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.

翻译：常微分方程是众多科学领域中刻画复杂动力学过程的基础工具。然而，由于对内部机制细节或抽象层次的不同理解，同一现象可能对应多个常微分方程模型，这带来了模型选择的挑战。本研究针对统计噪声环境下的常微分方程模型选择问题，提出了一种基于统计检验的方法。基于模型误设定框架，我们将经典统计范式的核心洞见（Vuong检验和Hotelling检验）适配至常微分方程场景，从而能够在非嵌套模型约束下对不同因果解释进行比较和排序。仿真实验验证了所提检验方法的理论鲁棒性，揭示了其一致的大小和检验功效。真实数据案例进一步凸显了该算法在实际应用中的适用性。为促进可访问性并推动实际应用，我们提供了所选模型算法的用户友好型Python实现，为科学界搭建起理论进展与实践工具之间的桥梁。