CbLDM: A Diffusion Model for recovering nanostructure from atomic pair distribution function

Abstract

The nanostructure inverse problem is an attractive problem that helps researchers to understand the relationship between the properties and the structure of nanomaterials. This study focuses on the problem of recovering the model system of monometallic nanoparticles (MMNPs) from their pair distribution function (PDF) and regards it as a highly ill-posed conditional generation task. This study proposes a Condition-based Latent Diffusion Model (CbLDM) as a feasible solution to this problem. This model demonstrates an acceleration approach within the framework of a latent diffusion model by using conditional priors to estimate the conditional posterior distribution, which is an approximate distribution of p(z|x). In addition, this study uses Laplacian matrix instead of distance matrix to recover the nanostructure, which helps to improve stability. Our study demonstrates that a latent diffusion model with a conditional prior can generate nanostructures that are consistent with PDF observations and physically meaningful, thereby laying the groundwork for subsequent more complex inverse problems.

Figures (11)

• Figure 1: CbLDM Model Architecture
• Figure 2: The simulated dataset generated seven structure types of data structures, and the number of different types is shown in the figure.
• Figure 3: Representative results of CbLDM on simulated data from seven structural types. Each unit consists of three components: the upper-left image shows the reference atomic structure, the lower-left image shows a structure generated by CbLDM, and the right image compares the corresponding PDFs, together with the residual curve and the associated $R_{wp}$ value. The blue curve denotes the reference PDF, while the red curve denotes the PDF calculated from the generated structure. For clarity, the residual curve is vertically shifted downward.
• Figure 4: The prediction results of different models on the validation dataset for the Oct structure are illustrated in this figure. From top to bottom and from left to right, the figure presents the ground-truth Oct structure, followed by the predictions generated by CbLDM, MLP, CNN, ResNet, Transformer, DeepStruc (CVAE), and MLstructureMining (XGBoost). The first and fourth columns indicate the corresponding model names, the second and fifth columns display the reconstructed atomic structures, and the third and sixth columns show the associated PDFs.
• Figure 5: The phenomenon of two seemingly different structures with the similar PDFs. The top left and bottom left are the two atomic structures, and the right is the comparison of PDFs, the residual and $R_{wp}$.