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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Organic mixed ionic electronic conductors (OMIECs) are a promising class of polymer materials for applications spanning neuromorphic computation to energy efficient electronics and bioelectronics. Despite being highly tunable, the relationship between structural features and key performance properties such as charge carrier mobility is poorly understood. Scanning nanodiffraction in the transmission electron microscope (TEM) is a powerful probe for elucidating this structure-property relationship, but produces large, noisy datasets that are difficult to interpret because polymer reflections exhibit several distinct morphologies. To address the complexity, we trained a machine learning (ML) model to detect these polymer diffraction peaks and their intensities from synthetic data. Compared to correlative peak detection algorithms, the conventional method for analyzing nanobeam 4D scanning transmission electron microscopy (4DSTEM) data, we show that the ML model is significantly faster and outperforms correlative algorithms in almost all cases, opening up the possibility of near-live visualization of 4DSTEM experiments.

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