微分模型的全局可辨识性
Global Identifiability of Differential Models
AI总结：
本文针对带参数的常微分方程组，提出了判定参数全局可辨识性的理论、算法与软件，通过严格推导代数判据产生确定性算法，并进一步随机化以提升效率，解决了以往无法处理的问题。
摘要：
许多现实世界的过程和现象使用带参数的常微分方程组进行建模。给定这样的系统，如果一个参数能够从输入和输出数据中唯一恢复，我们就称该参数是全局可辨识的。本文的主要贡献是提供了用于判定全局可辨识性的理论、算法和软件。首先，我们严格推导了全局可辨识性（这是一个解析性质）的代数判据，从而产生了一种确定性算法。其次，我们通过将算法随机化来提高效率，同时保证正确率的概率。利用我们的新算法，我们能够处理以前无法处理的问题。基于该算法的软件（称为SIAN）可在 https://github.com/pogudingleb/SIAN 获取。
英文摘要：
Many real-world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and output data. The main contribution of this paper is to provide theory, an algorithm, and software for deciding global identifiability. First, we rigorously derive an algebraic criterion for global identifiability (this is an analytic property), which yields a deterministic algorithm. Second, we improve the efficiency by randomizing the algorithm while guaranteeing the probability of correctness. With our new algorithm, we can tackle problems that could not be tackled before. A software based on the algorithm (called SIAN) is available at https://github.com/pogudingleb/SIAN.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
