Model discovery of compartmental models with Graph-Supported Neural Networks

Abstract

In this proposal, our objective is to create a neural network for the discovery of models using compartmental models as systems of Ordinary Differential Equations (ODEs), employing Graph-Supported Neural Networks (GSNN). We design the GSNN as a graph of transition functions of the structure of the model to ensure that the three properties of the ODE solution are satisfied: additivity to one, positivity, and boundness. Rather than directly estimating the solution, these neural networks approximate the transition functions. We present theoretical evidence substantiating that our GSNN maintains these properties, along with approximation outcomes from both simulated and real-world data. These outcomes demonstrate that our GSNN outperforms the non-graph-supported approach for these issues, with instances where it even surpasses full model-based solutions and Recurrent Neural Networks. Furthermore, an evolutionary algorithm successfully generated a consistent model using the data, offering a comprehensive framework for neural network-based model discovery in these scenarios.