The demand for accurate and efficient atomistic simulations and electronic structure calculations in materials science and quantum chemistry has motivated the development of novel computational methodologies. The rapid evolution of machine learning has brought new techniques for advancing the accuracy, efficiency, and predictive power of atomistic simulations and electronic structure calculations.
In this thesis, we explore the symmetry requirements and physics intuitions needed for developing machine-learning interatomic potentials, which are the most critical component in atomistic simulations. Specifically, we introduce a novel physics inspired graph neural network interatomic potential that enables accurate and efficient atomistic simulations of complex materials. The machine learning interatomic potential is trained on multiple datasets of ab initio quantum mechanical calculations, capturing the atomic environment and energy landscapes of various materials.
We also show that the machine learning interatomic potential accurately models the potential energy surface with ab initio accuracy while substantially reducing computational costs compared to ab initio calculations. We also employ machine learning techniques to examine the time-dependent Kohn-Sham system. This non-interacting, single-particle model corresponds to interacting electronic systems in time dependent density functional theory. We derive a “classical” form of the Kohn-Sham equations under the adiabatic approximation, which serves as the basis for constructing a neural network that maps time-dependent electron density to the Kohn-Sham energy functional. We also show that the machine-learned energy functional effectively reproduces the evolution of electron density.