相关论文: Gauge-equivariant neural networks as preconditione…
We demonstrate that gauge-equivariant pooling and unpooling layers can perform as well as traditional restriction and prolongation layers in multigrid preconditioner models for lattice QCD. These layers introduce a gauge degree of freedom…
Lattice QCD simulations are computationally expensive, with the solution of the Dirac equation being the major computational bottleneck of many calculations. We introduce a novel gauge-equivariant neural-network architecture for…
We propose a Transformer neural network architecture specifically designed for lattice QCD, focusing on preserving the fundamental symmetries required in lattice gauge theory. The proposed architecture is gauge covariant/equivariant,…
Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for…
In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the…
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body…
We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that…
Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…
We propose gauge-covariant neural networks along with a specialized training algorithm for lattice QCD, designed to handle realistic quarks and gluons in four-dimensional space-time. We show that the smearing procedure can be interpreted as…
We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs), which can be applied to generic machine learning problems in lattice gauge theory while exactly preserving gauge…
Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such…
This thesis deals with neural networks that respect symmetries and presents the advantages in applying them to lattice field theory problems. The concept of equivariance is explained, together with the reason why such a property is crucial…
The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge…
Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave…
Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, GNNs have been shown to be a…
In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…
Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional…
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…