Deep Bayesian local crystallography

Abstract

The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume of information on materials structures, structural distortions, and physical functionalities. Harnessing this knowledge regarding local physical phenomena necessitates the development of the mathematical frameworks for extraction of relevant information. However, the analysis of atomically resolved images is often based on the adaptation of concepts from macroscopic physics, notably translational and point group symmetries and symmetry lowering phenomena. Here, we explore the bottom-up definition of structural units and symmetry in atomically resolved data using a Bayesian framework. We demonstrate the need for a Bayesian definition of symmetry using a simple toy model and demonstrate how this definition can be extended to the experimental data using deep learning networks in a Bayesian setting, namely rotationally invariant variational autoencoders.

Latent Mechanisms of Polarization Switching from In Situ Electron Microscopy Observations

“…Previously, we applied the rVAE approach to explore the evolution of atomic‐scale structures in graphene under electron beam irradiation, [ 43 ] analyze the self‐assembly of protein nanorods, [ 44 ] investigate the domain wall dynamics in piezoresponse force microscopy, [ 45 ] and create a bottom‐up symmetry analysis workflow for atom‐resolved data. [ 46 ] Here, we demonstrate that this approach can be extended to explore domain evolution mechanisms via detailed analysis of the latent spaces of rVAE.…”

Automated Experiment in 4D-STEM: Exploring Emergent Physics and Structural Behaviors

“…Using deep kernel learning, we enable discovery of the behaviors of interest driven by the internal fields and demonstrate this approach for twisted bilayer graphene and mesoscale-ordered patterns in the MnPS 3 . We also note there are opportunities to increase the rate of the training by using preacquired data to train invariant variational autoencoders 39 and then use the pretrained weights to initialize the DNN part of the DKL. Similarly, the interventional strategies utilizing the knowledge derivable from physical deconvolution of the 4D-STEM patterns can be used to structure the latent space via conditioning or bootstrapping strategies, hence allowing for a more directed physical search.…”

Bayesian optimization in continuous spaces via virtual process embeddings

“…We subsequently explore the encoding of the generated functions into a low dimensional latent space via the variational autoencoder described in our previous works. 25,[32][33][34][35] Here, the trajectories generated as described above act as the input to the VAE. The VAE then builds the smooth encoding of trajectories, where the trajectories are mapped to an n-dimensional continuous latent space.…”