CAHR-Net: Condition-Adaptive Hysteresis Reconstruction for Compact and Interpretable Magnetic Core Loss Modeling

Chunye Gong; Cong Yao

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CAHR-Net: Condition-Adaptive Hysteresis Reconstruction for Compact and Interpretable Magnetic Core Loss Modeling

Chunye Gong, Cong Yao

arXiv:2609.01991v1Sep 2, 2026cs.LG

TL;DR

Existing core-loss models often let operating conditions affect only a terminal scalar, losing an intermediate hysteresis representation for loop reshaping. CAHR-Net instead reconstructs the magnetic field and injects conditions through FiLM before loop-area integration, achieving compact accuracy on the MagNet final A–E protocol. Its reported gains are associated with physical reconstruction, structured modulation, and matched optimization, within a stated five-material, steady-state scope without DC bias.

Problem
Existing scalar and data-driven models do not retain an intermediate hysteresis representation for operating conditions to reshape, despite conditions acting through loop geometry.
Method
CAHR-Net reconstructs Ĥ(t) from flux density, integrates the B–H loop, applies residual logarithmic loss correction, and uses FiLM to modulate intermediate features with operating conditions.
Results
CAHR-Net achieves 6.89% average p95 relative error with 1874 parameters, the lowest average p95 among compared methods on the MagNet final A–E protocol.
Takeaways & Limitations
The reported operating point combines physical loop interpretability, condition-adaptive reconstruction, and compact model size.
Takeaways & Limitations
The study is limited to per-material training on five MagNet ferrites and single-period steady-state excitation without DC bias.

Abstract

from arXiv · show

Magnetic core loss originates in the hysteresis loop: the energy dissipated per excitation cycle equals the loop area, and frequency, temperature, and waveform shape set the loss by reshaping the loop geometry. Most existing models let these conditions act only on a terminal scalar - empirical equations fold them into fitted exponents, and data-driven predictors append them to encoded features - so no intermediate hysteresis representation remains for the conditions to reshape. This paper proposes CAHR-Net, a condition-adaptive hysteresis reconstruction network that injects the operating conditions where they physically act. It preserves the interpretable chain from flux density waveform to magnetic field reconstruction, loop-area integration, and power loss estimation, and uses feature-wise linear modulation to inject frequency, temperature, and waveform statistics into the intermediate reconstruction representation. A matched large-batch training protocol based on AdamW, cosine scheduling, and a staged reconstruction-to-power-loss objective is also reported, because the modulation pathway takes effect only within it. On the MagNet final A-E material protocol, CAHR-Net attains an average p95 relative error of 6.89% with only 1874 parameters, the lowest among all compared methods, together with a lower worst-material p95 than the strongest black-box solution at about 48x fewer parameters; it reduces the average p95 of the physical reconstruction backbone from 7.47% to 6.89% and the p95 of material D, the most difficult material, from 16.40% to 14.87%. Ablation and condition-slice analyses attribute the improvement to the coupling of physical loop reconstruction, structured condition modulation, and the matched optimization trajectory.

I. INTRODUCTION

CAHR-Net addresses the loss of hysteresis geometry in scalar and black-box models by reconstructing the magnetic field and injecting operating conditions into that intermediate representation. It reports a compact, interpretable accuracy–parameter tradeoff on the MagNet protocol.

Core loss follows B–H loop area, while frequency, temperature, and waveform shape reshape the loop geometry.
Classical scalar laws absorb operating conditions into fitted exponents, limiting representation of arbitrary-waveform, wide-condition, and material-specific loop deformation.
Data-driven predictors improve accuracy but mostly abandon the hysteresis loop, whereas gray-box reconstruction retains it while still appending conditions as scalars.
CAHR-Net places frequency, temperature, and waveform statistics into FiLM scale-and-shift parameters acting on the intermediate reconstruction representation.
6.89% average p95 relative error with 1874 parameters was lowest among compared methods under the unified MagNet final A–E protocol.
The paper organizes its development, experimental setup, results, and conclusion across Sections II–V.

II. METHODOLOGY

CAHR-Net predicts volumetric core loss from a single-period flux-density waveform and operating vector through a physically structured reconstruction pathway rather than a direct scalar map.

The task maps a single-period flux-density waveform and operating vector s to volumetric core loss Pv.
Direct scalar prediction leaves no intermediate representation for operating conditions to reshape.
CAHR-Net reconstructs magnetic field waveform Ĥ(t), computes an initial loop-area estimate, and applies residual correction in the logarithmic loss domain.
The architecture combines temporal waveform encoding, scalar condition encoding, FiLM coupling, magnetic-field reconstruction with B–H integration, and residual power-loss correction.

B. Physical Loop Reconstruction Chain

The physical reconstruction chain extracts a waveform skeleton, modulates it with operating conditions, reconstructs Ĥ(t), integrates the B–H loop, and applies a logarithmic residual correction.

The temporal encoder extracts a waveform skeleton from the normalized 1024-point flux-density sequence.
The scalar branch maps operating conditions to modulation parameters before the reconstruction head generates the field waveform.
The reconstructed field waveform becomes an initial power-loss estimate through discrete B–H loop-area integration.
The integration uses excitation frequency, restored physical scale factors, and trapezoidal integration.
The final prediction is formed in the logarithmic domain, with a residual head correcting scale and integration bias.
Measured magnetic-field waveforms supervise Ĥ(t), while per-material normalization factors restore physical magnitudes from normalized waveforms.
The architecture modulates eleven of twelve encoder channels, bypassing one raw channel before field reconstruction.

C. Condition-Adaptive FiLM Modulation

CAHR-Net injects operating conditions into the intermediate hysteresis-reconstruction representation through feature-wise scaling and shifting, rather than terminal scalar correction. The modulation mirrors loop deformation by frequency and temperature while preserving the reconstruction pathway.

CAHR-Net generates condition-dependent modulation parameters from an encoded operating vector and applies them to intermediate reconstruction features.
Frequency, temperature, and waveform statistics act before magnetic-field reconstruction instead of merely correcting the final scalar loss.
FiLM uses channel-wise scaling and shifting to represent multiplicative and translational deformations of the hysteresis loop.Scaling corresponds to loop broadening and amplitude changes, while shifting corresponds to bias and remanence drift.
The authors do not claim one-to-one identification between individual FiLM parameters and specific loop features.The correspondence is stated only at the level of transformation families.

D. Deployment-Oriented Inference Optimization

The deployment setup targets single-point CPU inference for repeated loss evaluation, using an ONNX Runtime graph that explicitly implements loop integration and material normalization. Evaluation follows the MagNet final-stage A–E protocol and emphasizes tail-error metrics.

CAHR-Net is intended for single-operating-point CPU queries in converter design loops, design sweeps, and online estimation without an accelerator.
ONNX export rewrites trapezoidal loop-area integration as elementary slicing, arithmetic, and reduction operations.Per-material normalization constants are baked into the exported graph.
The MagNet final-stage A–E protocol uses 1024 waveform samples per period and scalar inputs containing frequency, temperature, and waveform statistics.
Results report average relative error, average p95 and p99 percentiles, and worst-material p95 across five materials.The protocol identifies material D as the worst-material case in the reported experiments.
The evaluation uses one trained model per method under the released MagNet Challenge and HARDCORE reporting convention.

B. Compared Methods

The comparison includes empirical equations, public challenge methods, and internal models evaluated under a shared protocol. CAHR-Net’s architecture and matched training procedure are documented alongside the physical reconstruction baseline and configuration details.

Compared Methods: Three baseline groups are compared: refitted empirical models, representative public challenge methods, and internal models evaluated under the same experimental chain.
Network Configuration: CAHR-Net’s waveform encoder uses five input channels, including normalized flux waveforms, time derivatives, and a saturation-emphasizing tangent transform.
Network Configuration: The operating vector contains logarithmic frequency, temperature, waveform-shape indicators, flux-density amplitude, and flux-slew statistics with logarithmic counterparts.
Network Configuration: Table I presents the complete layer-by-layer CAHR-Net configuration, whose parameter subtotals sum to 1874 parameters.
Training Protocol: The matched objective combines magnetic-field reconstruction and logarithmic power-loss losses with a schedule that shifts emphasis toward loss prediction.
Training Protocol: AdamW, cosine learning-rate scheduling, a learning rate of 2 × 10^-3, weight decay of 10^-4, batch size 512, and 10000 epochs define the reported training configuration.The modulation strength is α = 0.1.

IV. RESULTS AND DISCUSSION

Across the MagNet final A–E comparison, CAHR-Net combines the strongest reported average p95 with a substantially smaller parameter budget than black-box competitors. It also improves the physical reconstruction backbone and achieves the lowest worst-material p95.

Empirical equations remain in the 56.84%–78.30% average-p95 range even when fitted independently for each material.
6.89% average p95 is the lowest value in the comparison, versus 7.78% for Bristol and 7.94% for Fuzhou.
14.87% worst-material p95 is lower than Bristol’s 15.90%, while CAHR-Net uses only 1874 parameters.
CAHR-Net uses about 1/48 of Bristol’s parameter budget and 1/4.8 of Fuzhou’s.

B. Ablation Study

The ablation study separates gains from optimization, condition injection, and their interaction under a shared evaluation chain. CAHR-Net improves overall and difficult-material tail error while preserving performance across condition slices.

Applying the matched optimization protocol to the unchanged backbone lowers average p95 from 7.47% to 7.27% and worst-material p95 from 16.40% to 15.64%.
CAHR-Net lowers material-D p95 from 16.40% to 14.87%, while materials A, B, C, and E show no obvious degradation.
The material-D error distribution shifts left and contracts in the high-error region, reducing samples that would otherwise dominate design risk.
The clearest slice improvements occur in the lowest peak-flux-density quartile, from 10.91% to 8.53%, and the highest-error, lowest-loss-magnitude quartile, from 12.62% to 11.00%.
Some slices, including the second flux-density quartile, are essentially unchanged.

E. Injection–Optimization Interaction and Parameter Efficiency

FiLM’s advantage depends on the optimization protocol rather than appearing under every training setup. Within a similar parameter budget, CAHR-Net’s gains are linked to condition injection and matched training instead of simply increasing capacity.

Under NAdam with step decay, bias, SE, and FiLM injection perform similarly, but AdamW with cosine scheduling gives FiLM a stable advantage.
Widening the model or adding SE-style recalibration does not reliably outperform CAHR-Net under a similar parameter budget.
The dominant improvement comes from how condition information enters reconstruction and how that structure is trained, rather than from a simple increase in capacity.

F. Inference Latency Optimization

The deployment optimization exports CAHR-Net to ONNX Runtime, reducing single-sample CPU latency without changing accuracy. The reported gains reflect reduced framework overhead, while the deployment boundary remains a server-class CPU rather than a microcontroller.

ONNX Runtime reduces batch-1 latency from 0.82 ms to 0.19 ms per sample, a 4.4× speedup and 5.6× over eager execution, at zero accuracy cost.
At batch size 256, all four backends converge to approximately 150 µs per sample, indicating an arithmetic floor for the model on this CPU core.
At batch size 2048, ONNX Runtime remains at 174 µs while PyTorch-based backends rise to roughly 370 µs per sample.
The HARDCORE backbone shows the same 4.4× single-sample latency reduction, from 798 to 182 µs, indicating a shared compact-model deployment effect.
At 0.19 ms per sample on one CPU thread, the model supports more than 5000 loss evaluations per second per core without a GPU in the serving path.
The latency results are bounded by measurement on a server-class CPU core rather than a microcontroller, with integer quantization and sequence downsampling left for future work.

V. CONCLUSION

CAHR-Net places operating conditions inside an explicit hysteresis-loop reconstruction chain, combining structured modulation with matched optimization. It achieves strong accuracy and interpretability with a compact model, while remaining limited to five MagNet ferrites and single-period steady-state excitation without DC bias.

CAHR-Net places operating conditions in the hysteresis-loop reconstruction process, preserving the physical B(t) → Ĥ(t) → BH → P̂v prediction chain.Frequency, temperature, and waveform statistics modulate the intermediate representation from which the magnetic-field waveform is reconstructed.
1874 parameters yield the lowest average p95 relative error, 6.89%, among the compared methods under the MagNet A–E final protocol.This is an accuracy–parameter–interpretability tradeoff rather than a terminal scalar correction alone.
The study remains limited to per-material training on five MagNet ferrites and single-period steady-state excitation without DC bias.Future work is proposed for material recommendation, uncertainty-aware design margins, and deployment-oriented model compression.