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（ODEs）描述的动力模型是科学与工程领域的基本工具。精确约简旨在生成为一个低维模型，其中每个宏观变量可直接与原始变量相关联，因此这是迈向模型形式化分析与机理理解的必然步骤。我们提出了一种算法，对于给定的多项式ODE模型，能够计算该模型最长可能的精确线性约简链条，使得每次约简均是对前一次的细化，从而使用户能够控制约简所保留的细节层级。这显著推广了现有仅计算受限于特定方法约束的最低维度约简的方法。该算法将精确线性约简问题转化为有限维代数表示论问题。我们提供了该算法的实现，通过一组基准测试展示了其性能，并通过案例研究说明了其适用性。我们的实现已在 https://github.com/x3042/ExactODEReduction.jl 开源发布。