  This study proposes a novel approach to quantifying uncertainties of
constitutive relations inferred from noisy experimental data using inverse
modelling. We focus on electrochemical systems in which charged species (e.g.,
Lithium ions) are transported in electrolyte solutions under an applied
current. Such systems are typically described by the Planck-Nernst equation in
which the unknown material properties are the diffusion coefficient and the
transference number assumed constant or concentration-dependent. These material
properties can be optimally reconstructed from time- and space-resolved
concentration profiles measured during experiments using the Magnetic Resonance
Imaging (MRI) technique. However, since the measurement data is usually noisy,
it is important to quantify how the presence of noise affects the uncertainty
of the reconstructed material properties. We address this problem by developing
a state-of-the-art Bayesian approach to uncertainty quantification in which the
reconstructed material properties are recast in terms of probability
distributions, allowing us to rigorously determine suitable confidence
intervals. The proposed approach is first thoroughly validated using
"manufactured" data exhibiting the expected behavior as the magnitude of noise
is varied. Then, this approach is applied to quantify the uncertainty of the
diffusion coefficient and the transference number reconstructed from
experimental data revealing interesting insights.
