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arxiv: 2605.16683 · v1 · pith:7XZUX3FWnew · submitted 2026-05-15 · 📡 eess.SY · cs.SY

Health-Aware Fast Charging Using Homogenized Model with Heterogeneous Internal State Reconstruction

Alessio Alberto Lodge , Alessio Lombardo Pontillo , Feye S.J. Hoekstra , Robinson Medina , Steven Wilkins , Ilenia Battiato This is my paper

Pith reviewed 2026-05-20 15:21 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords lithium-ion batteriesfast charginglithium platinghomogenized modelPID controlanode potentialmodel-based control
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The pith

A homogenized model reconstructs 3D anode potentials from a 1D formulation to let a PID controller prevent lithium plating during fast charging.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a plating-free fast charging method for lithium-ion batteries that relies on a Homogenized Model coupled to a classical PID controller. The model comes from homogenization theory applied to the Poisson-Nernst-Planck equations and keeps the essential physics of the Doyle-Fuller-Newman description inside a one-dimensional double-continua setup. Precomputed closure variables then reconstruct the full three-dimensional distributions of electrochemical variables, so the controller can monitor heterogeneous anode potentials as if it had a virtual sensor. MATLAB-COMSOL co-simulations show that this combination keeps every point of the 3D anode potential above the plating threshold while using far less computation than a high-fidelity model.

Core claim

The central claim is that the Homogenized Model, obtained by homogenization of the Poisson-Nernst-Planck equations and expressed as a one-dimensional double-continua formulation, reconstructs three-dimensional anode-potential distributions from precomputed closure variables; when this reconstruction is fed to a PID controller in co-simulation, the charging current can be regulated in real time so that the entire 3D anode-potential field remains above the lithium-plating limit.

What carries the argument

The Homogenized Model (HM) in a one-dimensional double-continua formulation that uses precomputed closure variables to reconstruct three-dimensional distributions of electrochemical variables such as anode potential.

If this is right

  • Model-based fast charging becomes practical at a small fraction of the computational cost of high-fidelity models.
  • Heterogeneous anode potentials can be estimated continuously without physical sensors inside the cell.
  • Charging protocols can be made explicitly degradation-aware by enforcing a spatially resolved plating constraint.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reconstruction technique could be applied to other local degradation modes such as solid-electrolyte interphase growth or mechanical stress.
  • Embedding the homogenized model in an onboard battery-management system would allow real-time health-aware charging for electric-vehicle packs.
  • Electrode designs that reduce microstructural heterogeneity might further widen the safe fast-charging window once the model is used for optimization.

Load-bearing premise

The homogenized model with its precomputed closure variables accurately reconstructs the heterogeneous three-dimensional anode potential distribution from the one-dimensional double-continua equations.

What would settle it

A side-by-side comparison in which the three-dimensional anode potentials reconstructed by the homogenized model during fast charging deviate by more than the safety margin from the potentials obtained in a full three-dimensional reference simulation would show that the virtual-sensor control cannot reliably prevent plating.

Figures

Figures reproduced from arXiv: 2605.16683 by Alessio Alberto Lodge, Alessio Lombardo Pontillo, Feye S.J. Hoekstra, Ilenia Battiato, Robinson Medina, Steven Wilkins.

Figure 1
Figure 1. Figure 1: DFN (top) and HM (bottom). Domains: pseudo-2D ℓℓ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Snapshot of the 3D reconstruction of c s and c ℓ distributions, from Equation (8), HM solutions and closure variables χ(x, y, z). For demonstration purposes and without loss of general￾ity, the battery parameters and microstructure are taken from the microscale model provided in Lombardo Pon￾tillo et al. (2025), in which the transport, kinetic and thermodynamic parameters are those of a lithium-ion cell (G… view at source ↗
Figure 2
Figure 2. Figure 2: Closure variables χ s (left, solid phase) and χ ℓ (right, liquid phase) from the solution of the BVP in Equations (7a, 7b). 3. 3D RECONSTRUCTION It can be shown (see Battiato et al. (2019)) that the internal states for the concentration and potential in the liquid and solid phases can be approximated as a truncated series in the form of Φ(x, y, z) = Φ0 + ε χ(x, y, z) ∇Φ0 + O(ε 2 ) (8) in which Φ is a recon… view at source ↗
Figure 4
Figure 4. Figure 4: HM-based fast charging with PID controller. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: CC-CV vs HM anode potential control. 0 200 400 600 800 1000 1200 Time (s) 200 400 Current (A) 0 200 400 600 800 1000 1200 Time (s) 0 100 200 Anode potential (mV) HM-3D anode potential control HM-average anode potential control Threshold (10mV) 0 10 20 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: HM-3D anode potential control vs HM-average [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Fast charging of lithium-ion batteries is limited by lithium plating, which occurs when the anode potential drops below 0 V vs Li/Li+. Model-based control aims to maximize charging current while maintaining anode potentials above this threshold. In this work, a plating-free fast charging strategy is demonstrated using a Homogenized Model (HM) coupled with a classical PID controller. The HM, derived from homogenization theory applied to the Poisson-Nernst-Planck equations, retains the physics of the Doyle-Fuller-Newman model while capturing electrode microstructural heterogeneity in a one-dimensional double-continua formulation. By reconstructing three-dimensional distributions of electrochemical variables from precomputed closure variables, the HM enables non-invasive estimation of heterogeneous anode potentials, acting as a virtual sensor. Through MATLAB-COMSOL co-simulation, a PID controller regulates current to maintain the full 3D anode potential distribution above the plating limit, achieving model-based fast charging at a fraction of the computational cost of high-fidelity models. The results demonstrate the potential of HM-based control for safe, degradation-aware, and efficient fast charging of lithium-ion batteries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a homogenized model (HM) derived from the Poisson-Nernst-Planck equations for lithium-ion battery electrodes, cast in a one-dimensional double-continua formulation that retains Doyle-Fuller-Newman physics while incorporating microstructural heterogeneity via precomputed closure variables. These variables enable reconstruction of full three-dimensional electrochemical fields, particularly the anode potential distribution, which is used as a virtual sensor input to a classical PID controller. In MATLAB-COMSOL co-simulation, the controller modulates charging current to keep the reconstructed 3D anode potential above the 0 V lithium-plating threshold, claiming safe fast charging at substantially lower computational cost than high-fidelity 3D models.

Significance. If the reconstruction fidelity is confirmed, the work would provide a practical route to real-time, physics-based, health-aware fast charging that accounts for local heterogeneity without requiring online solution of full-order 3D models. This could influence battery management system design in electric vehicles and grid storage by demonstrating how homogenization theory can be closed for control purposes.

major comments (2)
  1. [Abstract and HM derivation] Abstract and HM derivation paragraph: The central claim that the 1D HM with precomputed closure variables reconstructs the heterogeneous 3D anode potential distribution with sufficient fidelity for plating prevention is not supported by any reported quantitative validation. No L2 norms, maximum pointwise errors, or other error metrics are given comparing the reconstructed fields to a resolved 3D reference solution under the same fast-charge current profiles. Because the PID controller acts exclusively on the reconstructed map, the absence of these bounds leaves open the possibility that local excursions below 0 V remain undetected.
  2. [Co-simulation results] Co-simulation results section: The manuscript asserts that the PID controller maintains the full 3D anode potential distribution above the plating limit, yet no quantitative performance indicators—such as fraction of time the threshold is violated, achieved charging time reduction relative to constant-current baselines, or sensitivity of the result to reconstruction error—are provided. Without these, the practical advantage over existing model-based strategies cannot be assessed.
minor comments (2)
  1. [HM derivation] Notation for the closure variables and the mapping from 1D double-continua states to 3D fields should be introduced with a clear table or diagram early in the HM section to aid readability.
  2. [Abstract] The abstract states that the approach achieves fast charging 'at a fraction of the computational cost'; a specific speedup factor or wall-clock comparison with the full-order model would strengthen this claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript arXiv:2605.16683. The comments highlight important aspects regarding validation and quantitative assessment that we will address in the revision. Below we provide point-by-point responses to the major comments.

read point-by-point responses

  1. Referee: [Abstract and HM derivation] Abstract and HM derivation paragraph: The central claim that the 1D HM with precomputed closure variables reconstructs the heterogeneous 3D anode potential distribution with sufficient fidelity for plating prevention is not supported by any reported quantitative validation. No L2 norms, maximum pointwise errors, or other error metrics are given comparing the reconstructed fields to a resolved 3D reference solution under the same fast-charge current profiles. Because the PID controller acts exclusively on the reconstructed map, the absence of these bounds leaves open the possibility that local excursions below 0 V remain undetected.

    Authors: We agree with the referee that quantitative validation metrics are essential to support the central claim of reconstruction fidelity. The current manuscript presents the homogenized model and demonstrates its use in co-simulation but does not report explicit error metrics such as L2 norms or maximum pointwise errors against a full 3D reference. This omission weakens the validation of the virtual sensor approach. In the revised version, we will include a new figure and accompanying text in the HM derivation or results section that compares the reconstructed 3D anode potential to a resolved 3D COMSOL simulation under identical fast-charge conditions. We will report L2 norms, maximum deviations, and confirm that the error bounds ensure no undetected local plating events within the controller's operation. revision: yes

  2. Referee: [Co-simulation results] Co-simulation results section: The manuscript asserts that the PID controller maintains the full 3D anode potential distribution above the plating limit, yet no quantitative performance indicators—such as fraction of time the threshold is violated, achieved charging time reduction relative to constant-current baselines, or sensitivity of the result to reconstruction error—are provided. Without these, the practical advantage over existing model-based strategies cannot be assessed.

    Authors: We acknowledge that the co-simulation results section would benefit from additional quantitative indicators to better evaluate the controller's performance and the method's advantages. While the manuscript shows through simulation that the potential is maintained above the limit, specific metrics like violation fractions, charging time savings, and error sensitivity are not quantified. We will revise this section to incorporate these metrics, including a comparison of charging times to constant-current protocols, the time fraction where the minimum anode potential stays above 0 V, and an analysis of how reconstruction errors affect the controller output. This will provide a clearer assessment of the practical benefits. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation from standard homogenization theory remains independent

full rationale

The paper derives the homogenized model directly from homogenization theory applied to the Poisson-Nernst-Planck equations, retaining Doyle-Fuller-Newman physics in a 1D double-continua formulation with precomputed closure variables for 3D reconstruction. These closure variables are computed offline from the underlying microstructure and are external to the online PID control loop. No step reduces a claimed prediction or reconstruction result to a fitted parameter or self-citation by construction; the central claim of plating-free fast charging via virtual sensing rests on the independent physics-based reconstruction rather than tautological redefinition of inputs. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the accuracy of homogenization applied to electrochemical transport and on the fidelity of precomputed closure variables for state reconstruction; no new particles or forces are introduced.

axioms (1)
  • domain assumption Homogenization theory applied to the Poisson-Nernst-Planck equations retains the essential physics of the Doyle-Fuller-Newman model while capturing microstructural heterogeneity in a 1D double-continua formulation.
    Invoked in the derivation of the HM (abstract description of model origin).

pith-pipeline@v0.9.0 · 5746 in / 1310 out tokens · 44563 ms · 2026-05-20T15:21:51.959807+00:00 · methodology

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Reference graph

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