Enhancing Comparative Model Analysis using Persistent Homology

Mathematical models are widely used to replicate natural phenomena. They represent the growing universe, as well as the spreading of diseases. By concentrating on the essentials of these systems, mathematical models are perfectly suited to study system behavior under altered conditions. Defining a model for a given system is a challenging task and is commonly an advancing process, where current models are updated and competing ones designed. Quality quantification is hence a central task in model development. In this paper, we focus on the comparative analysis of competing models. We integrate state-of-the-art techniques and propose a novel topology-based measure to quantify model quality. Our novel measure particularly concentrates on structural stability in parameter space. Additionally, we design a model landscape that communicates similarities among model candidates. Both methods are demonstrated and evaluated using an example from drug development.