Machine-learning accelerated Kohn-Sham calculations at extreme conditions

We discuss algorithms in the open-source SPARC electronic structure code [1] enabling systematically convergent Kohn-Sham calculations of isolated and extended systems, insulating as well as metallic, from one to a million atoms [2], from ambient conditions to plasma [3,4]. Key ideas include high-order discretization on a uniform real-space mesh to enable systematic convergence and computational locality for efficient parallel implementation; local formulation of electrostatics; polynomial filtering for eigenvector refinement in diagonalization based calculations to eliminate longstanding preconditioning bottlenecks; Spectral Quadrature (SQ) and Spectral Partition (SP) methods for Kohn-Sham calculations at extreme conditions; and machine learning acceleration. We discuss comparisons to established planewave codes and applications to warm- and hot-dense matter at temperatures up to a million kelvin.

    This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

[1] https://github.com/SPARC-X/SPARC.

[2] Suryanarayana, Xu, Pask, in Gavini et al., Model. Simul. Mater. Sci. Eng. 31, 063301 (2023).

[3] Sadigh, Aberg, Pask, Phys. Rev. E 108, 045204 (2023).

[4] Suryanarayana, Bhardwaj, Jing, Kumar, Pask, Phys. Plasmas 32, 033905 (2025).