Abstract:
Molecular dynamics is an e ective numerical simulation technique for investigating material behavior at an atomistic scale, where simulated motions of atoms and molecules within a physical system are governed by Newtonian mechanics. A primary concern in these simulations is to accurately calculate the potential energy surface of a chemical environment as this hypersurface is then di erentiated to calculate the atomic forces. These potential energy surfaces are de ned either using pre-de ned analytical expressions or carrying out rst-principle calculations based on the electronic structure of the system. The former is computationally inexpensive and therefore suitable for reaching large length and time scales with a compromise on accuracy, whereas the latter is restricted only to small systems containing few hundred atoms at most due to the tremendous computational burden but o ers high accuracy. Recently, machine learning potentials emerged as a third option to predict potential energy surfaces using nonlinear regression. These potentials are purely data driven and rely on reconstructing the map between chemical environments and corresponding potential energy surfaces, and promise high accuracy and e ciency at the same time. A major step towards developing a machine learning potential is to describe chemical environments in terms of some real-valued numbers, called `descriptors'. The performance and accuracy of the nal potential strongly depends on the performance and accuracy of the description. Despite this vital importance, however, no canonical set of descriptors has yet appeared in the literature as a solid base that could satisfy all the desired mathematical properties for a robust description. In this thesis, a novel set of descriptors, referred to as `Spherical Bessel descriptors', is introduced that are symmetrically invariant, continuous, di erentiable and optimally complete; this is a set of features that does not appear to be satis ed completely by any alternative. A systematic approach for testing completeness behavior in descriptors is devised. The performance of the presented Spherical Bessel descriptors is further validated in molecular dynamics simulations using neural network potentials, and compared to other commonly used descriptors in the literature.
