Generalization capabilities of neural networks in lattice applications
This work addresses the challenge of incorporating symmetries into neural networks for lattice applications, offering incremental improvements in domain-specific physics simulations.
The paper tackled the problem of improving performance and generalizability in lattice field theories by using translationally equivariant neural networks, demonstrating that these networks significantly outperform non-equivariant ones in regression and classification tasks, including generalization to unseen physical parameters and different lattice sizes.
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 lead to high reward in terms of performance and generalizability. A fundamental symmetry that usually characterizes physical systems on a lattice with periodic boundary conditions is equivariance under spacetime translations. Here we investigate the advantages of adopting translationally equivariant neural networks in favor of non-equivariant ones. The system we consider is a complex scalar field with quartic interaction on a two-dimensional lattice in the flux representation, on which the networks carry out various regression and classification tasks. Promising equivariant and non-equivariant architectures are identified with a systematic search. We demonstrate that in most of these tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.