As we try and find new technologies to solve some of mankind's toughest challenges such as abundant sustainable energy, environmental remediation, and health, we are increasingly seeking more and more complex materials. We already have devices that turn sunlight into electricity and use sunlight to split water into precious hydrogen fuel, but issues such as device efficiency and cost mean that the current technologies cannot be taken to the vast scale needed for our modern needs. This puzzle may be solved by the use of advanced materials that perform their tasks - energy conversion, cancer cell killer, or whatever it may be - with greater efficiency. This is inevitably leading us towards more complicated materials that consist of many different chemical elements and have engineered structures on multiple different length-scales from the atomic to the nano- and meso-scales all the way to macroscopic scales. The problem is that, because of their complexity, it becomes very difficult to even characterize these materials when we have made them, let alone design and engineer them at the nanoscale. Our usual tools based on the scattering of x-rays by crystals stop working for such nanoscale structures. The problem is not that we lack powerful enough x-ray beams. The problem is that the x-ray scattering signal from these complicated materials doesn't contain enough information to allow us to find a unique structure solution. It is as if we are looking at complex patterns of atomic arrangements through blurry, steamed up glasses. This project will bring greater clarity to this situation by marrying together advances in applied mathematics from diverse areas such as image recognition, information theory and machine learning, which are having transformative impacts in commerce, law enforcement and so on, and applying them to the problem of recognizing atomic arrangements in materials of the highest complexity.
approach will to solve multi-scale structures of materials by marrying together the latest advances in the processing of x-ray scattering data from nanomaterials, such as atomic pair distribution function (PDF) analysis, with other sources of input information such as small angle scattering, EXAFS and other spectroscopies, as well as inputs from first principle theory such as DFT, but place them in a rigorous mathematical framework and a robust computational framework such that the information content in the data may be utilized to the greatest extent possible whilst taking into account uncertainties from statistical and systematic uncertainties. The mathematical framework will utilize the latest developments in stochastic optimization, uncertainty quantification including function-space Bayesian methods, machine learning and image recognition.
