Parameterizing intersecting surfaces via invariants
Abstract
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 ( ) molecule in different configurations.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Volume
- 745
- Pages
- 54–85
- Publication date
- 13 May 2026
- Language
- EN