Sequential piezoresponse force microscopy and the ‘small-data’ problem

Abstract

The term big-data in the context of materials science not only stands for the volume, but also for the heterogeneous nature of the characterization data-sets. This is a common problem in combinatorial searches in materials science, as well as chemistry. However, these data-sets may well be 'small' in terms of limited step-size of the measurement variables. Due to this limitation, application of higher-order statistics is not effective, and the choice of a suitable unsupervised learning method is restricted to those utilizing lower-order statistics. As an interesting case study, we present here variable magnetic-field Piezoresponse Force Microscopy (PFM) study of composite multiferroics, where due to experimental limitations the magnetic field dependence of piezoresponse is registered with a coarse step-size. An efficient extraction of this dependence, which corresponds to the local magnetoelectric effect, forms the central problem of this work. We evaluate the performance of Principal Component Analysis (PCA) as a simple unsupervised learning technique, by pre-labeling possible patterns in the data using Density Based Clustering (DBSCAN). Based on this combinational analysis, we highlight how PCA using non-central second-moment can be useful in such cases for extracting information about the local material response and the corresponding spatial distribution.

From DFT to machine learning: recent approaches to materials science–a review

“…Another technique is the subgroup discovery, which finds local structure in data, as opposed to mapping a unique global relationship [449]. And the recent multi-fidelity learning which aims to be applied to small datasets, where in order to enhance the sampling and therefore learning capacity, one can combine lower precision data to overcome the scarcity of higher precision data [450].…”

Recent Advance of Machine Learning in Selecting New Materials

“…针对材料中 的数据量相对较少的问题. 在保证精度以及普适性的前 提下, 建立和发展精确的小数据分析模型 [126][127] 是目前 研究者亟待解决的问题, 例如迁移学习 [128] 、元学习 [129] 、 神经网络图灵机 [130] 、贝叶斯框架 [131] 等多种学习模 型 [132][133][134][135] .…”

Voting Data-Driven Regression Learning for Accelerating Discovery of Advanced Functional Materials and Applications to Two-Dimensional Ferroelectric Materials

“…AHC can identify the candidates similar to the cluster with high ionic conductivity through training on all materials containing lithium ion, 37 and PCA could extract actionable information for phase transition 38 and magnetoelectric effect. 39 We utilized AHC method to train a bottom-up clustering model of 2135 2D HBCs with only features based on element-related properties of the constituent atoms. It turns out that this large family can be classified into three clusters, as shown in Fig.…”

“…Unlike supervised machine learning that makes accurate predictions for the targeted materials properties or labels through training on the data set with existing properties or labels, unsupervised machine learning could draw boundaries between different clusters and extract information from the features regardless of whether the properties or labels exist or not, such as agglomerative hierarchical clustering algorithm (AHC) and principal component analysis (PCA) . AHC can identify the candidates similar to the cluster with high ionic conductivity through training on all materials containing lithium ion, and PCA could extract actionable information for phase transition and magnetoelectric effect . We utilized the AHC method to train a bottom-up clustering model of 2135 2D HBCs with only features based on element-related properties of the constituent atoms.…”