有理动力系统的精确线性约化
Exact linear reduction for rational dynamical systems
摘要：
在生命科学中使用的详细动态系统模型可能包括几十个甚至几百个状态变量。大维度的模型不仅从数值角度看更难（例如，用于参数估计或模拟），但是从这样的模型中获得机理见解也变得具有挑战性。精确模型降阶是通过找到相应动力系统的自洽低维投影来解决这个问题的一种方法。最近的一个算法CLUE允许一个构建一个精确的线性减少的最小可能的尺寸，这样的固定变量的兴趣被保留。然而，CLUE仅限于多项式动态系统。由于理性动力学经常出现在生命科学中（例如，Michaelis-Menten或Hill动力学），希望将CLUE扩展到具有理性动力学的模型。在本文中，我们提出了一个扩展的CLUE的情况下，合理的动力学，并证明其适用性的例子从文献中。我们的实现可以在https://github.com/pogudingleb/CLUE上的CLUE 1.5版本中找到。
英文摘要：
Detailed dynamical systems models used in life sciences may include dozens or even hundreds of state variables. Models of large dimension are not only harder from the numerical perspective (e.g., for parameter estimation or simulation), but it is also becoming challenging to derive mechanistic insights from such models. Exact model reduction is a way to address this issue by finding a self-consistent lower-dimensional projection of the corresponding dynamical system. A recent algorithm CLUE allows one to construct an exact linear reduction of the smallest possible dimension such that the fixed variables of interest are preserved. However, CLUE is restricted to systems with polynomial dynamics. Since rational dynamics occurs frequently in the life sciences (e.g., Michaelis-Menten or Hill kinetics), it is desirable to extend CLUE to the models with rational dynamics. In this paper, we present an extension of CLUE to the case of rational dynamics and demonstrate its applicability on examples from literature. Our implementation is available in version 1.5 of CLUE at https://github.com/pogudingleb/CLUE.
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。
