Speaker
Description
A longstanding problem in lattice QCD is critical slowing down by taking the continuum and infinite volume limit. One part, the critical slowing of solving the Dirac equation towards the continuum, is effectively solved with the introduction of very effective multi-level solvers. However, a universal solution for the other part, critical slowing down of the Markov Chain Monte Carlo (MCMC) simulation towards fine lattice spacings, is still unknown. The critical slowing down manifests itself via long autocorrelations times of the topological charge. The standard algorithm, the Hybrid Monte Carlo algorithm, can not move between different topological sectors. This, however, is essential to minimizing systematic effects in continuum extrapolations which requires generating ensembles of independent gauge configurations at very fine lattices.
A solution to overcome topological freezing in lattice QCD was originally proposed at CERN by Martin Luescher [1]. The basic idea is to trivialize the gauge fields via a flow equation by keeping essential physical information like correlations during the transformation. It turned out however, that the proposed expansion of the method quickly requires larger loops, which increases computation costs and thus is limited to relatively small flow time [2].
An idea to overcome the limitation is the application of normalizing flows to gauge theories. In 2D-U(1) this can overcome the sampling problem caused by topological freezing [3]. Using the gauge equivariant structure the method can be used as a proposal within a MCMC procedure, which makes the sampling procedure exact. First steps towards the application in SU(3) gauge theories are already done, however a major limitation is the scalability towards larger volumes. This can be in principle overcome by applying it within a localized area [4] or using the method within reweighting [5].
The application of generative models. which are equivariant under symmetries, are also applied to other fields in HEP and are in particular useful for speeding up computations like detector simulation [6]. Moreover the method has large potential to improve various applications in lattice computation, like the usage for contour deformations in order to mitigate signal to noise or sign problem in measurements [5,7].
We propose to support the research of generative models in lattice gauge theories at TH by a fellow. In particular by developing software solutions, i.e. an efficient open source package for SU(3) is currently missing, and by further understanding how symmetries like the cubic group H(4) can be included into the model application.
[1] Trivializing maps, the Wilson flow and the HMC algorithm, Martin Luscher, Commun.Math.Phys. 293 (2010), 899-919
[2] Learning trivializing gradient flows for lattice gauge theories, S. Bacchio et al., Phys.Rev.D 107 (2023) 5, L051504
[3] Equivariant flow-based sampling for lattice gauge theory G. Kanwar, et al., Phys.Rev.Lett. 125 (2020) 12, 121601
[4] Tackling critical slowing down using global correction steps with equivariant flows: the case of the Schwinger model, J. Finkenrath, e-Print: 2201.02216 [hep-lat]
[5] Applications of flow models to the generation of correlated lattice QCD ensembles, R. Abbott et al., Phys.Rev.D 109 (2024) 9, 094514
[6] Novel approach for computing gradients of physical observables, S. Bacchio, Phys.Rev.D 108 (2023) 9, L091508
[7] Machine learning and LHC event generation Anja Butter et al., SciPost Phys. 14 (2023) 4, 079, SciPost Phys. 14 (2023), 079
CERN group/ Experiment
TH, lattice QCD
| Working area | Area 1" Cutting Edge AI for Offline Data Processing |
|---|---|
| Project goals | Flow application within SU(3) and four dimension, open source application Investigation how to overcome scalability limits, application to reweighting or local flows |
| Timeline | Application to SU(N) with focus on N=3 (Y1), Application towards larger dimensions with the target of 4D (Y2), Software release (Y3) |
| Available person power | Connected to TH, group lattice-QCD, connected to on-going effort within NGT |
| Additional person power request | Fellow |
| Is this an already ongoing activity? | Yes |
| Indicative hardware resources needs | One node with GPUs for training and application |