Polytopes and Machine Learning

Brain Webs for Brane Webs

“…Neural Networks (NNs) are a primary tool within supervised ML, whose application on labelled data acts as a nonlinear function fitting to map inputs to outputs, both represented as tensors over Q using decimals. In recent years the advancement of computational power has played perfectly into the hands of these many-parameter techniques, leading to a programme of application of these tools to datasets arising in theoretical physics [18][19][20][21][22][23][24][25][26][27][28] and the relevant mathematics [29][30][31][32][33][34][35][36]. Motivated by this, we initiate the program of applying ML techniques to the classification of 5-brane webs and 5d SCFTs, concentrating on the simplest case of webs with exactly three external legs.…”

Machine Learning for Hilbert Series

“…PCA puts focus on a data representation's largest principal components, which are found through diagonalisation of the data's covariance matrix. ML has also been successfully applied to a variety of physically motivated scenarios, including: Calabi-Yau manifolds [32][33][34][35][36][37][38][39][40], polytopes [41,42], graph theory [43], knot theory [44,45], amoebae [46], brane webs [47], integrability [48], Seiberg duality among quivers [49], and the related dessin d'enfant Galois orbits [50].…”

Machine Learning Algebraic Geometry for Physics

“…In this work we review a selection of contemporary studies into the use of ML in algebraic geometry for physics. Specifically each section finds focus on application to: §2 hypersurfaces [28], §3 polytopes [29], §4 Hilbert series [30], §5 amoebae [31], §6 brane webs [32], §7 quiver mutation [33], §8 dessins d'enfants [34], and §9 Hessian manifolds.…”