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.

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

Newly-discovered materials have been central to recent technological advances. They have contributed significantly to breakthroughs in electronics, renewable energy and green buildings, and overall, have promoted the advancement of global human welfare. Yet, only a fraction of all possible materials have been explored. Accelerating the pace of discovery of materials would foster technological innovations, and would potentially address pressing issues in sustainability, such as energy production or consumption. The bottleneck of this discovery cycle lies, however, in the analysis of the materials data. As materials scientists have recently devised techniques to efficiently create thousands of materials and experimentalists have developed new methods and tools to characterize these materials, the limiting factor has become the data analysis itself. Hence, the goal of this paper is to stimulate the development of new computational techniques for the analysis of materials data, by bringing together the complimentary expertise of materials scientists and computer scientists. In collaboration with two major research laboratories in materials science, we provide the first publicly available dataset for the phase map identification problem. In addition, we provide a parameterized synthetic data generator to assess the quality of proposed approaches, as well as tools for data visualization and solution evaluation.