arxiv: 2604.10362 · v2 · submitted 2026-04-11 · 💻 cs.LG

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Battery health prognosis using Physics-informed neural network with Quantum Feature mapping

Anurag K. Srivastava, Md Fazley Rafy, Muhammad Imran Hossain, Sarika Khushalani Solanki

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:27 UTC · model grok-4.3

classification 💻 cs.LG

keywords battery state of healthphysics-informed neural networkquantum feature mappingSOH estimationdegradation modelingcross-chemistry transfer

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The pith

Physics-informed neural networks with quantum feature mapping estimate battery state of health at 99.46 percent average accuracy.

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

This paper proposes a method that projects raw battery sensor readings into a high-dimensional space using quantum feature mapping and then feeds those features into a neural network constrained by physical laws. The goal is to overcome the poor generalizability of ordinary neural networks when estimating state of health across different battery chemistries and operating conditions. The authors report that the resulting model reaches 99.46 percent average accuracy on a collection of 310705 samples drawn from 387 cells, reduces key error measures by more than 60 percent relative to existing techniques, and can move predictions from one chemistry to another without any labeled data from the target chemistry. A reader would care because reliable health estimates without repeated calibration would let energy-storage systems operate more safely and with less downtime across varied battery designs.

Core claim

The QPINN projects raw battery sensor data into a high-dimensional Hilbert space via the Nyström method to obtain expressive features that capture subtle non-linear degradation patterns; these features are then passed through a physics-informed network that enforces physical constraints, yielding an average SOH estimation accuracy of 99.46 percent on a large multi-chemistry dataset of 310705 samples from 387 cells while enabling label-free transfer between chemistries.

What carries the argument

Quantum feature mapping with the Nyström method that embeds sensor data into a high-dimensional Hilbert space, followed by a physics-informed neural network that applies physical constraints to the resulting features.

If this is right

Error metrics such as MAPE and RMSE drop by as much as 65 percent and 62 percent compared with state-of-the-art baselines.
The same trained model can be used on cells of a different chemistry without requiring any SOH labels from the new chemistry.
Performance holds across a dataset spanning 387 cells and multiple chemistries under varied operating conditions.
The approach directly addresses the limited generalizability that currently restricts battery health models in multi-scale energy storage.

Where Pith is reading between the lines

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

If the mapped features truly encode degradation physics, the same architecture might be adapted to forecast remaining useful life or capacity fade without additional labels.
The method could be examined on other sensor-driven systems where physical constraints and cross-domain transfer are both required, such as certain structural health monitoring tasks.
Varying the dimension of the Hilbert space produced by the Nyström approximation offers a concrete way to test how much additional expressive power is needed for more complex degradation regimes.

Load-bearing premise

The quantum feature mapping produces representations that genuinely reflect the underlying non-linear degradation physics and allow the network to impose constraints that remain valid when moving between battery chemistries.

What would settle it

A controlled test in which the model is applied to a new battery chemistry whose degradation physics differ markedly from the training set and the resulting accuracy falls below that of ordinary neural networks or physics-free baselines.

Figures

Figures reproduced from arXiv: 2604.10362 by Anurag K. Srivastava, Md Fazley Rafy, Muhammad Imran Hossain, Sarika Khushalani Solanki.

**Figure 2.** Figure 2: Degradation patterns in the TJU [16] battery dataset, comprising four [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Normalized Voltage Aging Profiles of Three Commercial 18650 Cells [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

Accurate battery health prognosis using State of Health (SOH) estimation is essential for the reliability of multi-scale battery energy storage, yet existing methods are limited in generalizability across diverse battery chemistries and operating conditions. The inability of standard neural networks to capture the complex, high-dimensional physics of battery degradation is a major contributor to these limitations. To address this, a physics-informed neural network with the Quantum Feature Mapping(QFM) technique (QPINN) is proposed. QPINN projects raw battery sensor data into a high-dimensional Hilbert space, creating a highly expressive feature set that effectively captures subtle, non-linear degradation patterns using Nystr\"om method. These quantum-enhanced features are then processed by a physics-informed network that enforces physical constraints. The proposed method achieves an average SOH estimation accuracy of 99.46\% across different datasets, substantially outperforming state-of-the-art baselines, with reductions in MAPE and RMSE of up to 65\% and 62\%, respectively. This method was validated on a large-scale, multi-chemistry dataset of 310,705 samples from 387 cells, and further showed notable adaptability in cross-validation settings, successfully transferring from one chemistry to another without relying on target-domain SOH labels.

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.

Desk Editor's Note private letter to a colleague

The paper combines Nyström quantum feature mapping with a PINN for battery SOH estimation and reports strong cross-chemistry transfer, but the abstract supplies almost no equations or implementation details to support those claims.

read the letter

The core idea is to map battery sensor data into a high-dimensional space via the Nyström approximation of a quantum kernel, then feed those features into a physics-informed network that adds constraint terms to the loss. They test this on a sizable collection of 310k samples from 387 cells spanning multiple chemistries and report 99.46% average accuracy plus big drops in MAPE and RMSE relative to baselines, plus the ability to transfer without target labels. That last part is the most interesting angle for practical use in mixed fleets of batteries. The dataset size and the multi-chemistry scope are clear strengths; most prior SOH work stays within one chemistry or uses smaller sets. The combination itself is presented as new, even if both quantum kernels and PINNs have separate histories. The performance numbers are eye-catching if they hold up. The main weakness is that the abstract gives no equations for the physics loss, no description of which constraints are enforced, no information on training splits or hyperparameter choices, and no concrete baseline methods. Battery degradation physics are not universal across chemistries, so any claim of label-free transfer needs to show that the loss terms are either general enough or that the quantum features somehow isolate the common parts. Without those details it is difficult to tell whether the reported gains come from the method or from other factors. The work is aimed at engineers and applied researchers who need better SOH estimators for real systems rather than theorists looking for new fundamental results. It is worth sending to referees so they can examine the actual loss formulation, the cross-validation protocol, and whether the transfer results survive closer scrutiny on the held-out chemistries.

Referee Report

4 major / 2 minor

Summary. The manuscript proposes a physics-informed neural network augmented with quantum feature mapping (QPINN) via the Nyström method. Raw battery sensor data are projected into a high-dimensional Hilbert space to capture non-linear degradation patterns; these features are then fed to a PINN that enforces physical constraints. The central claims are an average SOH estimation accuracy of 99.46% on a 310,705-sample, 387-cell multi-chemistry dataset, up to 65% MAPE and 62% RMSE reductions versus baselines, and successful label-free cross-chemistry transfer.

Significance. If the performance and transfer results are reproducible and the physics constraints are shown to be chemistry-agnostic, the work would offer a practical route to generalizable SOH models for heterogeneous battery fleets where target-domain labels are unavailable, addressing a key barrier in large-scale energy storage deployment.

major comments (4)

[Methods] Methods section: no explicit equations are given for the physics-informed loss terms or the precise physical constraints (e.g., capacity fade laws, SEI growth, or voltage limits) that are enforced. Without these, it is impossible to evaluate whether the constraints are sufficiently general to support the label-free cross-chemistry transfer claim or whether they implicitly encode chemistry-specific priors.
[Results] Results, cross-validation experiments: the headline 99.46% accuracy and transfer success are reported without error bars, number of independent runs, or details of the train/validation/test splits (especially the source-target chemistry partitions). This prevents assessment of statistical significance and raises the possibility that reported gains reflect favorable splits rather than genuine generalization.
[Transfer experiments] Transfer-learning subsection: no ablation isolates the contribution of the Nyström quantum feature map versus the physics loss (or versus a plain kernel PINN baseline) on identical splits. The skeptic concern that degradation physics differs markedly by chemistry (SEI vs. transition-metal dissolution) therefore remains unaddressed; the manuscript does not demonstrate that the reported transfer exceeds what a non-quantum PINN would achieve.
[Dataset] Dataset description: while the total size (310,705 samples, 387 cells) is stated, the distribution across chemistries, operating conditions, and the exact protocol for withholding target-domain SOH labels are not specified. This information is load-bearing for the cross-chemistry claim.

minor comments (2)

[Methods] Notation for the quantum feature map (Hilbert-space projection, Nyström approximation rank) is introduced without a clear reference to the underlying quantum kernel or its relation to battery physics.
[Figures] Figure captions and axis labels in the performance plots should explicitly state the baseline methods, the exact metric definitions (MAPE, RMSE), and whether shaded regions represent standard deviation or quartiles.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback, which highlights important areas for improving the clarity, reproducibility, and rigor of our work on QPINN for battery SOH estimation. We address each major comment point by point below and will revise the manuscript to incorporate the suggested enhancements.

read point-by-point responses

Referee: [Methods] Methods section: no explicit equations are given for the physics-informed loss terms or the precise physical constraints (e.g., capacity fade laws, SEI growth, or voltage limits) that are enforced. Without these, it is impossible to evaluate whether the constraints are sufficiently general to support the label-free cross-chemistry transfer claim or whether they implicitly encode chemistry-specific priors.

Authors: We agree that explicit equations are necessary for evaluating the generality of the constraints. In the revised manuscript, we will add the full mathematical formulation of the physics-informed loss function, including the specific capacity fade model (based on universal degradation bounds), SEI growth constraints, and voltage limit enforcements. These are formulated using chemistry-agnostic physical principles such as charge conservation and monotonic capacity fade applicable across Li-ion variants, without embedding chemistry-specific parameters. revision: yes
Referee: [Results] Results, cross-validation experiments: the headline 99.46% accuracy and transfer success are reported without error bars, number of independent runs, or details of the train/validation/test splits (especially the source-target chemistry partitions). This prevents assessment of statistical significance and raises the possibility that reported gains reflect favorable splits rather than genuine generalization.

Authors: We acknowledge this limitation in statistical reporting. The revised version will include error bars computed over multiple independent runs (with the exact number of seeds specified, e.g., 10), along with comprehensive details on the train/validation/test splits and source-target chemistry partitions to demonstrate that the cross-validation protocol avoids leakage and supports the generalization claims. revision: yes
Referee: [Transfer experiments] Transfer-learning subsection: no ablation isolates the contribution of the Nyström quantum feature map versus the physics loss (or versus a plain kernel PINN baseline) on identical splits. The skeptic concern that degradation physics differs markedly by chemistry (SEI vs. transition-metal dissolution) therefore remains unaddressed; the manuscript does not demonstrate that the reported transfer exceeds what a non-quantum PINN would achieve.

Authors: We will add ablation experiments on identical data splits comparing the full QPINN against (i) a standard PINN without quantum mapping and (ii) a kernel PINN baseline. These results will isolate the contributions of the Nyström quantum feature map and the physics loss to the observed cross-chemistry transfer performance, directly addressing whether the gains exceed those of non-quantum variants. revision: yes
Referee: [Dataset] Dataset description: while the total size (310,705 samples, 387 cells) is stated, the distribution across chemistries, operating conditions, and the exact protocol for withholding target-domain SOH labels are not specified. This information is load-bearing for the cross-chemistry claim.

Authors: We will expand the dataset section to provide the full breakdown of samples and cells by chemistry type, operating conditions (including temperature ranges and C-rates), and a precise description of the label-withholding protocol used in the transfer experiments. This will ensure full transparency regarding the multi-chemistry setup and cross-chemistry evaluation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript proposes QPINN by combining Nyström-approximated quantum feature mapping with a physics-informed loss for SOH regression. The abstract and available description report empirical accuracy (99.46 % average) and cross-chemistry transfer on 310 705 samples, but contain no equations, no fitted-parameter-to-prediction reductions, and no self-citation chains that bear the central claim. The method is presented as an architectural choice whose performance is validated externally on held-out cells and chemistries rather than derived by construction from its own inputs. Consequently the derivation chain remains self-contained against the reported benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, mathematical axioms, or new physical entities; the method description relies on standard neural network training augmented by an unspecified quantum mapping and unspecified physical constraints.

pith-pipeline@v0.9.0 · 5531 in / 1489 out tokens · 49089 ms · 2026-05-10T15:27:01.399352+00:00 · methodology

discussion (0)

Reference graph

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