  Ordinary differential equations (ODEs) are foundational in modeling intricate
dynamics across a gamut of scientific disciplines. Yet, a possibility to
represent a single phenomenon through multiple ODE models, driven by different
understandings of nuances in internal mechanisms or abstraction levels,
presents a model selection challenge. This study introduces a testing-based
approach for ODE model selection amidst statistical noise. Rooted in the model
misspecification framework, we adapt foundational insights from classical
statistical paradigms (Vuong and Hotelling) to the ODE context, allowing for
the comparison and ranking of diverse causal explanations without the
constraints of nested models. Our simulation studies validate the theoretical
robustness of our proposed test, revealing its consistent size and power.
Real-world data examples further underscore the algorithm's applicability in
practice. To foster accessibility and encourage real-world applications, we
provide a user-friendly Python implementation of our model selection algorithm,
bridging theoretical advancements with hands-on tools for the scientific
community.
