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Dynamical models described by ordinary differential equations (ODEs) are afundamental tool in the sciences and engineering. Exact reduction aims atproducing a lower-dimensional model in which each macro-variable can bedirectly related to the original variables, and it is thus a natural steptowards the model's formal analysis and mechanistic understanding. We presentan algorithm which, given a polynomial ODE model, computes a longest possiblechain of exact linear reductions of the model such that each reduction refinesthe previous one, thus giving a user control of the level of detail preservedby the reduction. This significantly generalizes over the existing approacheswhich compute only the reduction of the lowest dimension subject to anapproach-specific constraint. The algorithm reduces finding exact linearreductions to a question about representations of finite-dimensional algebras.We provide an implementation of the algorithm, demonstrate its performance on aset of benchmarks, and illustrate the applicability via case studies. Ourimplementation is freely available athttps://github.com/x3042/ExactODEReduction.jl

Exact hierarchical reductions of dynamical models via linear transformations