Generative models for scalar field theories: how to deal with poor scaling?
This addresses a bottleneck in computational physics for researchers using generative models in lattice field theories, but it is incremental as it builds on existing methods to improve scaling issues.
The paper tackles the problem of high training costs and poor scaling of generative models like normalizing flows for generating lattice gauge field configurations, especially on large lattices and near critical points, by exploring new architectures inspired by effective field theories and alternative methods to handle poor acceptance rates.
Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof of principle for simple models in two dimensions. However, further studies indicate that the training cost can be, in general, very high for large lattices. The poor scaling traits of current models indicate that moderate-size networks cannot efficiently handle the inherently multi-scale aspects of the problem, especially around critical points. We explore current models with limited acceptance rates for large lattices and examine new architectures inspired by effective field theories to improve scaling traits. We also discuss alternative ways of handling poor acceptance rates for large lattices.