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Machine learning (ML) accelerates the rational design and discovery of materials, where the feature plays a critical role in the ML model training. We propose a low-cost electron probability waves (EPW) descriptor based on electronic structures, which is extracted from highsymmetry points in the Brillouin zone. In the task of distinguishing ferromagnetic or antiferromagnetic material, it achieves an accuracy (ACC) at 0.92 and an area under the receiver operating characteristic curve (AUC) at 0.83 by 10-fold cross-validation. Furthermore, EPW excels at classifying metal/semiconductors and judging the direct/indirect bandgap of semiconductors. The distribution of electron clouds is an essential criterion for the origin of ferromagnetism, and EPW acts as an emulation of the electronic structure, which is the key to the achievements. Our EPW-based ML model obtains ACC and AUC equivalent to crystal graph features-based deep learning models for tasks with physical recognitions in electronic states.

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