Exact model reduction by Lie symmetry groups

We develop a model-reduction technique based on Lie group theory for general engineering models described by a system of algebraic, ordinary, and/or partial differential equations with an arbitrary number of inputs, outputs, and constant parameters. The proposed method reduces the parameter space of these models without changing their external behavior, that is, their input-output maps. We apply this method to phase-field models used for high-fidelity simulations in electrochemistry to accelerate the analysis and design of metal-ion batteries.