![]() Another critical drawback for ML methods is the lack of laws, understanding, and knowledge from their use because ML methods are treated as black box 6. ![]() Such limitations include, but are not limited to, measurement error 22, lack of generality and precision, reliance on high-quality data 23, inability to determine high level concept 24, prone to artifact 25, good in interpolation but poor in extrapolation 21, 26. Though ML is highly efficient, it has some limitation which reduces its accuracy in predicting properties. ![]() For example, ML models have been used for the prediction of mechanical properties of metal alloy 14, 15, band gap of crystals 16, 17, the formation energies of crystals 18, 19, 20, melting temperature of binary inorganic compounds 21. With given data, ML algorithms learn the rules and relationship that underlie a dataset by assessing the data and build a model to make prediction 13. The idea behind the use of ML methods for structure properties prediction is to analyze and map the relationship between the properties of materials and their characteristics by extracting information from existing data without knowing any explicit knowledge on how to draw conclusion from those data 12. Such input representation is known as descriptors or features. ![]() Generally speaking, the accuracy of a ML model depends on the effective input representation of the crystal structures, since the atomic positions are not suitable for direct input representation because they are not rotationally and translationally invariant 11. ML methods have been extensively used for materials properties prediction over the past decade, because ML models can be trained to have high efficiency and accuracy close to DFT 9, 10. Machine learning (ML) methods offer the possibility of bridging this gap 7, and the application of ML has already help in speeding the process for material discovery 8. Because of the computational cost of density functional theory (DFT) and the less accuracy of classical potential, an intuitive idea is to bridge the gap between DFT-level accuracy and classical-level efficiency. In contrast, prediction at the classical level (such as classical molecular dynamics) is highly efficient but less accurate since they usually scale linearly with the number of atoms 5, 6. However, high-throughput screening prediction at the quantum level (first principles) is, although highly accurate, less efficient, and hence time consuming and computationally expensive 3, 4. In the past decade, material scientists have been favorably using high-throughput screening for structure property prediction with high accuracy in searching for promising materials 3. The term extreme is defined as something farthest or of highest degree, which in terms of mechanical properties of materials imply unusual properties such as ultrahigh hardness 1 and extremely negative Poisson’s ratio 2. The algorithm is very promising for future materials discovery that can push materials properties to the limit with minimal DFT calculations on only ~1% of the structures in the screening pool. By screening 85,707 crystal structures, we identify 21 ultrahigh hardness structures and 11 negative Poisson’s ratio structures. We test the loop of training-recommendation-validation in mechanical property space. Validated data are then added into the training dataset for next round iteration. We use Stein novelty to recommend outliers and then verify using DFT. This combination not only improves the efficiency for screening large-scale materials with minimal DFT inquiry, but also yields properties beyond original training range. We deployed a boundless objective-free exploration approach to combine traditional ML and density functional theory (DFT) in searching extreme material properties. Despite the machine learning (ML) methods have been largely used recently, the predicted materials properties usually cannot exceed the range of original training data.
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