# Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

@article{Gerdes2022LearningLQ, 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={ArXiv}, year={2022}, volume={abs/2207.00283} }

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Quantum Field Theories. Instead of the deep architectures used so far for this task, our proposal is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the φ 4 theory, showing that it systematically outperforms previously proposed ﬂow-based methods in sampling eﬃciency, and the improvement is especially pronounced for…

## 6 Citations

### Geometrical aspects of lattice gauge equivariant convolutional neural networks

- Mathematics, Computer ScienceArXiv
- 2023

It is demonstrated how L-CNNs can be equipped with global group equivariance, which allows the formulation to be equivariant not just under translations but under global lattice symmetries such as rotations and reflections.

### Learning Deformation Trajectories of Boltzmann Densities

- Computer ScienceArXiv
- 2023

A training objective for continuous normalizing that can be used in the absence of samples but in the presence of an energy function is introduced that compares the reverse KL-divergence on Gaussian mixtures and on the φ 4 lattice lattice ﬁeld theory on a circle.

### Aspects of scaling and scalability for flow-based sampling of lattice QCD

- PhysicsArXiv
- 2022

Recent applications of machine-learned normalizing ﬂows to sampling in lattice ﬁeld theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However,…

### Deformation Theory of Boltzmann Distributions

- MathematicsArXiv
- 2022

Consider a one-parameter family of Boltzmann distributions p t ( x ) = 1 Z t e − S t ( x ) . In this paper we study the problem of sampling from p t 0 by ﬁrst sampling from p t 1 and then applying a…

### Deformations of Boltzmann Distributions

- Computer Science
- 2022

An equation relating Ψ and the corresponding family of unnormalized log-likelihoods S t is derived and it is demonstrated that normalizingows perform better at learning the Boltzmann distribution p τ than at learning p 0.

### Stochastic normalizing flows for lattice field theory

- PhysicsProceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)
- 2022

Stochastic normalizing ﬂows are a class of deep generative models that combine normalizing ﬂows with Monte Carlo updates and can be used in lattice ﬁeld theory to sample from Boltzmann distributions.…

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