论文标题
理性动力学系统的确切线性还原
Exact linear reduction for rational dynamical systems
论文作者
论文摘要
生命科学中使用的详细动力系统模型可能包括数十个甚至数百个状态变量。从数值角度来看（例如，对于参数估计或模拟），大尺寸的模型不仅更加困难，而且从此类模型中获得机械见解也变得越来越具有挑战性。确切的模型还原是通过找到相应动力学系统的自洽的下维投影来解决此问题的一种方法。最近的算法线索允许人们构建最小可能的尺寸的精确线性还原，以便保留感兴趣的固定变量。但是，线索仅限于具有多项式动力学的系统。由于理性动力学经常发生在生命科学（例如Michaelis-Menten或Hill动力学）中，因此希望将线索扩展到具有理性动力学的模型。在本文中，我们将线索扩展到理性动力学的情况下，并在文献中证明了其适用性。我们的实现可在线索的1.5版中获得，网址为https://github.com/pogudingleb/clue。
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.
