ICML 2025

A Machine Learning Approach to Duality in Statistical Physics
Prateek Gupta 1 Andrea E. V. Ferrari 2 3 Nabil Iqbal 4 5
Abstract
The notion of duality – that a given physical sys-
tem can have two different mathematical descrip-
tions – is a key idea in modern theoretical physics.
Establishing a duality in lattice statistical mechan-
ics models requires the construction of a dual
Hamiltonian and a map from the original to the
dual observables. By using neural networks to
parameterize these maps and introducing a loss
function that penalises the difference between cor-
relation functions in original and dual models, we
formulate the process of duality discovery as an
optimization problem. We numerically solve this
problem and show that our framework can redis-
cover the celebrated Kramers-Wannier duality for
the 2d Ising model, numerically reconstructing
the known mapping of temperatures. We further
investigate the 2d Ising model deformed by a pla-
quette coupling and find families of “approximate
duals”. We discuss future directions and prospects
for discovering new dualities within this frame-
work. 1.
1. Background
A key concept in physics is duality, i.e. the idea that the
same physical system can have two different mathematical
descriptions. Duality sits at the heart of modern theoretical
physics. In this work we seek to formalize the notion of
duality in statistical physics in a manner that allows modern
machine learning techniques to be used to systematically
search for dualities.
*Equal contribution 1Max Planck Institute for Human Develop-
ment, Berlin, Germany 2Deutsches Elektronen-Synchrotron DESY,
Germany 3School of Mathematics, The University of Edinburgh
4Department of Mathematical Sciences, Durham University, UK
5Amsterdam Machine Learning Laboratory, University of Ams-
terdam, Netherlands. Correspondence to: Prateek Gupta <con-
tact@pgupta.info>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Co...