonstrate that PINNs can yield accurate and consistent solutions, but their performance is highly sensitive to network architecture and hyperparameters tuning. These results underscore the need for customized configurations and robust optimization strategies. Overall, this study confirms the significant potential of PINNs to advance the understanding of dynamical systems in biology and epidemiology.

Keywords: Physics-Informed Neural Networks (PINNs); ordinary differential equation; deep learning; tumors growth model; gene expression model; epidemiological model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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