Machine learning for quantum chemistry has been gaining much traction in recent years. In this thesis, we address the problem of predicting the ground state energy from a collection of atoms defined by their positions and charges. The ground state energy of an atomic structure is invariant with respect to isometries and permutations. Additionally the energy is multiscale in nature and varies smoothly with movements of the atoms. We develop a wavelet scattering model which encodes all of these properties and scales better than commonly used computational chemistry models. We first demonstrate that this representation has excellent predictive ability on amorphous lithium silicon structures. We extend this model and improve its generalizability as displayed by predictions on several types of lithium silicon systems which are not included in the model training. Finally we take some of the principles from the wavelet scattering approach and apply them to a graph based model to generate a rich representation. This requires developing novel ways to encode the bond angle and multiscale aspects of the atomic structure for the graph. We test this model on a data set of quantum molecular dynamics simulations and get results that are competitive with the state of the art.
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