Abstract

Model reduction methods allow to significantly decrease the time required to solve a large ODE system in some cases by performing all calculations in a vector space of significantly lower dimension than the original one. These methods frequently require apriori information about the structure of the solution, possibly obtained by solving the same system for different values of parameters. We suggest a simple algorithm for constructing such a subspace while simultaneously solving the system, thus allowing one to benefit from model reduction even for a single system without significant apriori information, and demonstrate its effectiveness using the Smoluchowski equation as an example.

中文翻译：

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非平稳问题中减少基发现的方法

摘要

模型缩减方法允许在某些情况下通过在比原始维度低得多的向量空间中执行所有计算来显着减少求解大型 ODE 系统所需的时间。这些方法经常需要关于解结构的先验信息，这可能是通过针对不同的参数值求解同一系统而获得的。我们提出了一种在同时求解系统的同时构建这样一个子空间的简单算法，因此即使对于没有重要先验信息的单个系统，也可以从模型简化中受益，并以 Smoluchowski 方程为例证明其有效性。