Property-driven State-Space Coarsening for Continuous Time Markov Chains
This addresses the challenge of analyzing complex dynamical systems for researchers in computational modeling, though it appears incremental as it builds on existing coarsening methods by focusing on property-driven aggregation.
The authors tackled the problem of coarsening large state-spaces in continuous-time Markov chains by proposing a method that optimally preserves logical specifications about system trajectories, using Gaussian Process emulation and Multi-Dimensional Scaling, and demonstrated promising performance and high computational efficiency on a non-trivial example.
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however, focus on a priori state aggregation based on similarities in transition rates, which is not necessarily reflected in similar behaviours at the level of trajectories. We propose a way to coarsen the state-space of a system which optimally preserves the satisfaction of a set of logical specifications about the system's trajectories. Our approach is based on Gaussian Process emulation and Multi-Dimensional Scaling, a dimensionality reduction technique which optimally preserves distances in non-Euclidean spaces. We show how to obtain low-dimensional visualisations of the system's state-space from the perspective of properties' satisfaction, and how to define macro-states which behave coherently with respect to the specifications. Our approach is illustrated on a non-trivial running example, showing promising performance and high computational efficiency.