High-dimensional model representation of cyclic voltammograms

Digital simulation costs present an obstacle on the way to high-speed, real-time, on-line theoretical analysis of experimental data in cyclic voltammetry. To overcome this difficulty, we propose to use solution mapping based on a correlated, hierarchical expansion of multivariate functions, known as high-dimensional model representation (HDMR). The nonlinear dependencies of the simulated voltammograms on multiple model parameters are represented in the form of compact look-up tables, from which approximate voltammograms can be calculated rapidly by interpolation, for any model parameter combinations from a predefined domain. Most importantly, the HDMR does not suffer from the problem of the exponential growth of the look-up tables with the number of model parameters. The creation of a solution map requires a single effort of simulating many voltammograms. However, once the map is prepared, it can be stored and reused many times without the need to repeat costly simulations. HDMR maps are created and examined for five examples of cyclic voltammetry models at planar macroelectrodes in a one-dimensional spatial geometry under pure diffusion transport conditions. The usefulness of the maps for rapid visualization and exploration of the effects of the parameters on the voltammograms and for rapid simultaneous estimation of many parameters from cyclic voltammetric data is demonstrated through computational experiments.