Battery degradation models demand 3.1 decades of data to resolve distributed-order memory kernels

The arXiv preprint by Tetsassi Feugmo et al. (2026) tested memory-kernel identifiability using two mechanistic non-fractional models plus de Levie’s porous-electrode benchmark whose high-frequency order is exactly 0.5. Their weak-formulation estimator recovered the known order to within 5% noise from a single aging curve, yet separating tempered parameters (α, λ) needed multiple Arrhenius conditions; errors fell from (0.25, 0.43) with one temperature to (0.04, 0.07) with four.

A distributed-order kernel collapses into a single effective order when observation windows are shorter than 3.1 decades, producing better in-sample fits than the true spectrum. For saturating passivation films, however, the general kernel lifted R² from 0.862 to 0.998. Across twenty cells from two public repositories, no dataset met the 3.1-decade threshold, revealing a systematic mismatch between experimental practice and model requirements.

This measurement rule directly constrains next-generation battery and corrosion testing protocols. Labs designing accelerated aging campaigns must now allocate calendar time or temperature schedules to reach the required span, or accept that only effective single-order approximations are recoverable.

Future work should embed the 3.1-decade criterion into open battery-data standards and test whether hybrid physics-ML kernels can relax the data demand without sacrificing physical interpretability.