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Main Authors:	Gutleb, Timon S., Barrett, Rhyan, Westermayr, Julia, Ortner, Christoph
Format:	Preprint
Published:	2024
Subjects:	Numerical Analysis 65H04, 65H05
Online Access:	https://arxiv.org/abs/2407.03731
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author	Gutleb, Timon S. Barrett, Rhyan Westermayr, Julia Ortner, Christoph
author_facet	Gutleb, Timon S. Barrett, Rhyan Westermayr, Julia Ortner, Christoph
contents	We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of generality, value-sorted data. The problem is motivated by the desire to machine learn potential energy surfaces arising in molecular excited state computational chemistry applications. We present simplified models which reproduce the analytically predicted convergence and stability behaviors as well as two application-oriented numerical experiments: the electronic excited states of Graphene featuring Dirac conical cusps and energy surfaces corresponding to a sulfur dioxide ($SO_2$) molecule in different configurations.
format	Preprint
id	arxiv_https___arxiv_org_abs_2407_03731
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Parameterizing Intersecting Surfaces via Invariants Gutleb, Timon S. Barrett, Rhyan Westermayr, Julia Ortner, Christoph Numerical Analysis 65H04, 65H05 We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of generality, value-sorted data. The problem is motivated by the desire to machine learn potential energy surfaces arising in molecular excited state computational chemistry applications. We present simplified models which reproduce the analytically predicted convergence and stability behaviors as well as two application-oriented numerical experiments: the electronic excited states of Graphene featuring Dirac conical cusps and energy surfaces corresponding to a sulfur dioxide ($SO_2$) molecule in different configurations.
title	Parameterizing Intersecting Surfaces via Invariants
topic	Numerical Analysis 65H04, 65H05
url	https://arxiv.org/abs/2407.03731

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