Evaluating the Exp-Minus-Log Sheffer Operator for Battery Characterization

TL;DR

This paper evaluates the Exp-Minus-Log operator's effectiveness in battery modeling, finding it offers a complete, differentiable basis that can improve parameter estimation despite slower simulation.

Contribution

It introduces an analytical reformulation of the EML operator for battery circuit models and assesses its computational and modeling advantages.

Findings

EML-based parametrization is structurally complete and gradient-differentiable.

Direct EML simulation is approximately 25 times slower than classical methods.

Using EML for parametrization improves model structure without increasing runtime complexity.

Abstract

Odrzywolek (2026) recently introduced the Exp-Minus-Log (EML) operator eml (x, y) = exp(x) - ln(y) and proved constructively that, paired with the constant 1, it generates the entire scientific-calculator basis of elementary functions; in this sense EML is to continuous mathematics what NAND is to Boolean logic. We investigate whether such a uniform single-operator representation can accelerate either the forward simulation or the parameter identification of a six-branch RC equivalent-circuit model (6rc ECM) of a lithium-ion battery cell. We give the analytical EML rewrite of the discretized state-space recursion, derive an exact operation count, and quantify the depth penalty of the master-formula construction used for gradient-based symbolic regression. Our analysis shows that direct EML simulation is slower than the classical exponential-Euler scheme (a ~ 25x instruction overhead per RC branch), but EML-based parametrization offers a structurally complete, gradient-differentiable basis that competes favourably with non-parametric DRT deconvolution and metaheuristic optimisation when the cardinality of RC branches is unknown a priori. We conclude with a concrete recommendation: use EML only on the parametrization side of the 6rc workflow, keeping the classical recursion at runtime.