Defect Detection in Magnetic Systems Using U-Net and Statistical Measures

Abstract

Local material inhomogeneities can strongly influence magnetization dynamics and macroscopic magnetic properties, yet detecting such defects from magnetic imaging data remains challenging when thermal fluctuations and experimental noise obscure static contrast. Here, we investigate defect detection in strongly fluctuating magnetization regimes where signatures of inhomogeneities largely average out in time-resolved measurements. Using finite-temperature micromagnetic simulations with randomly distributed defects and material parameters representative of \ce{Ni80Fe20}, we compute per-pixel temporal mean, temporal standard deviation, and latent entropy and use them as inputs for U-Net-based semantic segmentation models. We find that the most effective descriptor depends on the noise level and, importantly, that robust detection requires training data that reflect the expected noise statistics. These results provide practical guidance for designing noise-robust defect-detection workflows in magnetic imaging.

Figures (4)

• Figure 1: Schematic overview of the data processing pipeline. Highly fluctuating time-series magnetization fields obtained from finite-temperature micromagnetic simulations are processed on a per-pixel basis to compute three statistical measures: the temporal mean $\mu$ (top, blue), temporal standard deviation $\sigma$ (center, yellow), and latent entropy $\mathrm{LE}$ (bottom, green). Each measure is then provided separately as a single-channel input to a U-Net trained to detect defect regions. For the example shown, the standard deviation and latent entropy perform best.
• Figure 2: Qualitative prediction overview for defect segmentation using the three input measures: temporal mean ($\mu$), temporal standard deviation ($\sigma$), and latent entropy (LE). Columns are grouped by measure, and within each group show (from left to right) the input measure map, the U-Net prediction, and the prediction difference relative to the ground truth shown in Fig. \ref{['fig:UNetSchematic']} (false positives/negatives highlighted in blue/red respectively). Rows are organized by magnetization component ($m_x$ top block, $m_z$ bottom block) and noise condition (no noise, additive Gaussian noise, and multiplicative speckle noise). Noisy examples are evaluated using models trained with matching noise statistics.
• Figure 3: Test-set Dice coefficients for defect segmentation from the three single-channel inputs ($\mu$, $\sigma$, LE). Top row: $m_x$; bottom row: $m_z$. The left column reports clean-data performance, while the center and right columns show performance versus noise variance for additive Gaussian and multiplicative speckle noise, respectively. For each measure and noise level, results are shown for models trained on clean data and for models trained with matching noisy data, as indicated in the legend.
• Figure 4: U-Net architecture used for defect segmentation. The network consists of a four-level encoder--decoder structure with feature sizes 64--128--256--512 and a 1024-channel bottleneck. Each block contains two $3 \times 3$ convolutional layers with ReLU activation. Downsampling is performed using $2 \times 2$ max pooling, and upsampling using $2 \times 2$ transposed convolutions. Skip connections concatenate encoder feature maps with the corresponding decoder levels. A final $1 \times 1$ convolution maps the features to two output channels (defect and non-defect logits). Numbers indicate feature-channel counts at each resolution level.