Neuro-Symbolic Discovery of Markov Population Processes

Markov population processes (MPPs) are the natural modeling choice in various application do- mains where multiple interacting entities evolve stochastically over time, including biology, queue- ing 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 inter- actions 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.