It is essential to achieve an optimal balance between computational accuracy and efficiency in order to fully exploit the potential of simulations conducted on massively parallel supercomputers. This study presents a design to accelerate and scale the resolution of large-scale sparse linear systems, which has the potential to facilitate routine materials science investigations on exascale clusters. This study is based on a two-pronged strategy, comprising the development of a spectral predictor system and the utilisation of an extensive database housing matrices that encapsulate the essence of the surrogate space within the materials domain. The management of the scale and intricacy of these systems, the optimisation of scalability on parallel architectures, and the addressing of the complexities of real-world materials are the biggest challenges in this field. While conventional approaches are efficacious to a certain extent, they are often constrained by scalability limitations, thereby necessitating the development of innovative strategies to overcome these barriers. The spectral predictor system employs deep learning techniques to prognosticate spectral properties vital for efficient linear system solving, while the expansive matrix dataset captures the spectrum of patterns inherent in materials science computations. The linear scaling of Density Functional Theory (DFT) codes, exemplified by BigDFT, will enable the simulation and analysis of intricate material systems with unparalleled precision and computational efficacy.
The efficacy of this study is contingent upon the implementation of a two-pronged approach, comprising the development of a spectral predictor system and the curation of an extensive database encompassing matrices reflective of the surrogate space within the materials domain. The spectral predictor system, which leverages intricate neural network architectures and broad training datasets, offers unparalleled accuracy and predictive capability. The recommender system, which accelerates and scales up the resolution of large-scale sparse linear systems, empowers simulations involving hundreds of thousands of atoms. This is not possible on current pre-exascale clusters. Furthermore, through the linear scaling of Density Functional Theory (DFT) codes, exemplified by BigDFT, access to a powerful toolkit is provided for simulating and analysing complex material systems with precision and computational efficiency. This capability not only facilitates the exploration of fundamental material properties but also benefits the design and optimisation of materials for diverse applications such as catalysis, energy storage, and electronic devices.