Neuro-Symbolic Discovery of Markov Population Processes

Markov population processes (MPPs) are the natural modeling choice in various application domains where multiple interacting entities evolve stochastically over time, including biology, queueing theory, finance, and robotics. Motivated by real-world scenarios where time-series data for MPP models is increasingly available, we here employ a neuro-symbolic approach for discovering explanations of such data in terms of local, agent-to-agent interactions. Concretely, we assume that equidistant time-series measurements of a Markov population chain are given. Then, we propose how to automatically learn the explanatory models written in form of Chemical Reaction Networks (CRNs). Our approach is to use a symbolic representation of a CRN in form of a weighted bipartite graph, and to employ a graph-based Variational Autoencoder (VAE) to jointly infer both the interactions and the accompanying kinetic parameters. We demonstrate our proposed framework over three simple case studies. Our contribution represents a proof-of-concept that interpretable models of complex dynamical systems can be discovered in a fully automated and data-driven fashion, and it is applicable both in scenarios where data is available via experiments, or when it is generated by a black-box simulator.