Physically Informed Graph-Based Deep Reasoning Net for Efficient Combinatorial Phase Mapping

Phase mapping is a crucial challenge in materials discovery, which entails determining crystalline phase distribution in condition space based on a collection of X-ray diffraction (XRD) data. This task involves exploring the space of potential phases, identifying existing phases, and determining their respective weight distribution in the condition space while adhering to strict physics constraints. In recent years, there has been a growing interest in leveraging machine learning (ML) techniques to tackle the phase mapping problem. ML methods offer the potential to handle larger and more complex phase mapping instances and provide enhanced accuracy compared to traditional approaches. Among promising ML approaches, DRNets, which formulates the phase mapping problem as an unsupervised pattern demixing problem, represents the current state of the art. Despite its practical effectiveness, DRNets does have certain limitations. For instance, it employs a single multiplicative factor to calculate the stick locations in XRD patterns, which may not accurately reflect the underlying physics of X-ray diffraction. Additionally, DRNets relies on an expensive path-based schema to enforce phase weight smoothness. To overcome these limitations, we propose a novel approach called Physically-informed Graph-based DRNet (PG-DRNet). PG-DRNet incorporates a physical decoder that estimates the crystals' lattice parameters and reconstructs XRD patterns based on Bragg's law. Additionally, we introduce a graph-based schema to enforce phase weight smoothness as well as lattice and peak intensity shift. This graph-based schema provides several advan-tages, including improved computational efficiency compared to the path-based schema utilized in DRNets. To thoroughly evaluate the effectiveness of our approach, we conducted experiments on various chemical systems. Notably, our evaluation went beyond the scope of previous studies that solely focused on varying compositions and extends to explore the additional dimensions of varying annealing time and temperature conditions. Our results demonstrate that PG-DRNet achieves higher accuracy, lower reconstruction loss and significantly faster performance when compared to DRNet results.