Contributor info: Prof. Miranda C. N. Cheng

Miranda C. N. Cheng, Niki Stratikopoulou

SciPost Phys. Lect. Notes 110 (2026) · published 7 January 2026 | Toggle abstract · pdf

Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or as the system approaches a critical point, especially in the presence of non-trivial topological structures in the theory. Rapid recent advances in machine learning provide a promising avenue for progress in this area. These lecture notes aim to give a brief account of lattice field theories, normalizing flows, and how the latter can be applied to study the former. The notes are based on the lectures given by the first author in various recent research schools.

Mathis Gerdes, Pim de Haan, Corrado Rainone, Roberto Bondesan, Miranda C. N. Cheng

SciPost Phys. 15, 238 (2023) · published 13 December 2023 | Toggle abstract · pdf

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the $\phi^4$ theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Furthermore, we demonstrate that our model can learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalizations further accentuate the advantages of machine learning methods.