Benchmarking Machine Learning Approaches for Polarization Mapping in Ferroelectrics Using 4D-STEM

Matej Martinc; Goran Dražič; Anton Kokalj; Katarina Žiberna; Janina Roknić; Matic Poberžnik; Sašo Džeroski; Andreja Benčan Golob

cond-mat.mtrl-sciMar 16, 2026

Benchmarking Machine Learning Approaches for Polarization Mapping in Ferroelectrics Using 4D-STEM

Authors: Matej Martinc, Goran Dražič, Anton Kokalj, Katarina Žiberna, Janina Roknić, Matic Poberžnik, Sašo Džeroski, Andreja Benčan Golob

Organizations: Jožef Stefan Institute, Jamova 39, Ljubljana, Slovenia

Abstract

Four-dimensional scanning transmission electron microscopy (4D-STEM) provides rich, atomic-scale insights into materials structures. However, extracting specific physical properties - such as polarization directions essential for understanding functional properties of ferroelectrics - remains a significant challenge. In this study, we systematically benchmark multiple machine learning models, namely ResNet, VGG, a custom convolutional neural network, and PCA-informed k-Nearest Neighbors, to automate the detection of polarization directions from 4D-STEM diffraction patterns in ferroelectric potassium sodium niobate. While models trained on synthetic data achieve high accuracy on idealized synthetic diffraction patterns of equivalent thickness, the domain gap between simulation and experiment remains a critical barrier to real-world deployment. In this context, a custom made prototype representation training regime and PCA-based methods, combined with data augmentation and filtering, can better bridge this gap. Error analysis reveals periodic missclassification patterns, indicating that not all diffraction patterns carry enough information for a successful classification. Additionally, our qualitative analysis demonstrates that irregularities in the model's prediction patterns correlate with defects in the crystal structure, suggesting that supervised models could be used for detecting structural defects. These findings guide the development of robust, transferable machine learning tools for electron microscopy analysis.

Figures & tables

Figure 1: (a) Crystal structure of orthorhombic KNN viewed along the $[100]_{\rm pc}$ zone axis with a graph showing 8 possible Nb displacement directions, and examples of the corresponding (b) simulated and (c) experimental diffraction patterns.

Figure 2: Methodologies used. The upper part shows standard classification approaches and regression with mapping to classes, while the lower part shows the prototype-representation-based approach.

Dataset	Conv (Reg)	Conv (Cls)	Conv (Proto)	VGG (Reg)	VGG (Cls)	VGG (Proto)	ResNet (Reg)	ResNet (Cls)	ResNet (Proto)	PCA
Synthetic test	$100.0\pm 0.0$	$\mathbf{100.0}\pm\mathbf{0.0}$	$99.6\pm 0.5$	$78.0\pm 26.9$	$70.6\pm 36.0$	$84.2\pm 13.1$	$99.5\pm 0.2$	$99.8\pm 0.3$	$95.4\pm 0.8$	$95.1\pm 0.2$
1S-LU-6x6-20nm	$0.0\pm 0.0$	$43.2\pm 2.7$	$47.5\pm 3.0$	$0.0\pm 0.0$	$41.8\pm 28.8$	$54.3\pm 12.5$	$0.0\pm 0.0$	$\mathbf{63.1}\pm\mathbf{2.2}$	$50.6\pm 3.9$	$24.8\pm 0.0$
Maj. Class	RU	LU	LU	RU	LU	LU	RU	LU	LU	LU
3S-RM-2x2-20nm	$\mathbf{100.0}\pm\mathbf{0.0}$	$\mathbf{100.0}\pm\mathbf{0.0}$	$99.9\pm 0.0$	$99.9\pm 0.2$	$70.6\pm 39.6$	$76.2\pm 17.9$	$100.0\pm 0.0$	$99.8\pm 0.3$	$95.5\pm 2.0$	$97.9\pm 0.1$
Maj. Class	RM	RM	RM	RM	RM	RM	RM	RM	RM	RM
5S-RU-6x6-20nm	$41.8\pm 7.5$	$96.5\pm 1.1$	$95.5\pm 0.7$	$43.9\pm 28.5$	$63.6\pm 36.4$	$77.0\pm 16.5$	$37.9\pm 26.8$	$\mathbf{98.4}\pm\mathbf{0.4}$	$91.0\pm 2.2$	$52.0\pm 0.2$

Table 1: Accuracy (top row) and majority class prediction (bottom row) for the no augmentation and no filtering configuration. The highest accuracy in each row is bolded . Green indicates the predicted majority matches the ground truth, while red indicates a mismatch.

Dataset	Conv (Reg)	Conv (Cls)	Conv (Proto)	VGG (Reg)	VGG (Cls)	VGG (Proto)	ResNet (Reg)	ResNet (Cls)	ResNet (Proto)	PCA
Synthetic test	$96.9\pm 1.0$	$82.0\pm 34.9$	$12.8\pm 0.4$	$12.7\pm 0.3$	$12.4\pm 0.3$	$96.3\pm 1.3$	$98.8\pm 0.5$	$\mathbf{99.7}\pm\mathbf{0.1}$	$14.4\pm 0.4$	$36.7\pm 0.3$
1S-LU-6x6-20nm	$0.0\pm 0.0$	$30.3\pm 15.4$	$10.1\pm 7.9$	$0.0\pm 0.0$	$0.0\pm 0.0$	$\mathbf{51.8}\pm\mathbf{4.0}$	$0.0\pm 0.0$	$51.0\pm 9.8$	$10.4\pm 6.2$	$44.4\pm 0.4$
Maj. Class	RU	LU	MD	RU	MU	LU	RU	LU	RD	LU
3S-RM-2x2-20nm	$87.2\pm 8.3$	$48.6\pm 24.7$	$15.9\pm 3.8$	$24.1\pm 38.8$	$20.0\pm 40.0$	$69.8\pm 3.0$	$\mathbf{88.2}\pm\mathbf{9.0}$	$81.7\pm 9.3$	$14.5\pm 8.7$	$75.4\pm 1.4$
Maj. Class	RM	RM	MD	RU	MU	RM	RM	RM	RD	RM
5S-RU-6x6-20nm	$46.4\pm 9.2$	$54.1\pm 28.4$	$12.5\pm 3.8$	$\mathbf{76.0}\pm\mathbf{38.8}$	$4.0\pm 8.0$	$70.7\pm 1.6$	$48.0\pm 4.8$	$75.0\pm 2.2$	$15.0\pm 8.2$	$68.1\pm 1.1$

Table 2: Accuracy (top row) and Majority Class Prediction (bottom row) for the augmentation and no filtering configuration . The highest accuracy in each row is bolded . Green indicates the predicted majority matches the ground truth, while red indicates a mismatch.

Dataset	Conv (Reg)	Conv (Cls)	Conv (Proto)	VGG (Reg)	VGG (Cls)	VGG (Proto)	ResNet (Reg)	ResNet (Cls)	ResNet (Proto)	PCA
Synthetic test	$96.0\pm 0.9$	$99.3\pm 0.1$	$79.9\pm 6.1$	$98.7\pm 0.5$	$45.0\pm 40.3$	$94.5\pm 4.3$	$98.4\pm 0.6$	$\mathbf{99.5}\pm\mathbf{0.3}$	$92.4\pm 2.1$	$38.8\pm 0.4$
1S-LU-6x6-20nm	$0.0\pm 0.0$	$26.5\pm 9.0$	$15.2\pm 2.5$	$0.0\pm 0.0$	$6.6\pm 8.5$	$\mathbf{32.4}\pm\mathbf{5.8}$	$0.0\pm 0.0$	$24.9\pm 2.5$	$28.2\pm 3.0$	$25.6\pm 0.7$
Maj. Class	RU	LU	LU	RU	MD	LU	RU	LU	LU	LU
3S-RM-2x2-20nm	$62.7\pm 9.5$	$32.0\pm 2.9$	$26.3\pm 3.0$	$\mathbf{73.8}\pm\mathbf{8.8}$	$18.4\pm 22.4$	$35.7\pm 7.4$	$65.6\pm 7.6$	$42.8\pm 3.3$	$34.0\pm 2.9$	$36.6\pm 0.5$
Maj. Class	RM	RM	RM	RM	MD	RM	RM	RM	RM	RM
5S-RU-6x6-20nm	$50.8\pm 9.8$	$33.1\pm 1.5$	$23.5\pm 4.5$	$48.8\pm 13.8$	$14.8\pm 18.4$	$36.6\pm 8.2$	$\mathbf{53.2}\pm\mathbf{8.7}$	$40.4\pm 1.8$	$33.4\pm 2.2$	$36.3\pm 1.1$

Table 3: Accuracy (top row) and Majority Class Prediction (bottom row) for the augmentation and filtering configuration . The highest accuracy in each row is bolded . Green indicates the predicted majority matches the ground truth, while red indicates a mismatch.

Figure 3: Prediction distribution on the synthetic test datasets for the Conv (Proto) and PCA methods with standard deviation across 5 seeds.

Figure 4: Prediction distribution on the experimental test datasets for the Conv (Proto) and PCA methods with standard deviation across 5 seeds.

Figure 5: Polarization classification (different color per each class) for each diffraction pattern in a $128\times 128$ structure across all synthetic structures. We take a majority vote across five seeds for each prediction.

Figure 6: Polarization classification (different color per each class) for each diffraction pattern in a $128\times 128$ structure across all experimental structures for PCA and Conv (Proto). We take a majority vote across five seeds for each prediction.

Figure 7: a) Polarization classification map for the 3S-RM-2x2-20nm. b) Unit cell area, with an overlaid KNN structural model and c) the corresponding electron beam shift vector field calculated from the center of mass (CoM).

Figure 8: Polarization classification (different color per each class) for each diffraction pattern in a $128\times 128$ RD structure with defect across three configurations for Conv (Proto) and PCA approaches.

Sim-to-Real Transfer

Simulation-to-reality transfer adapts models and policies trained in simulation for reliable performance in physical or otherwise real-world settings.

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Materials Science Electron Microscopy Scanning Transmission Electron Microscopy

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Four-dimensional scanning transmission electron microscopy (4D-STEM) records a two-dimensional diffraction pattern at each electron-probe position, yielding spatially resolved reciprocal-space information but large, heterogeneous data volumes. Here we describe 4D-ImageNet, a collection of 174,000 diffraction patterns comprising 145,000 experimental patterns selected from 29 acquisitions and 29,000 multislice simulations. The experimental data cover acquisition-level labels for Ag, Au, mixed Au-Ag, CoO, Pd and ZnO specimens across multiple fields of view, scan dimensions, camera lengths and exposure times. Each acquisition contributes 5,000 quality-ranked patterns with source scan coordinates and acquisition metadata. A set-prediction detector provides model-derived pseudo-labels for the direct-beam position and Bragg-disk centres, with a confidence score for each disk. The simulation data cover 13 crystal structures and include Euler rotations, reciprocal-space sampling and approximate low-index beam directions. A grouped mixed-domain masked-reconstruction benchmark is provided to assess leakage-resistant loading and evaluation across experimental and simulated data. The dataset is intended for representation learning, disk detection, diffraction-pattern retrieval, orientation analysis and simulation-to-experiment studies.

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Abstract

Sim-to-Real Transfer

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