Algorithm enhances electronic correlation energy calculations for a wide range of fields

A first-of-its-kind algorithm developed at Georgia Tech is helping scientists study interactions between electrons. This innovation in modeling technology can lead to discoveries in physics, chemistry, materials science, and other fields.

The new algorithm is faster than existing methods while remaining highly accurate. The solver surpasses the limits of current models by demonstrating scalability across chemical system sizes ranging from large to small.

Computer scientists and engineers benefit from the algorithm’s ability to balance processor loads. This work allows researchers to tackle larger, more complex problems without the prohibitive costs associated with previous methods.

Its ability to solve block linear systems drives the algorithm’s ingenuity. According to the researchers, their approach is the first known use of a block linear system solver to calculate electronic correlation energy.

The Georgia Tech team won’t need to travel far to share their findings with the broader high-performance computing community. They will present their work in Atlanta at the 2024 International Conference for High Performance Computing, Networking, Storage and Analysis (SC24), held Nov. 17–22 at the Georgia World Congress Center in Atlanta.

“The combination of solving large problems with high accuracy can enable density functional theory simulation to tackle new problems in science and engineering,” said Edmond Chow, professor and associate chair of Georgia Tech’s School of Computational Science and Engineering (CSE).

Density functional theory (DFT) is a modeling method for studying electronic structure in many-body systems, such as atoms and molecules.

An important concept of DFT models is electronic correlation, the interaction between electrons in a quantum system. Electron correlation energy is the measure of how much the movement of one electron is influenced by the presence of all other electrons.

Random phase approximation (RPA) is used to calculate electron correlation energy. While RPA is very accurate, it becomes computationally more expensive as the size of the system being calculated increases.

Georgia Tech’s algorithm enhances electronic correlation energy computations within the RPA framework. The approach circumvents inefficiencies and achieves faster solution times, even for small-scale chemical systems.

The group integrated the algorithm into existing work on SPARC, a real-space electronic structure software package for accurate, efficient, and scalable solutions of DFT equations. School of Civil and Environmental Engineering Professor Phanish Suryanarayana is SPARC’s lead researcher.

The group tested the algorithm on small chemical systems of silicon crystals numbering as few as eight atoms. The method achieved faster calculation times and scaled to larger system sizes than direct approaches.

“This algorithm will enable SPARC to perform electronic structure calculations for realistic systems with a level of accuracy that is the gold standard in chemical and materials science research,” said Suryanarayana.

RPA is expensive because it relies on quartic scaling. When the size of a chemical system is doubled, the computational cost increases by a factor of 16.

Instead, Georgia Tech’s algorithm scales cubically by solving block linear systems. This capability makes it feasible to solve larger problems at less expense.

Solving block linear systems presents a challenging tradeoff in solving different block sizes. While larger blocks help reduce the number of steps of the solver, using them demands higher computational cost per step on computer processors.

Tech’s solution is a dynamic block size selection solver. The solver allows each processor to independently select block sizes to calculate. This solution further assists in scaling, and improves processor load balancing and parallel efficiency.

“The new algorithm has many forms of parallelism, making it suitable for immense numbers of processors,” Chow said. “The algorithm works in a real-space, finite-difference DFT code. Such a code can scale efficiently on the largest supercomputers.”

Georgia Tech alumni Shikhar Shah, Ph.D., Hua Huang, Ph.D., and Ph.D. student Boqin Zhang led the algorithm’s development. The project was the culmination of work for Shah and Huang, who completed their degrees this summer. John E. Pask, a physicist at Lawrence Livermore National Laboratory, joined the Georgia Tech researchers on the work.

Shah, Huang, Zhang, Suryanarayana, and Chow are among more than 50 students, faculty, research scientists, and alumni affiliated with Georgia Tech who are scheduled to give more than 30 presentations at SC24. The experts will present their research through papers, posters, panels, and workshops.

“The project’s success came from combining expertise from people with diverse backgrounds ranging from numerical methods to chemistry and materials science to high-performance computing,” Chow said. “We could not have achieved this as individual teams working alone.”