Competition between order parameters in a material can induce fascinating properties, but also makes these materials difficult to study, and their properties difficult to predict. Ziatdinov et al. applied machine learning techniques to analyze competing order parameters in Sm-doped BiFeO3, allowing them to parse high-resolution microscopy data for new, interesting physics.

The researchers studied samples of the multiferroic material BiFeO3, where each sample had a different concentration of Sm doping. This difference in concentration induced phase transitions, and the team observed the corresponding structural changes on the atomic level using high-resolution electron microscopy.

“This allowed us to fly through the compositional space of the system and see how the change of concentration resulted in complex structures at the phase transition,” Ziatdinov said.

The researchers then used Gaussian Process (GP) regression, a probabilistic machine learning algorithm, to establish a correlative relationship between two sets of parameters, such as the atomic coordinate within a lattice and the local polarization. Notably, the predictions made by this machine learning model come with well-defined uncertainties, which can illuminate the significance of a prediction, or the significance of a deviation from expected behavior.

Deviations where the correlations between parameters are broken are what they’re looking for, Ziatdinov said. “In places where we didn’t expect to see anything unusual, these measurements tell us that there is something interesting going on. It’s like seeing ocean waves break above an underwater stone, but you cannot see the stone.”

These probabilistic machine learning techniques can be used to discover novel physical processes in both experimental data and theoretical models, and the team plans to develop and deploy more advanced algorithms, such as Bayesian neural nets.

Source: “Predictability as a probe of manifest and latent physics: The case of atomic scale structural, chemical, and polarization behaviors in multiferroic Sm-doped BiFeO3,” by Maxim Ziatdinov, Nicole Creange, Xiaohang Zhang, Anna Morozovska, Eugene Eliseev, Rama K. Vasudevan, Ichiro Takeuchi, Chris Nelson, and Sergei V. Kalinin, Applied Physics Reviews (2021). The article can be accessed at