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Pie Chart

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A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each indicating numerical proportions. It is also used to show the relative sizes of data in a single chart.
In a pie chart, the central angle, the arc length of each slice, and the area are directly proportional to the quantity or percentage it represents. Some real-world examples that can be depicted using pie charts include marks obtained by students...
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Interpretable Machine Learning for the Design of (K, Na)NbO3-Based Piezoceramics Using Combinatorial and

Heng Hu1, Bin Wang1, Didi Zhang1

  • 1State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.

ACS Applied Materials & Interfaces
|October 14, 2025
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Summary

This study introduces an interpretable framework using machine learning to identify key features for enhancing piezoelectric properties in potassium sodium niobate (KNN) ceramics. The findings guide the rational design of KNN materials for improved performance.

Keywords:
feature engineeringinterpretable machine learningmaterials descriptorspiezoceramicspotassium−sodium niobate

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Area of Science:

  • Materials Science
  • Ceramics Engineering
  • Computational Materials Science

Background:

  • Potassium sodium niobate (KNN)-based ceramics exhibit promising piezoelectric properties, crucial for sensor and actuator applications.
  • Enhancing KNN piezoelectricity via chemical modification is effective but lacks efficient screening methods for optimal dopant selection.
  • Machine learning (ML) offers potential for predicting piezoelectric performance but often lacks interpretability.

Purpose of the Study:

  • To develop an interpretable framework for identifying critical features influencing piezoelectric constant (d33) in KNN ceramics using ML.
  • To quantitatively analyze the impact of material features on d33 predictions, uncovering nonlinear and interactive effects.
  • To create combinatorial descriptors for improved ML model performance and interpretability in KNN material design.

Main Methods:

  • Utilized Shapley Additive exPlanations (SHAP) to analyze feature importance and interactions in ML models predicting d33.
  • Employed Sure Independence Screening and Sparsifying Operator (SISSO) to generate combinatorial descriptors from key features.
  • Trained and evaluated ML models using individual features and novel combinatorial descriptors, assessing performance metrics like MAE and R^2.

Main Results:

  • Identified critical features and their tipping points (e.g., sintering temperature) that significantly influence KNN piezoelectricity (d33).
  • Developed combinatorial descriptors that exhibit approximate linearity with d33, enabling transparent linear models.
  • Achieved high performance with ML models incorporating combinatorial descriptors, reaching MAE < 30 pC/N and R^2 > 0.9.

Conclusions:

  • The developed interpretable framework effectively guides the rational design of KNN-based ceramics for enhanced piezoelectric performance.
  • Feature engineering through combinatorial descriptors significantly improves both the interpretability and predictive accuracy of ML models.
  • This feature-centric approach provides valuable insights into the complex mechanisms governing piezoelectric enhancement in KNN materials.