# HARDCORE: H-field and power loss estimation for arbitrary waveforms with residual, dilated convolutional neural networks in ferrite cores

arXiv: https://arxiv.org/abs/2401.11488 · HTML: https://mlsanity.com/paper/2401.11488/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 21 Jan 2024.

## Builds on (most cited first, 6 of 6)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [A better measure of relative prediction accuracy for model selection and model estimation](https://mlsanity.com/paper/2105.05249/) (2021)

## Built on by (most cited first, 5 of 5)

- [Data-driven Power Loss Identification through Physics-Based Thermal Model Backpropagation](https://mlsanity.com/paper/2504.00133/) (2025)
- [CAHR-Net: Condition-Adaptive Hysteresis Reconstruction for Compact and Interpretable Magnetic Core Loss Modeling](https://mlsanity.com/paper/2609.01991/) (2026)
- [Spectral entropy prior-guided deep feature fusion architecture for magnetic core loss](https://mlsanity.com/paper/2512.11334/) (2025)
- [A Physics-Informed Hybrid Neural Operator for Transient Magnetization Prediction in Power Magnetics](https://mlsanity.com/paper/2608.02965/) (2026)
- [Cross-Material Support Transfer for Core-Loss Prediction Under Waveform Covariate Shift](https://mlsanity.com/paper/2609.31659/) (2026)

## Abstract (arXiv)

The MagNet Challenge 2023 calls upon competitors to develop data-driven models for the material-specific, waveform-agnostic estimation of steady-state power losses in toroidal ferrite cores. The following HARDCORE (H-field and power loss estimation for Arbitrary waveforms with Residual, Dilated convolutional neural networks in ferrite COREs) approach shows that a residual convolutional neural network with physics-informed extensions can serve this task efficiently when trained on observational data beforehand. One key solution element is an intermediate model layer which first reconstructs the bh curve and then estimates the power losses based on the curve's area rendering the proposed topology physically interpretable. In addition, emphasis was placed on expert-based feature engineering and information-rich inputs in order to enable a lean model architecture. A model is trained from scratch for each material, while the topology remains the same. A Pareto-style trade-off between model size and estimation accuracy is demonstrated, which yields an optimum at as low as 1755 parameters and down to below 8,% for the 95-th percentile of the relative error for the worst-case material with sufficient samples.