From Formal Models to Learned Dynamics: a Continuous Petri Net–Neural Network Framework for Liver Iron Metabolism

Complex biological systems require effective modelling of their structure, dynamics, and interactions. Graphical and formal modelling methods like Petri nets enable intuitive modelling and simulation of such systems. However, the majority of biological models usually exhibit unknown parameters that hinder their accurate analysis. Systems biology informed neural networks have been recently introduced to simulate such models by capturing their dynamics via the training of deep neural networks. In this paper, we propose an efficient and intelligent implementation of liver iron metabolism by integrating continuous Petri nets with systems biology informed neural networks. According to our framework, continuous Petri nets are used to graphically depict the model dynamics, while neural networks reproduce the actual simulation traces, without the solid requirements of all the kinetic parameters being completely known. Simulation results show that the underlying neural network successfully learned all kinetics parameters that were not explicitly provided. The resulting modelling framework provides a flexible, accurate and more robust approach f or simulating biological models where not all kinetic parameters are known.