Exploring causal physical mechanisms via non-gaussian linear models and deep kernel learning: applications for ferroelectric domain structures

TL;DR

This paper introduces a novel analysis framework combining linear causal models and deep kernel learning to uncover physical mechanisms and relationships in complex multimodal imaging data, specifically applied to ferroelectric domain structures.

Contribution

It develops a new causal analysis method for Piezoresponse Force Microscopy data and extends it with deep kernel learning to predict physical properties from domain structures.

Findings

Linear causal analysis reveals relationships between PFM observables and material properties.

Deep kernel learning accurately predicts morphology and physical parameters from imaging data.

The approach uncovers mutual interactions between surface conditions and material properties.

Abstract

Rapid emergence of the multimodal imaging in scanning probe, electron, and optical microscopies have brought forth the challenge of understanding the information contained in these complex data sets, targeting both the intrinsic correlations between different channels and further exploring the underpinning causal physical mechanisms. Here, we develop such analysis framework for the Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain non-observed properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that this approach can be extended to complex descriptors using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc. at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. This analysis is universal and can be extended to explore the correlative relationships of other multi-channel datasets.