arXiv subjects
Publications and source records attributed to Timo Eichhorn.
We present an algorithm that addresses topological freezing in lattice QCD simulations by combining parallel tempering with collective-variable-based enhanced sampling methods, and apply it to a particularly challenging system with $N_f = 2$ staggered fermions. We find that the algorithm unfreezes the system, which is otherwise completely frozen for approximately 40000 Molecular Dynamics Units with the Rational Hybrid Monte Carlo algorithm.
In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating distinct sectors. With appropriately constructed bias potentials, Metadynamics and related enhanced sampling techniques can mitigate this problem and significantly reduce the integrated autocorrelation times of the topological charge and associated observables. We test strategies to accelerate the buildup of bias potentials and the possibility of extrapolating potentials from small to large volumes. We also investigate the effectiveness of orthogonal algorithmic improvements, such as longer HMC trajectories and HMC variants, which may benefit conventional simulations as well.
When approaching the continuum limit in lattice QCD or other theories in a setup with topological sectors, conventional update algorithms experience a particularly severe form of critical slowing down that is caused by high action barriers between the sectors. The qualitative scaling behavior of this critical slowing down appears to be universal across different update algorithms and (gauge) actions. We demonstrate that a combination of Metadynamics with parallel tempering, along with other modifications, can significantly reduce autocorrelation times while avoiding the need for reweighting. We also discuss strategies to extend the methods to QCD simulations with dynamical fermions, and present first results for $N_f = 2$ simulations at unphysical pion masses.
In the era of Big Data and the growing support for Machine Learning, Deep Learning and Artificial Intelligence algorithms in the current software systems, there is an urgent need of standardized application benchmarks that stress test and evaluate these new technologies. Relying on the standardized BigBench (TPCx-BB) benchmark, this work enriches the improved BigBench V2 with three new workloads and expands the coverage of machine learning algorithms. Our workloads utilize multiple algorithms and compare different implementations for the same algorithm across several popular libraries like MLlib, SystemML, Scikit-learn and Pandas, demonstrating the relevance and usability of our benchmark extension.
At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories with or without fermions are plagued by slow modes that give rise to large autocorrelation times. This can lead to simulation runs that are effectively stuck in one topological sector, a problem known as topological freezing. Here, we demonstrate that for a relevant set of parameters, Metadynamics can be used to unfreeze 4-dimensional SU(3) gauge theory. However, compared to local update algorithms and the Hybrid Monte Carlo algorithm, the computational overhead is significant in pure gauge theory, and the required reweighting procedure may considerably reduce the effective sample size. To deal with the latter problem, we propose modifications to the Metadynamics bias potential and the combination of Metadynamics with parallel tempering. We test the new algorithm in 4-dimensional SU(3) gauge theory and find that it can achieve topological unfreezing without compromising the effective sample size, thereby reducing the autocorrelation times of topological observables by at least two orders of magnitude compared to conventional update algorithms. Additionally, we observe significantly improved scaling of autocorrelation times with the lattice spacing in 2-dimensional U(1) gauge theory.
Topological freezing is a well known problem in lattice simulations: with shrinking lattice spacing a transition between topological sectors becomes increasingly improbable, leading to a problematic increase of the autocorrelation time regarding several observables. We present our investigation of metadynamics as a solution for topological freezing in the Schwinger model. Specifically, we take a closer look at the collective variable and its scaling behaviour, visualize the effects of topological freezing and how metadynamics helps in that respect and explore alternatives for a more efficient building process. Possible implications for and differences to four-dimensional SU(3) theory are briefly discussed.
At fine lattice spacings, lattice simulations are plagued by slow (topological) modes that give rise to large autocorrelation times. These, in turn, lead to statistical and systematic errors that are difficult to estimate. We study the problem and possible algorithmic solutions in 4-dimensional SU(3) gauge theory, with special focus on instanton updates and Metadynamics.
In modern lattice simulations, conventional update algorithms do not allow for tunneling between topological sectors at fine lattice spacings. We compare the viability of multiple less commonly used algorithms (metadynamics, instanton updates, and multiscale thermalization) with respect to proper sampling of all topological sectors in the Schwinger model. We briefly comment on the prospects of applying these methods to 4-dimensional SU(3) simulations.