Abstraction-Guided Truncations for Stationary Distributions of Markov Population Models

TL;DR

This paper introduces an innovative truncation-based method that uses state-space lumping to efficiently approximate stationary distributions of Markov population models, especially for complex non-linear systems.

Contribution

It presents a novel iterative approach that refines finite-state projections using state-space lumping, improving approximation accuracy for stationary distributions.

Findings

Effective for complex non-linear models

Provides well-justified finite-state projections

Demonstrates broad applicability

Abstract

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection tailored to the stationary behavior. We demonstrate the method's applicability to a wide range of non-linear problems with complex stationary behaviors.