Cross-Material Support Transfer for Core-Loss Prediction Under Waveform Covariate Shift

Cong Yao; Chunye Gong

cs.LGSep 15, 2026

Cross-Material Support Transfer for Core-Loss Prediction Under Waveform Covariate Shift

Authors: Cong Yao, Chunye Gong

Organizations: School of Computer Science and Technology, Changsha University of Science and Technology, Changsha 410076, China · College of Computing, National University of Defense Technology, Changsha 410073, China · National Supercomputer Center in Tianjin, Tianjin 300457, China · Laboratory of Digitizing Software for Frontier Equipment, National University of Defense Technology, Changsha 410073, China

Abstract

Power magnetic materials are characterized on the sinusoidal and triangular waveforms that excitation hardware conveniently produces, whereas deployed converters expose cores to trapezoidal, PWM-shaped flux trajectories, so loss models must predict exactly where their training data are thinnest. The final test of the MagNet Challenge embeds a deliberately extreme instance of this characterization-deployment mismatch: for material D, trapezoids form 16.4% of the test set but only 1.4% of the training set. The 95th-percentile relative error, hereafter p95, of the best submission, built on sequential transfer learning, stalled at 15.9%, the worst among the five materials. This paper shows that the obstacle is missing information under covariate shift rather than class imbalance, and that the missing support can be borrowed from sibling materials instead of being extrapolated. Controlled experiments first refute the imbalance reading: four standard remedies fail, and raising the trapezoidal share to the test-set level degrades accuracy further. The proposed material-identity support transfer, MIST, then trains one 2784-parameter predictor jointly on all five challenge materials. Material identity enters through feature-wise linear modulation, or FiLM, the scarce material's true-label loss is reweighted, and material D receives no fine-tuning, so that the bias of its trapezoid-free training set is never re-installed. MIST lowers the five-seed material-D p95 from 20.39+/-2.03% to 12.38+/-0.92% and the trapezoidal-class p95 from 37.4+/-8.8% to 15.16+/-1.69%, surpassing the best submission with one-sixth of its parameters and no fine-tuning stage; removing material identity at matched capacity inflates the error by an order of magnitude. These results argue that scarce materials should be characterized jointly with their siblings.

Figures & tables

Fig. 1: The designed waveform challenge of material D. (a) The trapezoidal share rises from $1.4\%$ of the training set to $16.4\%$ of the test set, a twelvefold ratio unique to this class. (b) The eight training trapezoids (stars) stop at $199$ kHz, whereas the 1198 test trapezoids (dots) extend to $397$ kHz: the shaded high-frequency band has zero training support. This is a designed covariate shift with missing support.

Waveform class	Training ( $n=580$ )	Test ( $n=7299$ )
Sinusoidal	153 (26.4%)	1357 (18.6%)
Triangular	335 (57.8%)	4335 (59.4%)
Trapezoidal	8 (1.4%)	1198 (16.4%)
Square-like	84 (14.5%)	409 (5.6%)

TABLE I: Waveform Composition of the Material-D Training and Test Sets

Fig. 2: The oversampling paradox that motivates this paper. Replicating the eight training trapezoids of material D until their share reaches or exceeds the test-set share (dashed line) makes the trapezoidal-class

p95

worse and inflates its cross-seed variance (five-seed mean

\pm

std). If the difficulty were class imbalance, share matching would be the textbook remedy; its failure identifies the difficulty as missing information.

Fig. 3: The proposed MIST architecture. All five materials train a single 2784-parameter gray-box predictor that follows the shared chain $\mathbf{B}\rightarrow\hat{\mathbf{H}}\rightarrow BH\rightarrow\hat{P}_{\mathrm{v}}$ ; material identity enters through the scalar $\rightarrow$ FiLM conditioning pathway, the scarce material’s true-label loss is reweighted ( $w_{\mathrm{D}}=5$ ), and material D is deployed directly from the joint model without fine-tuning.

Fig. 4: Measured trapezoidal support in the $(f,B_{\mathrm{pp}})$ plane. The 2447 A/B/C/E training trapezoids (open circles) blanket the material-D test trapezoids (dots): $99.3\%$ of the latter have a sibling neighbor within $\pm 10\%$ in both flux swing and frequency, whereas material D’s own eight trapezoids (stars) cover only $40\%$ .

Route	D $p95$ (%)	D trap. $p95$ (%)	Outcome
Baseline (per-material model)	$20.39\pm 2.03$	$37.4\pm 8.8$	reference
(a) Representation replacement (three seeds, bs1024; one-hot at bs1024: $17.96$ , seed 0)
Continuous waveform descriptors	$28.18\pm 1.26$	$42.9$ – $63.5$	variance halved, mean collapses
(b) Synthetic trapezoids with iGSE pseudo-labels
Zero-weight control ( $\lambda=0$ )	$19.88\pm 2.32$	—	reproduces baseline
Pseudo-labels ( $\lambda=0.05$ )	$26.77\pm 2.72$	—	degradation attributable to pull

TABLE II: Single-Material Routes on the Material-D Waveform Challenge (Five Seeds Unless Noted; Baseline in Each Block for Reference)

Fig. 5: Material-D

p95

by waveform class (five-seed mean

\pm

std). MIST cuts the trapezoidal class from

37.4\%

15.2\%

and the mixed other class from

16.7\%

12.6\%

, while the well-supported sinusoidal and triangular classes concede at most two percentage points.

Method	Params	D $p95$	Agg. $p95$	D trap. $p95$
(a) Single-material regime (each model sees only its own material)
Baseline: five per-material CAHR-Net models [ 17 ]	$5\times 1874$	$20.39\pm 2.03$	$7.89\pm 0.36$	$37.4\pm 8.8$
HARDCORE [ 16 ] ¶	$5\times 1755$	$23.44\pm 3.79$	$8.37\pm 0.87$	$40.8\pm 6.9$
(b) Sequential-transfer regime (pretraining on the legacy materials, then fine-tuning on each material including D)
MagLearn [ 31 ] ‡	16449 ∗	15.90	7.78	22.9
Fuzhou ‡	$5\times 8914$	20.70	7.94	27.6

TABLE III: Main Comparison on the MagNet Final A–E Protocol: Material-D, Aggregate, and Material-D Trapezoidal-Class

p95

(%) (Five-Seed Mean

\pm

Std Unless Noted)

Fig. 6: Material-D trapezoidal

p95

by frequency band (five-seed mean

\pm

std). The baseline degrades and destabilizes above

200

kHz, where material D has no training trapezoid; MIST closes most of that gap.

Fig. 7: (a) A shallow single-valley response curve over the reweighting factor

K

(seed 0, 3000 epochs) indicates a genuine mechanism rather than a tuned constant. (b) Longer training improves both configurations on every seed (open circles: individual seeds; filled: mean

\pm

std); already at 3000 epochs the reweighted five-seed mean reaches the level of MagLearn’s

15.9\%

Configuration	Agg. $p95$	D $p95$	D trap. (%)
No FT (proposed) †	$7.32\pm 0.19$	$12.38\pm 0.92$	$15.16\pm 1.69$
FT-head on D ∗	8.02	14.71	17.1
FT-full on D	7.98	16.03	25.2
Strong FT mix †	$7.49\pm 0.61$	$15.23\pm 2.32$	$31.7\pm 16.8$
MIST+FT, D untouched †	$7.24\pm 0.50$	$14.01\pm 1.93$	$18.08\pm 4.18$

TABLE IV: Per-Material Fine-Tuning After Joint Pretraining (Seed 0 Unless Noted)

Configuration	D $p95$	D trap.	Agg.
Zero-shot ∗	$15.49\pm 1.25$	19.8	8.78
Few-shot reference †	$14.01\pm 1.94$	$18.1\pm 4.3$	$8.60\pm 0.46$
A–E pool only ‡	$14.17\pm 0.54$	18.8	9.51
$+$ 10 legacy materials ‡	$12.57\pm 1.88$	16.6	8.36
Proposed §	$\mathbf{12.38\pm 0.92}$	$\mathbf{15.16\pm 1.69}$	$\mathbf{7.32\pm 0.19}$

TABLE V: Zero-Shot Transfer and Data Scaling on Material D

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Cross-Material Magnetic Core Loss Prediction via Operating-Condition Matching and Partial Optimal Transport

Cong Yao, Yu Zheng, Zehao Hou, Rui Xu

Changsha University of Science and Technology, Changsha, China · School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, China · University of Arkansas, Fayetteville, AR 72701, USA

Cross-Domain Transfer Learning Materials Property Prediction

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Cross-material magnetic core loss prediction requires adapting to new material responses with limited measurements. Global feature alignment overlooks differences in source and target excitation coverage. This motivates selecting comparable samples and controlling each source measurement's alignment contribution. This paper proposes T-PCOT, a Transformer transfer method based on condition-supported partial optimal transport. Frequency, flux excursion, temperature, and waveform descriptors define a sparse graph of comparable operating conditions. A capacity-constrained transport plan distributes alignment across source measurements and leaves costly target mass unmatched. The plan is constructed from measured inputs before training and guides local waveform-feature consistency. An importance-weighted sampling scheme preserves both uniform source regression and the transport objective during minibatch optimization. Experiments on three material pairs and three target label budgets show that T-PCOT reduces mean relative error (MRE) and 95th-percentile error (P95) relative to Transformer-based multiple-kernel maximum mean discrepancy (T-MKMMD) in all nine comparisons. Macro MRE decreases from 12.60% to 9.65%, and macro P95 from 30.94% to 25.06%, corresponding to relative reductions of 23.41% and 19.01%. Controlled comparisons and ablations examine the roles of input processing, condition correspondence, and source capacity. The results demonstrate the predictive advantage of organizing cross-material alignment through operating-condition support over the compared global alignment method. The proposed method achieves state-of-the-art predictive performance in magnetic core loss transfer learning.

Abstract

Materials Property Prediction

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