Robustness of declarative modeling languages: Improvements via probability-one homotopy

Robustness issues with steady-state initialization remain a barrier in the practical use of declarative modeling languages for multi-domain modeling of large, complex, and heterogeneous technical systems. The objective of this paper is to illustrate how probability-one homotopy, an established method from topology, can solve this issue. This is achieved by establishing a framework for application-specific probability-one homotopy in declarative modeling languages. The analysis is based on domain-specific probability-one homotopy maps, which were reformulated in a declarative fashion. Additionally, a novel probability-one homotopy map and associated coercivity proof is introduced for a class of thermo-fluid dynamics problems. It was found that the approach enables robust initialization for declarative modeling languages on several test cases and leads to a concise declarative problem formulation.