arXiv subjects

Piotr Korcyl

Publications and source records attributed to Piotr Korcyl.

At least 37 records · Page 2Linked to original sources

arXiv2023

Simulating first-order phase transition with hierarchical autoregressive networks

We apply the Hierarchical Autoregressive Neural (HAN) network sampling algorithm to the two-dimensional $Q$-state Potts model and perform simulations around the phase transition at $Q=12$. We quantify the performance of the approach in the vicinity of the first-order phase transition and compare it with that of the Wolff cluster algorithm. We find a significant improvement as far as the statistical uncertainty is concerned at a similar numerical effort. In order to efficiently train large neural networks we introduce the technique of pre-training. It allows to train some neural networks using smaller system sizes and then employing them as starting configurations for larger system sizes. This is possible due to the recursive construction of our hierarchical approach. Our results serve as a demonstration of the performance of the hierarchical approach for systems exhibiting bimodal distributions. Additionally, we provide estimates of the free energy and entropy in the vicinity of the phase transition with statistical uncertainties of the order of $10^{-7}$ for the former and $10^{-3}$ for the latter based on a statistics of $10^6$ configurations.

cond-mat.stat-mech↗

arXiv2023

Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions

We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing $N_f=2+1$ flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from $a\approx 0.10\,$fm down to below $0.04\,$fm. The light pion mass varies from $M_π\approx 429\,$MeV down to $127\,$MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than $2.3\,$fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales $\sqrt{t_{0,{\rm ph}}}=0.1449^{(7)}_{(9)}\,$fm and $t_0^*\approx t_{0,{\rm ph}}$ from the octet cascade ($Ξ$ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass $m_N=941.7^{(6.5)}_{(7.6)}\,$MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the $Ω$ baryon sigma~terms $σ_{πN}=43.9(4.7)\,$MeV, $σ_{πΛ}=28.2^{(4.3)}_{(5.4)}\,$MeV, $σ_{πΣ}=25.9^{(3.8)}_{(6.1)}\,$MeV, $σ_{πΞ}=11.2^{(4.5)}_{(6.4)}\,$MeV and $σ_{πΩ}=6.9^{(5.3)}_{(4.3)}\,$MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action.

hep-lat↗

arXiv2023

Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

We provide a deepened study of autocorrelations in Neural Markov Chain Monte Carlo (NMCMC) simulations, a version of the traditional Metropolis algorithm which employs neural networks to provide independent proposals. We illustrate our ideas using the two-dimensional Ising model. We discuss several estimates of autocorrelation times in the context of NMCMC, some inspired by analytical results derived for the Metropolized Independent Sampler (MIS). We check their reliability by estimating them on a small system where analytical results can also be obtained. Based on the analytical results for MIS we propose a new loss function and study its impact on the autocorelation times. Although, this function's performance is a bit inferior to the traditional Kullback-Leibler divergence, it offers two training algorithms which in some situations may be beneficial. By studying a small, $4 \times 4$, system we gain access to the dynamics of the training process which we visualize using several observables. Furthermore, we quantitatively investigate the impact of imposing global discrete symmetries of the system in the neural network training process on the autocorrelation times. Eventually, we propose a scheme which incorporates partial heat-bath updates which considerably improves the quality of the training. The impact of the above enhancements is discussed for a $16 \times 16$ spin system. The summary of our findings may serve as a guidance to the implementation of Neural Markov Chain Monte Carlo simulations for more complicated models.

cond-mat.stat-mech↗

arXiv2022

Hierarchical autoregressive neural networks for statistical systems

It was recently proposed that neural networks could be used to approximate many-dimensional probability distributions that appear e.g. in lattice field theories or statistical mechanics. Subsequently they can be used as variational approximators to asses extensive properties of statistical systems, like free energy, and also as neural samplers used in Monte Carlo simulations. The practical application of this approach is unfortunately limited by its unfavorable scaling both of the numerical cost required for training, and the memory requirements with the system size. This is due to the fact that the original proposition involved a neural network of width which scaled with the total number of degrees of freedom, e.g. $L^2$ in case of a two dimensional $L\times L$ lattice. In this work we propose a hierarchical association of physical degrees of freedom, for instance spins, to neurons which replaces it with the scaling with the linear extent $L$ of the system. We demonstrate our approach on the two-dimensional Ising model by simulating lattices of various sizes up to $128 \times 128$ spins, with time benchmarks reaching lattices of size $512 \times 512$. We observe that our proposal improves the quality of neural network training, i.e. the approximated probability distribution is closer to the target that could be previously achieved. As a consequence, the variational free energy reaches a value closer to its theoretical expectation and, if applied in a Markov Chain Monte Carlo algorithm, the resulting autocorrelation time is smaller. Finally, the replacement of a single neural network by a hierarchy of smaller networks considerably reduces the memory requirements.

cond-mat.stat-mech↗

arXiv2022

Gradient estimators for normalising flows

Recently a machine learning approach to Monte-Carlo simulations called Neural Markov Chain Monte-Carlo (NMCMC) is gaining traction. In its most popular form it uses neural networks to construct normalizing flows which are then trained to approximate the desired target distribution. In this contribution we present new gradient estimator for Stochastic Gradient Descent algorithm (and the corresponding \texttt{PyTorch} implementation) and show that it leads to better training results for $ϕ^4$ model. For this model our estimator achieves the same precision in approximately half of the time needed in standard approach and ultimately provides better estimates of the free energy. We attribute this effect to the lower variance of the new estimator. In contrary to the standard learning algorithm our approach does not require estimation of the action gradient with respect to the fields, thus has potential of further speeding up the training for models with more complicated actions.

stat.ML↗

arXiv2021

Scale Setting for CLS 2+1 Simulations

We present an update of the scale setting for $N_f=2+1$ flavor QCD using gradient flow scales and pseudo-scalar decay constants. We analyze the latest ensembles with $2+1$ flavors of non-perturbatively improved Wilson fermions generated by CLS for improved precision. Special care is taken to correct for mistuning by measuring directly the mass derivatives of the various observables. We determine $t_0$ with input taken from a combination of leptonic decay rates of the Pion and the Kaon.

hep-lat↗

arXiv2021

Implementation of the conjugate gradient algorithm for heterogeneous systems

Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear systems is the conjugate gradient (CG) approach. In this work we present an implementation of CG that can be executed on different devices, including CPUs, GPUs, and FPGAs. This is achieved by using the SYCL/DPC++ framework, which allows the execution of the same source code on heterogeneous systems.

hep-lat↗

arXiv2021

Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation

We revisit the numerical construction of the initial condition for the dipole amplitude from the McLerran-Venugopalan model in the context of the JIMWLK evolution equation. We observe large finite volume effects induced by the Poisson equation formulated on a torus. We show that the situation can be partially cured by introducing an infrared regularization. We propose a procedure that has negligible finite volume corrections. The control of the finite volume and finite lattice spacings effects is crucial when considering the numerical solutions of the JIMWLK evolution equation with the collinear improvement.

hep-ph↗

arXiv2021

Evaluation of $SU(3)$ smearing on FPGA accelerator cards

Recent FPGA accelerator cards promise large acceleration factors for some specific computational tasks. In the context of Lattice QCD calculations, we investigate the possible gain of moving the $SU(3)$ gauge field smearing routine to such accelerators. We study Xilinx Alveo U280 cards and use the associated Vitis high-level synthesis framework. We discuss the possible pros and cons of such a solution based on the gathered benchmarks.

hep-lat↗

arXiv2021

Study of a lattice 2-group gauge model

Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum Field Theory introduced by Yetter. We discuss a common generalisation of both the Yetter's model and Yang-Mills theory and in particular we focus on the lattice formulation of such model for finite 2-groups. In the second part we present a particular realization based on a 2-group constructed from $\mathbb Z_4$ groups. In the selected model, independent degrees of freedom are associated to both links and faces of a four-dimensional lattice and are subject to a certain constraint. We present the details of this construction, discuss the expected dynamics in different regions of phase space and show numerical results from Monte Carlo simulations corroborating these expectations.

hep-lat↗

arXiv2021

Dynamics of a lattice 2-group gauge theory model

We study a simple lattice model with local symmetry, whose construction is based on a crossed module of finite groups. Its dynamical degrees of freedom are associated both to links and faces of a four-dimensional lattice. In special limits the discussed model reduces to certain known topological quantum field theories. In this work we focus on its dynamics, which we study both analytically and using Monte Carlo simulations. We prove a factorization theorem which reduces computation of correlation functions of local observables to known, simpler models. This, combined with standard Krammers-Wannier type dualities, allows us to propose a detailed phase diagram, which form is then confirmed in numerical simulations. We describe also topological charges present in the model, its symmetries and symmetry breaking patterns. The corresponding order parameters are the Polyakov loop and its generalization, which we call a Polyakov surface. The latter is particularly interesting, as it is beyond the scope of the factorization theorem. As shown by the numerical results, expectation value of Polyakov surface may serve to detects all phase transitions and is sensitive to a value of the topological charge.

hep-lat↗

arXiv2021

Numerical package for solving the JIMWLK evolution equation in C++

Precise and detailed knowledge of the internal structure of hadrons is one of the most actual problems in elementary particle physics. In view of the planned high energy physics facilities, in particular, the Electron-Ion Collider constructed in Brookhaven National Laboratory, the Chinese Electron-Ion Collider of China, or upgraded versions of CERN's LHC experiments, it is important to prepare adequate theoretical tools to compare and correctly interpret experimental results. One of the model frameworks allowing to estimate hadron structure functions is the combination of the McLerran-Venugopalan initial condition model together with the JIMWLK equation which describes the evolution in rapidity of the initial distribution. In this package, we present a parallel C++ implementation of both these ingredients. In order to allow a thorough assessment of systematic effects, several discretizations of the JIMWLK kernel are implemented both in position and momentum spaces. The effects of the running coupling in three different definitions are provided. The main code is supplemented with test and check programs for all main functionalities. The clear structure of the code allows easy implementation of further improvements such as the collinear constraint.

hep-ph↗

arXiv2021

On systematic effects in the numerical solutions of the JIMWLK equation

In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: "square root" and "noise" prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases.

hep-ph↗

arXiv2020

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors. The calculation is carried out on 35 different CLS ensembles with $N_f=2+1$ flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to $a=0.039\,$fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane. The present arXiv version (v3) includes an Addendum where we update the results using the recently calculated three-loop matching factors for the conversion from the RI'/SMOM to the $\overline{\text{MS}}$ scheme. We find $a_2^π=0.116^{+19}_{-20}$ for the pion, $a_1^K=0.0525^{+31}_{-33}$ and $a_2^K=0.106^{+15}_{-16}$ for the kaon. We also include the previous values, which were obtained with two-loop matching.

hep-lat↗

arXiv2020

Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD

In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), $α^{\overline{\mathrm{MS}}}_s(μ)$, for $\overline{\mathrm{MS}}$ renormalization scales $μ\in (1,\,2)$ GeV. The computation uses gauge field configuration ensembles with $\mathcal{O}(a)$-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has never been applied before in this context. We convert the results perturbatively to the QCD $Λ$-parameter and obtain $Λ_{\overline{\mathrm{MS}}}^{N_f=3} = 342 \pm 17$ MeV, which agrees with the world average published by the Particle Data Group and has competing precision. The latter was made possible by a unique combination of state-of-the-art CLS ensembles with very fine lattice spacings, further reduction of discretization effects from a dedicated numerical stochastic perturbation theory simulation, combining data from vector and axial-vector channels and matching to high-order perturbation theory.

hep-lat↗

arXiv2019

Towards Lattice Quantum Chromodynamics on FPGA devices

In this paper we describe a single-node, double precision Field Programmable Gate Array (FPGA) implementation of the Conjugate Gradient algorithm in the context of Lattice Quantum Chromodynamics. As a benchmark of our proposal we invert numerically the Dirac-Wilson operator on a 4-dimensional grid on three Xilinx hardware solutions: Zynq Ultrascale+ evaluation board, the Alveo U250 accelerator and the largest device available on the market, the VU13P device. In our implementation we separate software/hardware parts in such a way that the entire multiplication by the Dirac operator is performed in hardware, and the rest of the algorithm runs on the host. We find out that the FPGA implementation can offer a performance comparable with that obtained using current CPU or Intel's many core Xeon Phi accelerators. A possible multiple node FPGA-based system is discussed and we argue that power-efficient High Performance Computing (HPC) systems can be implemented using FPGA devices only.

cs.DC↗

arXiv2019

Hyperon couplings from $N_f = 2 + 1$ lattice QCD

We compute various (generalized) isovector charges of the octet baryons. These include $g_A$, $g_T$ and $g_S$ as well as the unpolarized, polarized and transversity parton distribution function (PDF) momentum fractions $\langle x\rangle_{u^+-d^+}$, $\langle x\rangle_{Δu^--Δd^-}$ and $\langle x\rangle_{δu^+-δ^+}$. The simulations are carried out on a subset of the (isospin symmetric) $N_f=2+1$ flavour Coordinated Lattice Simulations (CLS) gauge ensembles with lattice spacings ranging from $a\approx 0.086\,$fm down to $a\approx 0.050\,$fm. First results on the breaking of flavour symmetry and the low energy constants $F$ and $D$ are presented. While SU(3) flavour symmetry violations are found to be sizeable for $g_A=\langle 1\rangle_{Δu^+-Δd^+}$, these are quite small for $g_T=\langle 1\rangle_{δu^--δd^-}$ and $\langle x\rangle_{u^+-d^+}$.

hep-lat↗

arXiv2019

Light-cone distribution amplitudes of octet baryons from lattice QCD

We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039\,\mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit.

hep-lat↗