Integrability Ex Machina

Abstract

Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of relevant structures, the Lax pair and Lax connection respectively. By formulating this search as an optimization problem, we are able to identify appropriate structures via machine learning techniques. We test our method on standard systems of classical integrability and find that we can single out some integrable deformations of a system. Due to the ambiguity in defining a Lax pair our algorithm identifies novel Lax pairs which can be easily verified analytically.

Evolving Heterotic Gauge Backgrounds: Genetic Algorithms versus Reinforcement Learning

“…[11] using GAs and Markov chain Monte Carlo methods, while in Ref. [12] the same methods were used, as well as RL.…”

Ising Machines for Diophantine Problems in Physics

“…In particular it will be interesting to employ them in the string theory landscape context, and compare them to the genetic algorithmic and machine learning techniques that have been studied in Refs. [6, 69–86].…”

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.…”