Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to the original variables, and it is thus a natural step towards the model's formal analysis and mechanistic understanding. We present an algorithm which, given a polynomial ODE model, computes a longest possible chain of exact linear reductions of the model such that each reduction refines the previous one, thus giving a user control of the level of detail preserved by the reduction. This significantly generalizes over the existing approaches which compute only the reduction of the lowest dimension subject to an approach-specific constraint. The algorithm reduces finding exact linear reductions to a question about representations of finite-dimensional algebras. We provide an implementation of the algorithm, demonstrate its performance on a set of benchmarks, and illustrate the applicability via case studies. Our implementation is freely available at https://github.com/x3042/ExactODEReduction.jl

翻译：由常微分方程描述的动力学模型是科学和工程领域的基础工具。精确约简旨在生成一个低维模型，其中每个宏观变量都能直接与原变量相关联，因此它是对模型进行形式化分析和机理理解的必经步骤。我们提出了一种算法：给定一个多项式常微分方程模型，该算法能够计算该模型在精确线性约简下的最长可行链，使得每个后续约简均对前一结果进行精化，从而让用户能够控制约简所保留的细节程度。这显著推广了现有方法——后者仅在特定方法约束下计算最低维度的约简。该算法将精确线性约简问题转化为有限维代数表示的相关问题。我们提供了算法的实现代码，通过一组基准测试展示了其性能，并借助案例研究说明了其适用性。实现代码已开源发布于 https://github.com/x3042/ExactODEReduction.jl