Model-reduction techniques for {PDE} models with Turing type electrochemical phase formation dynamics

Next-generation battery research will heavily rely on physico-chemical models, combined with deep learning methods and high-throughput and quantitative analysis of experimental datasets, encoding spectral information in space and time. These tasks will require highly efficient computational approaches, to yield rapidly accurate approximations of the models. This paper explores the capabilities of a representative range of model reduction techniques to face this problem in the case of a well-assessed electrochemical phase-formation model. We consider the Proper Orthogonal Decomposition (POD) with a Galerkin projection and the Dynamic Mode Decomposition (DMD) techniques to deal first of all with a semi-linear heat equation 2D in space as a test problem. As an application, we show that it is possible to save computational time by applying POD-Galerkin for different choices of the parameters without recalculating the snapshot matrix. Finally, we consider two reaction–diffusion (RD) PDE systems with Turing-type dynamics: the well-known Schnackenberg model and the DIB model for electrochemical phase formation. We show that their reduced models obtained by POD and DMD with suitable low-dimensional projections are able to approximate carefully both the Turing patterns at the steady state and the reactivity dynamics in the transient regime. Finally, for the DIB model we show that POD-Galerkin applied for different choices of parameters, by calculating once the snapshot matrices, is able to find reduced Turing patterns of different morphology.