**Simon Billinge**

**Professor of Applied Physics, Applied Mathematics and Materials Science**

**Columbia University, New York**

**Scientist, Brookhaven National Laboratory, Upton, New York**

Prof. Billinge earned his Ph.D. in Materials Science and Engineering from University of Pennsylvania in 1992, following a BA at Oxford University. He spent 2 years at Los Alamos National Laboratory in New Mexico as a post-doc before joining the faculty as an Assistant Professor in the Department of Physics and Astronomy at Michigan State University in 1994. He became Associate professor in 1999 and full professor in 2003. In 2008 he took up his current position as Professor of Applied Physics, Applied Mathematics and Materials Science at Columbia University and Scientist at Brookhaven National Laboratory.

His research focuses on the study of local-structure property relationships of disordered crystals and nanocrystals using advanced x-ray and neutron diffraction techniques. In particular he is a leader in the development of the atomic pair distribution function (PDF) method applied to complex materials. These methods are applied to the study of nanoscale structure and its role in the properties of diverse materials of interest, for example, in energy, catalysis, environmental remediation and pharmaceuticals. A major activity is the study of the nanostructure inverse problem (NIP) where the goal is to obtain the 3D arrangement of atoms from structures with nanoscale atomic structures from scattering data. It is a non trivial ill-posed inverse problem that requires novel applied math and computational approaches to solve.

Prof. Billinge has published more than 200 papers in scholarly journals. He is a fellow of the American Physical Society and the Neutron Scattering Society of America, a former Fulbright and Sloane fellow and has earned a number of awards including being honored in 2011 for contributions to the nation as an immigrant by the Carnegie Corporation of New York, the 2010 J. D. Hanawalt Award of the

International Center for Diffraction Data, University Distinguished Faculty award at Michigan State, the Thomas H. Osgood Undergraduate Teaching Award. He is Section Editor of Acta Crystalographica Section A: Advances and Foundations. He regularly chairs and participates in reviews of major facilities and federally funded programs.

**Abstract**

**THE MATERIALS COMPLEXITY FRONTIER: APPLIED MATH AND COMPUTATIONAL CHALLENGES**

S. J. L. Billinge^{1},^{2}*,

^{1}Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027

^{2}Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973

*email: sb2896@columbia.edu

Many modern materials under study for technologies from energy to the environment to health, are highly complex, often heterogeneous and nano structured. Just as nature uses highly complex proteins to design in highly specific functionality, our synthetic materials, both inorganic and organic, are also increasing in complexity. A full understanding of the structure-property relationship requires us to go beyond traditional crystallography and to study the local structure, which is a major experimental challenge. There are recently emerging powerful experimental developments, for example, using the atomic pair distribution function technique (PDF), among others. However a general problem is that the information content in the data is limited, and often decreases with increasing structural complexity of the material, whereas the degrees of freedom needed to fully describe the structure increase. This rapidly leads to an information gap, and the nanostructure inverse problem becomes ill-posed. This is a critical bottleneck for understanding materials at the complexity frontier. It is an applied math and computational problem as much as an experimental one, and one where modern computation and AM developments such as uncertainty quantification, can be expected to have a transformative role. I will discuss some of these issues and our efforts to address them, highlighting our computational and algorithmic needs.

I will describe Complex Modeling which is an attempt to close the information gap in cases where the inverse problem is ill posed. This requires encoding and complexing data sources that are complementary to the basic scattering data to arrive at a robust and unique structure solution. We are exploring the use of data analytical approaches to address this problem. Application of data analytics approaches to extract information from physical data from materials is a relatively novel activity, distinct from materials prediction using theoretical approaches such as DFT, but in my view equally important.