In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This criterion is better able to encompass changes in the quality of the parameter estimate due to increased noise in the data (compared to existing criteria based solely on average relative errors). Furthermore, we leverage a weak-form equation error-based method of parameter estimation for systems with unobserved variables to assess practical identifiability far more quickly in comparison to output error-based parameter estimation. We do so by generating weak-form input-output equations using differential algebra techniques, as previously proposed by Boulier et al [1], and then applying Weak form Estimation of Nonlinear Dynamics (WENDy) to obtain parameter estimates. This method is computationally efficient and robust to noise, as demonstrated through two classical biological modelling examples.

翻译：本文定义了一种实用可辨识性准则——(e, q)-可辨识性，该准则基于反映观测变量噪声的参数e和反映参数估计器均方误差的参数q。相较于仅基于平均相对误差的现有准则，该准则能更好地涵盖数据噪声增加导致的参数估计质量变化。此外，我们利用基于弱形式方程误差的参数估计方法（适用于含未观测变量的系统），与基于输出误差的参数估计方法相比，能更快速地评估实用可辨识性。具体而言，我们采用Boulier等人[1]提出的微分代数技术生成弱形式输入-输出方程，随后应用非线性动力学弱形式估计方法（WENDy）获取参数估计值。如两个经典生物建模案例所示，该方法具有计算高效性和噪声鲁棒性。