Nuclear reactions, from fission in reactors to fusion in stars, depend on interactions between protons and neutrons that are building blocks of atomic nuclei.
Describing all of the nuclei and the reactions between them, however, demands powerful algorithms running on high-performance computers.
The Universal Nuclear Energy Density Functional (UNEDF) collaboration, which was created by the Department of Energy’s Scientific Discovery through Advanced Computing (SciDAC) program, focuses on developing such descriptions.
The UNEDF collaboration includes researchers from seven national laboratories – Ames, Argonne, Lawrence Berkeley, Lawrence Livermore, Los Alamos, Oak Ridge, and Pacific Northwest – and nine universities: Central Michigan, Iowa State, Michigan State, Ohio State, San Diego State, North Carolina at Chapel Hill, Tennessee-Knoxville, Texas A&M in Commerce and University of Washington. Recently, researchers in this collaboration made a significant advance [1]through the use of density functional theory (DFT).
On Earth, only about 300 kinds of nuclei – specific combinations of protons and neutrons – exist. In accelerators and stars, the number of known nuclei grows to about 3,000, and it could eventually expand to around 6,000. Many of these tiny systems prove extremely difficult to study, largely because they live such short lives before decaying.
Consequently, researchers need ways to accurately simulate these elusive species. Other applications also require extremely precise simulations of interacting nuclei. For example, the National Nuclear Security Administration (NNSA) Stockpile Stewardship Program requires such simulations to assess the safety and functionality of the weapons in the U.S. nuclear stockpile.
Witold Nazarewicz, professor of physics at the University of Tennessee and co-director of UNEDF, describes the basic structure: “A nucleus resembles a droplet of liquid, where there’s a high density inside and a surface area where it drops, and there’s little outside.” Moreover, the quantum behavior of the protons and neutrons at that surface determines the energy of the nucleus and how it interacts with other nuclei. “We need to know how the nuclear energy is generated in a nucleus to use it.”
Talented teamwork
DFT provides an extremely useful, but not necessarily easy, approach to modeling nuclei. For one thing, DFT includes many parameters that must be determined. As Stefan Wild, assistant computational mathematician in the Laboratory for Advanced Numerical Simulations at Argonne and a fellow in the Computation Institute at the University of Chicago, asks, “What are the best parameters to calibrate these new models to experimental data?”
In the past, scientists searched for the best parameters with what Wild, an alumnus of DOE’s Computational Science Graduate Fellowship [2], calls “a lot of hand-tuning. They used intuition to pick the values of parameters, ran a simulation, saw how close the answer came to observed data, made small adjustments and ran the simulation again.”
Given the increasing complexity of nuclear simulations, however, “hand-tuning was like looking for a needle in a haystack and far too time consuming to do anything rigorous or thorough.”
As high-performance computing grew more powerful, though, Wild says that “people started thinking about doing something more mathematical” with DFT. For example, Wild and Jorge Moré, an Argonne Distinguished Fellow and director of Argonne’s Laboratory for Advanced Numerical Simulations, developed an algorithm and computer code called POUNDERS (for “practical optimization using no derivatives for sums of squares”).
“This algorithm exploits the mathematical structures of the data-fitting problem and can be run on very general computer simulations,” Wild says.
In the case of DFT, scientists can now use more parameters and optimize their functionals faster and more accurately. “This accelerates the discovery process; what used to take them a year can now be done in two hours,” Wild says.
In part, that comes from the algorithm. “We have to do fewer nuclear simulations because the mathematical algorithm quickly finds better parameter values,” Wild explains. In addition, POUNDERS takes advantage of highly parallel computer architecture. For instance, Wild and his colleagues often run DFT on Argonne’s Fusion cluster, which consists of 2,560 Intel CPU cores and 12 terabytes of memory. By using only about 600 of Fusion’s cores, says Wild, “we can simulate key properties of six dozen nuclei in a minute.”
Getting to that advance, however, took teamwork. As Wild says, “A considerable challenge is bridging the gap between mathematical theory and the actual implementation that works for the physicists.”
As that work continues, Wild asks: “Can you build a single description that predicts properties of nuclei across the entire range of possibilities?” The answer to this question, he says, is “only computationally tractable with the right optimization tools.”
As Wild and his colleagues reported in the August 2010 Physical Review C, they have used POUNDERS to crank out data for 72 nuclei orders of magnitude faster than possible with previous techniques. That work relied on 5,616 cores of a Cray supercomputer called Franklin at the National Energy Research Scientific Computing Center.
Increasing accuracy
Beyond simulating nuclei, this new approach provides measurements of accuracy. “The Argonne team provides us with correlations and error bars on the observables,” Nazarewicz says. As a result, POUNDERS can be used to simulate experiments. “What will happen if I change a particular data point based on the mass? Will this impact the final parameters very much? This will tell us how robust the final fit is.”
The uncertainty in the results also can be used to validate simulations. Nazarewicz explains: “I’d like to use this functional to calculate properties that would be useful to science or, say, for modeling nuclear reactors. I’d like to go to regions of nuclei that have never been, and probably will never be, measured. We’d like to extrapolate.”
In some ways, the extrapolation is underway.
“When we started this project,” Nazarewicz says, “I had limited imagination about what this partnership between computer scientists and applied mathematician can offer.” He quickly adds: “I was very wrong, because it brought us into a completely new world. The resulting progress in science has been transformational.”
Now researchers can simulate more nuclei than ever, faster and more accurately. In addition, the computational power of POUNDERS lets scientists explore nuclear interactions to unveil new aspects of basic science or create new applications.