Abstraction of Markov Population Dynamics via Generative Adversarial Nets

TL;DR

This paper introduces a novel generative adversarial network-based approach to abstract Markov Population Models, enabling efficient simulation of complex stochastic dynamics in continuous space and time, with applications in systems biology.

Contribution

It presents a new method using advanced generative models to learn stochastic trajectories from Markov Population Models, improving over previous neural network-based approaches.

Findings

Successfully learned stochastic trajectories from original models

Reduced computational cost for simulating large or stiff systems

Demonstrated effectiveness in systems biology applications

Abstract

Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when a massive number of simulations has to be performed (e.g. in a multi-scale model). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous works and constructing a generator capable of producing stochastic trajectories in continuous space and discrete time. This generator is learned automatically from simulations of the original model in a Generative Adversarial setting. Compared to previous works, which rely on deep neural networks and Dirichlet processes, we explore the use of state of the art generative models, which are flexible enough to learn a full trajectory rather than a single transition kernel.