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REVIEW 5 major objections 5 minor 25 references

Modeling of Core Loss Based on Machine Learning and Deep Learning

T0 review · 5 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read One data-driven model can predict magnetic core loss across four ferrite materials, three waveforms, and a range of temperatures, with accuracy far above classical Steinmetz-type equations.

desk verdict Plausible and useful applied-ML result for core-loss modeling, but the hybrid model's numbers are inflated by test-set weight tuning and the temperature generalization claim overreaches; both are fixable. read the letter →

arxiv 2502.05487 v1 pith:BJ4VG3TM submitted 2025-02-08 cs.LG eess.SP

Junqi He , Yifeng Wei , Daiguang Jin This is my paper · ORCID
classification cs.LGeess.SP
keywords magneticcorelosspredictionmachinelearningdeepCNN-FCNNXGBoostSteinmetzequationferritematerials
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper is trying to establish that a single data-driven model, trained once, can predict magnetic core loss for multiple different ferrite materials under varying temperature, frequency, and excitation waveform, with accuracy far beyond traditional empirical equations. This matters because conventional practice requires fitting separate Steinmetz-type equations for each material and operating condition, and even then prediction errors remain large. The paper reports that its proposed CNN-FCNN Mix Neural Network (MNN), and especially a weighted hybrid of MNN with XGBoost, reaches $R^2=0.997$ on held-out test samples, with mean absolute percentage error around 12 percent. If correct, this would make core-loss modeling a one-model task instead of a case-by-case fitting exercise.

What carries the argument

The load-bearing machinery is the Mix Neural Network (MNN), a CNN-FCNN hybrid. Its embedding layer turns the categorical material and waveform labels into dense vectors; its two convolutional layers (16 and 32 channels, kernel size 3) read local temporal patterns from the 1024-point magnetic-flux-density waveform; and its fully connected layers concatenate the resulting features with the scalar inputs (temperature, frequency) to regress loss per unit volume. On the tree side, XGBoost handles the same task after manual feature extraction: 33 features derived from the waveform sequence plus material, waveform, temperature, and frequency. The final hybrid model is a fixed weighted average of the two, with the weights chosen by grid search to minimize MSE. The paper's argument is that giving the models the full waveform, material identity, waveform type, and temperature is what lets a single model cover conditions that classical equations either ignore or require separate fits for.

What would settle it

Measure core loss at a temperature not used in training, for example 35 or 80 degrees Celsius, on the same four ferrite materials and waveforms, and feed the same features to the trained hybrid model; if its mean absolute percentage error rises well above the reported 12 percent or its predictions drift systematically, the claimed full-temperature-range generalization is falsified. A second check is to test on a different batch of the same material grade, since the paper only demonstrates generalization across the four grades in the training set.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that a single data-driven model can replace the traditional practice of fitting separate empirical equations for each magnetic material and operating condition. Using a subset of the open-source measured core-loss database—four ferrite grades (3C94, 77, N27, N87), three waveforms (sine, triangular, trapezoidal), four temperatures (25, 50, 70, 90 degrees Celsius), and frequencies from 50 to 500 kHz, with magnetic flux density given as a 1024-point sequence—the paper trains one model that handles all conditions jointly. The proposed Mix Neural Network (MNN), built from an embedding layer for categorical features, convolutional layers for the waveform sequence, and fully connected layers for regression, reaches a test mean squared error (MSE) of 593,100,352, MAPE of 20.25 percent, and $R^2=0.995$. Weighted combination of MNN with XGBoost predictions (weights 0.4764 and 0.5236) improves these numbers to MSE 334,314,144, MAPE 12.09 percent, and $R^2=0.997$. The paper further claims that because temperature enters as a continuous input feature, the trained model predicts the whole temperature range, not only the four measured points.

Load-bearing premise

The universal-model claim rests on the assumption that the subset of 12,400 measured samples—four ferrite materials, four temperatures, three waveforms, and 50 to 500 kHz—is representative enough for one trained model to interpolate the whole temperature range and generalize across the four materials.

Editorial extensions

If this is right

  • A single trained model replaces the case-by-case Steinmetz fitting procedure: the paper reports accurate joint prediction for four ferrite materials in one training run.
  • Temperature can be treated as a continuous feature, so the model predicts not only the four measured temperatures but, by the paper's claim, the whole temperature range between them.
  • Non-sinusoidal waveforms are handled without waveform-specific correction equations such as iGSE, which the paper reports as having maximum errors above 370 percent for some materials.
  • Combining the best tree model and the best neural model through weighting improves accuracy, reaching a test $R^2$ of 0.997.
  • New materials or operating conditions can be added by adding data and retraining, rather than deriving a new physical equation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The accuracy gap may come more from the richer input features than from the specific neural architecture; a well-featurized tree model already matches the deep network here, so low-cost baselines should be tried before committing to deep learning on other core-loss datasets.
  • The full-temperature-range generalization is an interpolation claim, and it has not been demonstrated at temperatures between or outside the four training points; testing at 35 or 80 degrees Celsius would settle it.
  • The same input structure invites natural extensions to DC bias, core geometry, material batch variation, or higher frequencies, and whether one universal model can absorb them is an open question the paper's approach raises.
  • If the weights found by grid search (0.4764 for XGBoost, 0.5236 for MNN) are stable across datasets, weighted ensembling of a tree model and a deep sequence model could be a general recipe for regression tasks with mixed categorical, scalar, and sequence inputs; if the weights are dataset-specific, the reported improvement may not transfer.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The manuscript proposes a Mix Neural Network (MNN) that combines embeddings, CNN, and fully connected layers to predict magnetic core loss from the MagNet dataset, using a single model across four ferrite materials, four temperatures, three waveforms, and frequencies from 50 to 500 kHz. The authors compare MNN with Random Forest, XGBoost, and MLP-LSTM, and with traditional Steinmetz-equation and iGSE fits, and then form a weighted hybrid of MNN and XGBoost. The central claim is that a single data-driven model can replace per-material empirical equation fits across the tested operating envelope, with accuracy far exceeding the traditional equations.

Significance. If the claims hold, the paper would provide a practically useful single-model alternative to per-material, per-condition empirical core-loss equations, building on the public MagNet database. The study reports clear train/validation/test splits, standard regression metrics, and a comparison of several model families, which are strengths. However, the headline hybrid accuracy is compromised by test-set-based weight selection, the temperature generalization claim is only asserted and not tested, and the comparison to traditional equations is confounded by the much richer feature set provided to the ML models. The evidence supports a narrower claim: supervised models with engineered features and deep sequence models outperform basic Steinmetz-family fits on this data subset, but not the full generalization claims in the abstract and Section III-D.

major comments (5)
  1. [III-D, Eq. (21), Table VII] The hybrid weights W1 and W2 are selected by a grid search on the test set with the explicit objective of minimizing MSE. Consequently, the reported test-set metrics of MSE 334,314,144, MAPE 12.09%, and R²=0.997 are optimistically biased estimates of the hybrid model's generalization performance, and the statement that the hybrid 'could continue to improve' is not supported by the experiment as designed. Please select the weights using the validation set (or nested cross-validation) and report test-set metrics only for the final fixed weights.
  2. [III-D, final paragraph] The sentence claiming that the trained model 'can not only predict the core loss at these four temperature points, but also predict the entire temperature range' is unsupported by any experiment in the manuscript. All temperatures in the dataset are 25, 50, 70, and 90 °C, and no held-out temperature points are evaluated. Please either add an explicit interpolation/extrapolation experiment with temperatures not used in training or restrict the claim to the four trained temperatures.
  3. [III-A vs. III-B and III-D] The comparison between traditional equations and ML models is confounded by feature set. The Steinmetz and iGSE fits in Tables II and III use only frequency and flux-density information, fit per material, while the ML models receive material identity, waveform type, temperature, and the full 1024-point B waveform. The observed accuracy gap could therefore be due to the richer input features rather than the modeling method. Please add controlled experiments with matched feature sets (e.g., per-material ML models on the same inputs as SE/iGSE, or extending the equations with temperature) or explicitly frame the comparison as 'data-driven models with richer features'.
  4. [II-A and III-D] The dataset curation and split are not described in enough detail to support the generalization claim. The paper reports 12,400 samples from four materials, four temperatures, three waveforms, and frequencies from 50 to 500 kHz, but it does not state the number of samples per condition, whether the split is stratified, or whether samples from the same material/temperature/waveform condition appear in both training and test sets. Without this information, the test-set metrics do not demonstrate robustness to new material batches, temperatures, or waveforms. Please provide a detailed data sheet and split description.
  5. [III-B, feature extraction] The 33 manually extracted sequence features used for Random Forest and XGBoost are not listed or defined. Since these features form part of the input for two of the four compared models and contribute to the reported results, the experiments cannot be fully reproduced or assessed without a precise definition. Please include a table listing all hand-crafted features and their extraction formulas.
minor comments (5)
  1. [III-D, Eq. (21)] There is a typo in the weights: the text says 'W1 = 0.4764 and W1 = 0.5236'; the second should be W2.
  2. [II-E] Max APE is used as a performance index in Tables II, III, and VII but is never defined. Please add its formula.
  3. [II-C, Eq. (12)] 'Sigmod' should be 'Sigmoid'.
  4. [III-C, Table V] The MLP-LSTM entry lists 'patience 50' and early stopping, but the manuscript does not state what data (training or validation) is monitored for early stopping. Please clarify.
  5. [III-D, Figure 10] The y-axis of Figure 10 is described as 'error distribution', but the precise quantity (e.g., percentage error bins, MAPE per bin) is not defined in the text or caption. Please specify.

Circularity Check

1 steps flagged · score 4.0 of 10

Hybrid-model weights are selected on the test set, so the reported hybrid improvement is partly a fitted value; the main single-model result remains independently grounded.

  1. fitted input called prediction [Section III-D, Eq. (21), Table VII]
    "Adopt bPHM = W1 × bPXGBoost + W2 × bPMNN ... By conducting a grid search to find the optimal weight, with the goal of finding the minimum MSE, we finally obtained W1 = 0 .4764 and W1 = 0 .5236. Under weighted conditions, we obtained the minimum MSE value as shown in Table VII."

    The two hybrid weights are the only free parameters of the hybrid model. They are selected by minimizing MSE, and the same test-set performance is then reported in Table VII as the model's accuracy. Thus the hybrid MSE, MAPE, and R² are fit statistics on the data used to choose the weights, not out-of-sample predictions. Within the searched grid, the reported MSE is by construction the minimum on that test set, so the claimed improvement over XGBoost and MNN is an optimized value rather than a discovered generalization. This does not affect the independent holdout evaluation of the individual MNN and XGBoost models, but it makes the specific claim that hybrid accuracy 'could continue to improve' partially circular.

full rationale

The paper's central claim—that a single MNN can predict core loss across four materials, four temperatures, three waveforms, and a frequency range—is evaluated on a proper holdout test set after a 7:1.5:1.5 split, so it is not circular. The individual MNN and XGBoost results in Table VII are genuine out-of-sample evaluations, and the comparison to per-material Steinmetz/iGSE fits is a fair external benchmark. No self-citation chain or imported uniqueness theorem is present; the MagNet dataset and XGBoost are external prior work by other authors. The only circular step is the hybrid model: the weights W1 and W2 are chosen by grid search to minimize MSE on the test set, and the resulting test-set metrics are then presented as evidence that the hybrid improves accuracy. That improvement is partly forced by construction. The temperature-range generalization claim (predicting the 'entire temperature range' from four discrete training temperatures) is an unsupported extrapolation and a correctness risk, but it is not circularity because it is not derived from the training data by definition. Overall, the central result is independently grounded, with one secondary fitted-result issue, giving a score of 4.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim is an empirical ML benchmark; the free parameters are the hand-chosen hyperparameters, the unenumerated features, and the test-set-tuned ensemble weights. The axioms are the representativeness of MagNet and the validity of the selected features.

free parameters (4)
  • Hybrid ensemble weights W1, W2 = 0.4764, 0.5236
    Chosen by grid search on the test set to minimize MSE (Section III-D), which leaks test information into the reported hybrid accuracy.
  • MNN architecture hyperparameters (layers, kernel sizes, embedding dimensions) = see Table VI
    Hand-selected; no sensitivity analysis shown, so reported performance may depend on these choices.
  • Hand-crafted sequence features for Random Forest and XGBoost = 33 features
    Feature set is not enumerated; the predictive performance of the tree models depends on these unstated choices.
  • Dataset subset selection = 12,400 samples
    The exact sampling criteria from MagNet are not fully specified; this determines the difficulty and coverage of the benchmark.
assumptions (4)
  • domain assumption MagNet database measurements are accurate and representative of ferrite core loss.
    The entire training and evaluation rests on the public dataset [23] with no independent check of measurement quality.
  • domain assumption Core loss depends only on the selected features: material, waveform type, temperature, frequency, and the flux density waveform.
    Section II-A selects these features; unmodeled factors (DC bias, harmonics, core geometry) are ignored.
  • domain assumption The 7:1.5:1.5 random split produces independent and identically distributed train/validation/test sets.
    Section II-A states the split ratio but not the splitting method; if split is random at sample level, samples from the same measurement sequence may appear in both train and test.
  • ad hoc to paper Interpolation between the four trained temperature points is valid for the full temperature range.
    Section III-D asserts this generalization without validation data at intermediate temperatures.

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Pith. "Pith review of Modeling of Core Loss Based on Machine Learning and Deep Learning." pith.science (2026). https://pith.science/paper/BJ4VG3TM

@misc{pith2026250205487,
  author       = {Pith},
  title        = {Pith review of: Modeling of Core Loss Based on Machine Learning and Deep Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BJ4VG3TM}},
  note         = {Machine review of arXiv:2502.05487}
}
read the original abstract

This article proposes a Mix Neural Network (MNN) based on CNN-FCNN for predicting magnetic loss of different materials. In traditional magnetic core loss models, empirical equations usually need to be regressed under the same external conditions. When the magnetic core material is different, it needs to be classified and discussed. If external factors increase, multiple models need to be proposed for classification and discussion, making the modeling process extremely cumbersome. And traditional empirical equations still has the problem of low accuracy, although various correction equations have been introduced later, the accuracy has always been unsatisfactory. By introducing machine learning and deep learning, it is possible to simultaneously solve prediction problems with low accuracy of empirical equations and complex conditions. Based on the MagNet database, through the training of the newly proposed MNN, it is found that a single model is sufficient to make predictions for at least four different materials under varying temperatures, frequencies, and waveforms, with accuracy far exceeding that of traditional models. At the same time, we also used three other machine learning and deep learning models (Random Forest, XGBoost, MLP-LSTM) for training, all of which had much higher accuracy than traditional models. On the basis of the predicted results, a hybrid model combining MNN and XGBoost was proposed, which predicted through weighting and found that the accuracy could continue to improve. This provides a solution for modeling magnetic core loss under different materials and operating modes.

Figures

Figures reproduced from arXiv: 2502.05487 by the authors.

Figure 1
Figure 1. MLP-LSTM architecture. C. MLP-LSTM architecture Multi-Layer Perception (MLP) and Long Short-Term Mem￾ory (LSTM) are two neural network architectures. MLP can extract features from discrete data through linear transforma￾tions and nonlinear mappings. LSTM can be used to process data related to time series, where the input sequence has temporal characteristics and the same time steps, and the wave￾form sequence of mag… view at source ↗
Figure 2
Figure 2. LSTM architecture. Output Gate: ot = σ(Wo · [ht−1, xt] + bo) (10) Hidden State: ht = ot · tanh(Ct) (11) among them, W are different weight matrices respec￾tively, b represents different bias vectors, and σ is the activation function of Sigmod. The expression is σ(x) = 1 1 + e−x (12) However, due to its inherent structure, LSTM is difficult to extract features from the entire sequence, so a more ef￾fective processing… view at source ↗
Figure 3
Figure 3. Mix Neural Networks architecture. III. MODEL TRAINING RESULTS A. Traditional model fitting Use the SE to perform nonlinear regression fitting on the dataset. Based on the limitations of the SE, we only selected data with sine excitation waveforms from the dataset for training, and the predicted results are shown in Table II. According to the performance indexes, we can find that R2 is around 0.95, MAPE is around 40,… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Error distribution of iGSE prediction results. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Error histogram of Random Forest prediction results. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Error histogram of XGBoost prediction results. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Error histogram of MLP-LSTM Forest prediction results. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: Error histogram of MNN prediction results. [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: Error histogram of hybrid model prediction results. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Error distribution of all models prediction results. [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Comparison between the predicted results of the hybrid model and [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 12
Figure 12. Figure 12: Percentage of residual between predicted and actual values of all [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]

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