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arxiv: 2409.08044 · v2 · submitted 2024-09-12 · 📡 eess.SP

A Glass-Box Deep-Learning Method for Electrical Energy System Modeling Based on Kolmogorov-Arnold Network

Zhenghao Zhou , Yiyan Li , Zelin Guo , Zheng Yan , Mo-Yuen Chow This is my paper

Pith reviewed 2026-05-23 20:51 UTC · model grok-4.3

classification 📡 eess.SP
keywords Kolmogorov-Arnold Networkglass-box modelingelectrical energy systemsinterpretabilitysymbolificationdeep learningphysical system modeling
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The pith

Kolmogorov-Arnold Networks produce explicit mathematical formulas for electrical energy system models while preserving nonlinear fitting power.

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

The paper introduces Kolmogorov-Arnold Networks as a replacement for conventional deep neural networks in modeling electrical energy systems. Standard deep learning approaches deliver accurate predictions but hide the internal relationships inside opaque weights, which limits their use when engineers need to inspect or verify the captured physics. KAN replaces fixed activations with learnable univariate functions on the edges, then applies sparse training followed by symbolification to collapse the trained network into short, readable symbolic expressions. Experiments on three different energy-system examples show that the resulting models remain accurate, robust to noise, and able to generalize to unseen conditions. A reader would care because the method supplies both the predictive strength of deep learning and the transparency required for physical-system analysis and control design.

Core claim

KAN can express the physical process with concise and explicit mathematical formulas while retaining the nonlinear-fitting capability of deep neural networks, achieved through its architecture of learnable activation functions on network edges together with sparse training and a subsequent symbolification step that converts the model into symbolic form.

What carries the argument

Kolmogorov-Arnold Network using learnable univariate functions on edges, sparse regularization during training, and symbolification to extract explicit formulas from the trained structure.

If this is right

  • Energy-system models become directly inspectable, allowing engineers to read off relationships such as voltage-current dependencies without post-hoc explanation tools.
  • The same accuracy, robustness, and generalization performance reported for the three test systems can be expected when the method is applied to other electrical energy modeling tasks.
  • Symbolification yields compact expressions that can be inserted into existing simulation or control software without retraining a neural network.
  • Interpretability gains do not require sacrificing the ability to capture strong nonlinearities that defeat purely linear or low-order symbolic regression methods.

Where Pith is reading between the lines

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

  • The approach could be tested on other physical domains that already possess known governing equations, such as mechanical or thermal systems, to measure how often the recovered symbols align with established laws.
  • If the extracted formulas prove reliable, they could serve as starting points for hybrid physics-informed models that combine data-driven terms with first-principles constraints.
  • Widespread adoption might reduce reliance on separate explainability techniques because the model itself is already in symbolic form.

Load-bearing premise

The symbolification step after sparse training recovers the true underlying physical relationships without introducing significant distortion or spurious terms.

What would settle it

Apply KAN to a simple, analytically known electrical system such as an RLC circuit, derive the symbolic formula, and check whether that formula matches the known differential equations to within measurement noise or produces large prediction errors on held-out data.

Figures

Figures reproduced from arXiv: 2409.08044 by Mo-Yuen Chow, Yiyan Li, Zelin Guo, Zhenghao Zhou, Zheng Yan.

Figure 7
Figure 7. Figure 7: Fitting results of KAN and MLP. 4) Sensitivity analysis of model configuration Configuring hyper-parameters for a neural network is generally considered empirical and may significantly influence the model performance. In this section, we further evaluate the KAN model performance with different structures to see whether KAN is sensitive to the model configuration. According to equation (16), Vout is depend… view at source ↗
Figure 9
Figure 9. Figure 9: Plots of KAN fitting results. (a) SOC variation with U when I is fixed at -3A. (b) SOC variation with I when U is fixed at 3.45V [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: KAN fitting results under different configurations. (a) KAN model with initialized structure [1,3,1] and D as the single input. (b) KAN model with initialized structure [2,5,1] and D, (1-D) as double inputs. B. State of Charge Estimation of Lithium-ion Battery Dara-driven approaches have been widely used for the state of charge (SOC) estimation of lithium-ion batteries [22]-[24], of which the key is to est… view at source ↗
read the original abstract

Deep learning methods have been widely used as an end-to-end modeling strategy of electrical energy systems because of their conveniency and powerful pattern recognition capability. However, due to the "closed-box" nature, deep learning methods have long been blamed for their poor interpretability when modeling a physical system. In this paper, we introduce a novel neural network structure, Kolmogorov-Arnold Network (KAN), to achieve "glass-box" modeling for electrical energy systems to enhance the interpretability. The most distinct feature of KAN lies in the learnable activation function together with the sparse training and symbolification process. Consequently, KAN can express the physical process with concise and explicit mathematical formulas while remaining the nonlinear-fitting capability of deep neural networks. Simulation results based on three electrical energy systems demonstrate the effectiveness of KAN in the aspects of interpretability, accuracy, robustness and generalization ability.

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 / 1 minor

Summary. The manuscript proposes Kolmogorov-Arnold Networks (KAN) as a glass-box deep-learning approach for modeling electrical energy systems. It highlights the use of learnable univariate activation functions, sparse training, and a subsequent symbolification step to derive concise explicit mathematical formulas that represent the underlying physical processes, while retaining the nonlinear approximation power of neural networks. Effectiveness is asserted via simulations on three electrical energy systems in terms of interpretability, accuracy, robustness, and generalization.

Significance. If the central claims hold, the work would offer a practically useful bridge between black-box neural modeling and explicit symbolic representations in power-system applications, potentially enabling domain-expert inspection of learned dynamics without sacrificing fitting flexibility.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'KAN can express the physical process with concise and explicit mathematical formulas' while accurately representing the systems rests on the symbolification step after sparse training, yet the abstract supplies no quantitative metrics, error bars, baseline comparisons, or validation against known physical equations for the three systems.
  2. [Method] Method description of symbolification (likely §3): the assumption that thresholding and basis-function fitting on the learned univariate functions recovers the true underlying relationships without systematic mismatch or artifacts is load-bearing for the glass-box interpretability claim, but the manuscript provides no explicit check (e.g., substitution of the derived symbolic expressions back into the system dynamics or residual analysis against the original nonlinear terms).
minor comments (1)
  1. [Method] Notation for the KAN layers and the symbolification threshold should be defined once and used consistently; currently the transition from numerical activations to symbolic expressions is described only qualitatively.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help improve the clarity and rigor of our manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'KAN can express the physical process with concise and explicit mathematical formulas' while accurately representing the systems rests on the symbolification step after sparse training, yet the abstract supplies no quantitative metrics, error bars, baseline comparisons, or validation against known physical equations for the three systems.

    Authors: We agree that the abstract would be strengthened by including quantitative support for the claims. In the revised manuscript, we have updated the abstract to report key accuracy metrics (MSE with standard deviations from repeated trials), baseline comparisons against standard neural networks, and explicit references to validation of the derived symbolic expressions against the known physical equations of the three systems. revision: yes

  2. Referee: [Method] Method description of symbolification (likely §3): the assumption that thresholding and basis-function fitting on the learned univariate functions recovers the true underlying relationships without systematic mismatch or artifacts is load-bearing for the glass-box interpretability claim, but the manuscript provides no explicit check (e.g., substitution of the derived symbolic expressions back into the system dynamics or residual analysis against the original nonlinear terms).

    Authors: The referee is correct that an explicit post-symbolification verification step would strengthen the interpretability claims. While the original simulations already demonstrate low fitting errors and physical consistency, we have added to the revised manuscript a dedicated verification subsection. This includes substituting the symbolic expressions back into the system dynamics and performing residual analysis against the original nonlinear terms for all three case studies, confirming negligible systematic mismatch. revision: yes

Circularity Check

0 steps flagged

No circularity: KAN application imports external architecture and demonstrates via simulation

full rationale

The paper applies the Kolmogorov-Arnold Network (introduced in independent prior work) to electrical energy systems. Its central claims rest on the properties of sparse training and symbolification as defined in that external reference, followed by empirical validation on three systems. No load-bearing step reduces by the paper's own equations or self-citation to a fitted input or self-defined quantity; the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no information on free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5691 in / 985 out tokens · 37665 ms · 2026-05-23T20:51:30.832214+00:00 · methodology

discussion (0)

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