# Lin Lin of UC Berkeley Receives the 2017 SIAG/CSE Early Career Prize

Dr. Lin Lin of UC Berkeley was awarded the 2017 SIAG/CSE Early Career Prize, March 2, at the SIAM Conference on CS&E (CSE17) in Atlanta, Georgia.

Dr. Lin is assistant professor in the Department of Mathematics at UC Berkeley and a faculty scientist at Lawrence Berkeley National Laboratory. He received his PhD in applied and computational mathematics from Princeton University in 2011.

The prize honors him for his significant contributions to numerical methods and high-performance computational tools for materials science, enabling scalable electronic structure calculations.

This is the first award of the SIAG/CSE Early Career Prize, which will be awarded every two years at the CSE conference.

SIAG/CSE awards the prize to an outstanding early career researcher in the field of CSE for distinguished contributions to the field within seven years of PhD. It is awarded for a significant research contribution to the development and use of mathematical and computational tools and methods for the solution of science and engineering problems. The award recognizes an individual who has made outstanding, influential, and potentially long-lasting contributions within seven years of receiving the PhD as of January of the year of the award.

### Why are you excited to be winning the prize?

I am greatly honored to receive the SIAM CSE Early Career prize. While electronic structure theory has been playing a major role in computational quantum physics, chemistry, and materials science for decades, this field has not received much attention within SIAM until relatively recently. Personally, I found electronic structure theory very attractive for a number of reasons. First, it has amazing predictability for a vast range of scientific and engineering problems, from spectroscopic measurements to chemical reactions to materials design, all requiring only the most fundamental inputs such as atomic species and atomic positions. Second, as Dirac pointed out nearly a century ago, the "true answer" to electronic structure theory is out there: the solution to the many body Schrodinger equation. This makes electronic structure theory a well-defined mathematical problem. Third, the solution to the many-body Schrodinger equation is extremely complex. This calls for new mathematical and numerical techniques to solve it, and it has been widely acknowledged that high performance computing will play an increasingly important role. Hence I think electronic structure theory is a natural and beautiful subject for applied mathematics, and the CSE community can potentially make significant contribution to this important field. I feel greatly encouraged that the community recognizes my work in electronic structure theory, and I sincerely hope to see that this field will continue to grow rapidly within SIAM.

### What does your research mean to the public?

First principle electronic structure theories, particularly represented by Kohn-Sham density functional theory (KSDFT), have been developed into workhorse tools with a wide range of scientific applications in chemistry, physics, materials science, and biology. Both ground state and excited state electronic structure calculations are revolutionizing processes such as chemical synthesis, materials design and discovery. However, tackling increasingly larger and more complicated systems presents new challenges: we need to design far more efficient numerical

algorithms. Progress of new numerical algorithms may significantly accelerate the design of next-generation materials in e.g. batteries, clean water generation, solar energy harvest, and waste heat recovery.

### Could you tell us a bit about the research that won you the prize?

My approach to these challenges has been to focus on the core difficulty in physics problems, and to weave physical insights together with new techniques in applied mathematics and high performance computing. As an example, the solution of the Kohn-Sham density functional theory (KSDFT) typically requires solving a large number of eigenvalues and eigenfunctions. As a result, the computational complexity scales cubically with respect to the number of atoms in the system. Our pole expansion and selected inversion (PEXSI) approach reformulates KSDFT using a Green's function formalism, and can accurately solve KSDFT without involving any eigenvalue or eigenfunction. The PEXSI method reduces the computational complexity to at most quadratic with respect to the number of atoms, and enables first principle computation of difficult metallic systems, especially low-dimensional quantum systems, with more than ten thousand atoms. One key aspect of the success of the PEXSI method is its scalability: it can efficiently utilize more than 100,000 processors on high performance computers, which reduces the time-to-solution for large scale quantum systems by orders of magnitude.

### What does being a SIAM member mean to you?

I have been a SIAM member since I was a graduate student, and have been actively participating in a number of SIAM conferences series such as CSE, MS, LA, PP and OPT. SIAM conferences have always been a valuable source for me to meet with people within and beyond my field, to broaden my view, and to seek for new possibilities of collaboration.