  Electrochemical phenomena in ferroelectrics are of particular interest for
catalysis and sensing applications, with recent studies highlighting the
combined role of the ferroelectric polarisation, applied surface voltage and
overall switching history. Here, we present a systematic Kelvin probe
microscopy study of the effect of relative humidity and polarisation switching
history on the surface charge dissipation in ferroelectric
Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ thin films. We analyze the interaction of surface
charges with ferroelectric domains through the framework of physically
constrained unsupervised machine learning matrix factorization, Dictionary
Learning, and reveal a complex interplay of voltage-mediated physical processes
underlying the observed signal decays. Additional insight into the observed
behaviours is given by a Fitzhugh-Nagumo reaction-diffusion model, highlighting
the lateral spread and charge passivation process contributors within the
Dictionary Learning analysis.
