Bayesian Compressive Sensing in Materials Science Computer Experiments

Economic progress depends critically on the high-performance materials such as lightweight alloys, high-energy-density battery materials, recyclable motor vehicle and building components, and energy-efficient lighting.  Industrial growth areas depend, in part, on fundamental understanding of materials science and the atomic particle behavior. We discuss the role of statistical model selection in complex computational models of crystal structure in material properties. Density functional theory suggests that the stationary electronic state can be expressed through many-electron time-independent Schrödinger equation and this presents a high dimensional model selection problem.  The cluster expansion formulation allows rapid assessment of a wide variety of alloy combinations and prediction of important materials science properties.  We propose a Bayesian compressive sensing approach to perform model selection in the sparse basis formed by the cluster expansion based on computer experiments run with ab initio codes (VASP). The methods are illustrated by applying the  approach to two common alloy systems and extensions to 700 other systems are discussed.  The value in the methodology is that physically interpretable bases and sparseness prior implementations are demonstrated to be faster and more feasible for large systems with small training datasets.