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Ho, Cheuk Hin

University of British Columbia

The Atomic Cluster Expansion (ACE) (Drautz, Phys. Rev. B 99, 2019) has been widely applied in machine learning of high energy physics, quantum mechanics and atomistic modeling to construct many-body interaction models respecting physical symmetries. Computational efficiency is achieved by allowing non-physical self-interaction terms in the model. In this thesis, we propose and analyze an efficient method to evaluate and parameterize an orthogonal, or, non-self-interacting cluster expansion model, which also leads to an efficient algorithm for constructing a high order symmetric tensor product basis from conventional polynomials. We further present numerical experiments demonstrating improved conditioning and more robust approximation properties than the original expansion in regression tasks, both in simplified toy problems and in applications in the machine learning of interatomic potentials.

Text

2024-04-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/87929

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/