Machine learning parameter systems, Noether normalisations and quasi-stable positions
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In: Journal of Symbolic Computation Volume 126 / (2024-06-25) , S. ; eissn:1095-855X
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We discuss the use of machine learning models for finding “good coordinates” for polynomial ideals. Our main goal is to put ideals into quasi-stable position, as this generic position shares most properties of the generic initial ideal, but can be deterministically reached and verified. Furthermore, it entails a Noether normalisation and provides us with a system of parameters. Traditional approaches use either random choices which typically destroy all sparsity or rather simple human heuristics which are only moderately successful. Our experiments show that machine learning models provide us here with interesting alternatives that most of the time make nearly optimal choices.
@article{doi:10.17170/kobra-2024070510466, author ={Hashemi, Amir and Mirhashemi, Mahshid and Seiler, Werner M.}, title ={Machine learning parameter systems, Noether normalisations and quasi-stable positions}, keywords ={510 and Maschinelles Lernen and Parameteridentifikation and Noether-Theorem}, copyright ={http://creativecommons.org/licenses/by/4.0/}, language ={en}, journal ={Journal of Symbolic Computation}, year ={2024-06-25} }