Connecting Different Approaches for Cell Cycle Modeling: Learning Ordinary Differential Equations from Individual-Based Models

We investigate the feasibility of deriving surrogate ordinary differential equations (ODEs) from individual-based models (IBMs) simulated in the PhysiCell platform. As a preliminary demonstration, we focus on data generated from simulations of several cell cycle models, each with varying complexities and corresponding ODE representations. Our approach begins with an evaluation of the stochastic characteristics, computational requirements, and accuracy of PhysiCell simulations. These simulations heavily depend on parameters such as the time step governing cell phase transitions, initial cell population, and the number of replicates. We then demonstrate the application of a sparse identification machine learning tool, SINDy-SA, to construct surrogate ODE-based models for IBMs. The SINDy-SA framework effectively identified the mathematical structures for all cell cycle models used in our study. Given the ability of surrogate models to reduce computational costs while maintaining accuracy, we believe that the insights from this study will aid researchers in modeling hybrid discrete-continuous multiscale systems using the PhysiCell platform and in developing corresponding surrogate models through the SINDy-SA framework.