Machine Learning Algebraic Geometry for Physics

Abstract

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics. This is a chapter contribution to the book Machine learning and Algebraic Geometry, edited by A. Kasprzyk et al.

Машинное Обучение В Хорошо Известных Сюжетах

“…Кажется, что эта идея достаточно очевидна, и тем не менее появляются все новые и новые статьи, в которых МО "применяется" к науке (см., например, [16]- [20]), так что может сложиться впечатление, что научные проблемы и в самом деле можно разрешить с помощью МО. Это короткое эссе ставит своей целью объяснить, почему и в каком смысле это впечатление, возможно, неверно.…”

Machine learning of the well known things

“…This seems to be a rather obvious idea, still more and more papers appear where ML is "applied" to science, we list just a few typical references from hep-th [6]- [10] -and an impression can mount that one can solve scientific problems in this way. This short essay is to explain, why and in what sense this impression is (can be?)…”

“…In fact some references in[6]-[10] also deal with this kind of approach, rather than with the true ML.…”

Dual Geometry of Entanglement Entropy via Deep Learning

“…In Ref. [18][19][20][21][22], the authors utilized deep layers satisfying a specific recurrence relation. In this case, experimental or observational data allow us to find the recurrence relation determining the bulk geometry.…”