We propose a simulation-based technique for the parameterization and the stability analysis of parametric Ordinary Differential Equations. This technique is an adaptation of Statistical Model Checking, often used to verify the validity of biological models, to the setting of Ordinary Differential Equations systems. The aim of our technique is to estimate the probability of satisfying a given property under the variability of the parameter or initial condition of the ODE, with any metrics of choice. To do so, we discretize the values space and use statistical model checking to evaluate each individual value w.r.t. provided data. Contrary to other existing methods, we provide statistical guarantees regarding our results that take into account the unavoidable approximation errors introduced through the numerical integration of the ODE system performed while simulating. In order to show the potential of our technique, we present its application to two case studies taken from the literature, one relative to the growth of a jellyfish population, and the other concerning a well-known oscillator model.

我们提出了一种基于模拟的技术，用于参数化常微分方程的参数化和稳定性分析。该技术是统计模型检查（通常用于验证生物模型的有效性）对常微分方程系统设置的改编。我们技术的目的是估计在参数变化或 ODE 初始条件下（使用任何选择的度量）满足给定属性的概率。为此，我们将值空间离散化，并使用统计模型检查来评估所提供数据的每个单独值。与其他现有方法相反，我们为我们的结果提供统计保证，其中考虑了通过模拟时执行的 ODE 系统数值积分引入的不可避免的近似误差。为了展示我们技术的潜力，我们将其应用到文献中的两个案例研究中，一个与水母种群的增长有关，另一个与众所周知的振荡器模型有关。