Learning lattice quantum field theories with equivariant continuous flows

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

doi:10.21468/SciPostPhys.15.6.238

SciPost Physics

Learning lattice quantum field theories with equivariant continuous flows

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

SciPost Phys. 15, 238 (2023) · published 13 December 2023

doi: 10.21468/SciPostPhys.15.6.238
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Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.238
TI  - Learning lattice quantum field theories with equivariant continuous flows
PY  - 2023/12/13
UR  - https://scipost.org/SciPostPhys.15.6.238
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 238
A1  - Gerdes, Mathis
AU  - de Haan, Pim
AU  - Rainone, Corrado
AU  - Bondesan, Roberto
AU  - Cheng, Miranda C. N.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.6.238,
	title={{Learning lattice quantum field theories with equivariant continuous flows}},
	author={Mathis Gerdes and Pim de Haan and Corrado Rainone and Roberto Bondesan and Miranda C. N. Cheng},
	journal={SciPost Phys.},
	volume={15},
	pages={238},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.238},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.238},
}

Cited by 4

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Machine learning (ML)

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¹ Mathis Gerdes,
² ³ Pim de Haan,
³ Corrado Rainone,
³ Roberto Bondesan,
¹ ² ⁴ Miranda C. N. Cheng