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UBC Theses and Dissertations

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UBC Theses and Dissertations

Implementation of a nonlinear Atomic Cluster Expansion Ross, Andres


In this thesis, we present a proof of concept implementation of linear and nonlinlear models based on the Atomic Cluster Expansion (ACE) introduced in [16]. We introduce machine-learned interatomic potentials and derive the ACE as an atomic descriptor. This produces a model linear in its coefficient that serves to approximate the energies and forces of an atomic configuration. We train its coefficients for Silicon, Copper, and Molybdenum, and analyze the fit accuracy for energies and forces benchmark training sets [37]. Furthermore, we extend the ACE model to approximate energies and forces through a nonlinear combination of linear ACE models. We describe how to implement this model, and in particular, how to efficiently compute the derivatives, and present example results for the same data sets. We summarize the Julia implementation of these nonlinear models and provide an overview of the direction the code base will take in the future.

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