# The Tenth International Workshop on Lattice QFT and Numerical Analysis (QCDNA X)

Europe/Lisbon
Department of Physics, University of Coimbra, Portugal
Description

The Tenth International Workshop on Lattice QFT and Numerical Analysis (QCDNA X), will be held this year in Coimbra, Portugal, in the week following the Lattice conference in Granada, Spain. The workshop will run from Tuesday 27th June to Thursday 29th June, in the Physics Department of the University of Coimbra.

This workshop aims to bring together applied mathematicians, theoretical physicists, and experts in software and hardware in order to further improve the current status of lattice QCD simulations.

Confirmed speakers:

Anthony Kennedy (The University of Edinburgh)

Richard Brower (Boston University)

James Brannick (The Pennsylvania State University)

Mattia Dalla Brida (Università di Milano-Bicocca & INFN)

Organizers:

Paulo J. Silva, O. Oliveira, Anthony D. Kennedy, Oliver Witzel

CFisUC

NVIDIA

Participants
• Alessandro Barp
• Alexei Strelcehnko
• Anthony Kennedy
• Artur Strebel
• Bartosz Kostrzewa
• Daniel Richtmann
• Edward White, Jr.
• Eloy Romero Alcalde
• Evan Weinberg
• Helvio Vairinhos
• James Brannick
• Kate Clark
• Marco Garofalo
• Matthias Rottmann
• Mattia Dalla Brida
• Nuno Cardoso
• Oliver Witzel
• Orlando Oliveira
• Paulo Silva
• Pedro Bicudo
• Peter Georg
• Protick Mohanta
• Richard Brower
• Ruizi Li
• Subhasish Basak
Support
• Tuesday, June 27
• 9:00 AM
Registration
• 1
HMC: Geometry and Applications
Speaker: Alessandro Barp
• 2
Deflation for Monte-Carlo estimation of the trace of a matrix inverse

In the context of computing disconnected diagrams, we investigate the
efficient estimation of the trace of large-scale matrix inverses. Our approach
is based on the Hutchinson method (Monte-Carlo averaging over matrix
quadratures). Previous work showed that combining deflation against the lowest
part of the spectrum with Hierarchical Probing can accelerate the convergence
significantly. As the size of the matrix grows, however, the computation of
enough singular vectors to achieve a reduction in the variance can be a
bottleneck.

In this work we take advantage of the fact that the singular vectors
corresponding to the lowest modes can be represented well in a sparse basis.
This allows us to compute and store efficiently the first 500~1000 lowest modes
of the matrix spectrum, which is enough to obtain a good reduction in the
variance. Moreover we discuss different projectors for deflating and the
performance impact when the matrix is close to singular.

Speaker: Mr Eloy Romero Alcalde (College of William and Mary )
• 10:45 AM
Coffee break
• 3
Progress and Challenge of Lattice Quantum Finite Elements (QFE) on Spheres

Extending lattice field to ultraviolet complete quantum field theory on any smooth Riemann manifolds is a challenging problem. By adapting element methods (FEM) and Regge geometry one recovers classical (IR) solution in the continuum. However to correctly handle UV divergences requires new counter terms to construct a what we call a "Quantum Finite Elements" (QFE) discrete Lagrangian on the simplicial complex. These UV counters for 2d phi 4th theory and free fermions on the two sphere (S2) have been tested numerically to high precession against the exact Ising solution. Methods to generalize the QFE construction to radial quantized 3d super renormalizable theories on R x S2 and challenges for asymptotical free 4d gauge theories on R x S3 will be presented.

Speaker: Dr Richard Brower (Boston University)
• 12:30 PM
Lunch
• 4
Lattice Quantum Field Theory: Numerical Integration in an Infinite Number of Dimensions

Relativistic Quantum Field Theory (QFT) is the formalism upon which the Standard Model of particle physics is built, and it is remarkably successful and accurate. When the interactions are weak then the techniques of renormalized perturbation theory using Feynman diagrams works beautifully, but when the interactions are strong we have to turn to numerical evaluation of the functional integrals that define the quantum theory. The only way we know of to evaluate such infinite-dimensional integrals is to use Markov Chain Monte Carlo (MCMC) techniques. I shall attempt to give an overview of the functional integral formalism of QFT, and how MCMC integration works. If time permits I will discuss how fermions (half-integer spin) are dealt with, and maybe introduce the Hybrid (or Hamiltonian) Monte Carlo algorithm.

Speaker: Prof. Anthony Kennedy (Higgs Centre for Theoretical Physics, The University of Edinburgh)
• 5
Lattice QCD with mixed action - Borici-Creutz valence quarks on staggered sea

We used Borici-Creutz fermion to study discrete chiral symmetry breaking
at strong coupling in 2-dim Gross-Neveu model and mass spectra in 2-dim
field theories. Mixed action lattice QCD study with Borici-Creutz valence
quarks on staggered sea quarks is carried out. The counter terms are fixed
nonperturbatively to restore the broken symmetries. The effect of partial
quenching and unitarity violation is investigated.

Speaker: Subhasish Basak (NISER)
• 6
Quark-antiquark excited flux tube

We present color field profiles for some of the first SU(3) gluonic excitations of the flux tube in the presence of a static quark-antiquark pair.

Speaker: Nuno Cardoso (IST)
• 4:00 PM
Coffee break
• 7
DD-αAMG on QPACE 3

We describe our experiences porting the Regensburg implementation of
the DD-αAMG solver from QPACE 2 to QPACE 3. We first review porting from
the first generation Intel Xeon Phi processor (Knights Corner) to its
successor (Knights Landing). Secondly, we present an overview of
Omni-Path, comparing it to the well-known competitor InfiniBand.
Finally, we present the performance of the code on a single processor as
well as the scaling on many nodes.

Speakers: Mr Daniel Ritchmann (University of Regensburg ), Mr Peter Georg (University of Regensburg)
• 8
MILC code performance on high end CPU and GPU supercomputer clusters

With recent developments in parallel supercomputing architecture,
many core, multi-core, and GPU processors
are now commonplace resulting in more levels of parallelism, memory
hierarchy, and programming complexity. It has been necessary to adapt
the MILC code to these new processors starting with NVIDIA
GPUs and more recently the Intel Xeon Phi processors. We report on
our efforts to port and optimize our code for the Intel Knights Landing
architecture. We consider performance of the MILC code with MPI and OpenMP,
and optimizations with QOPQDP and QPhiX. For the latter approach we
concentrate on the staggered conjugate gradient and gauge force. We also
consider performance on recent NVIDIA GPUs using the QUDA library.

Speaker: Ruizi Li
• 7:00 PM
• 8:15 PM
Workshop Dinner at "Solar do Bacalhau"
• Wednesday, June 28
• 9

Numerical stochastic perturbation theory (NSPT) is a powerful tool that allows perturbation expansions in QCD and other interesting theories to be estimated to high order in the interactions. The standard algorithms on which NSPT is based on, however, suffer from several limitations which in practice restrict the potential of these techniques. In this talk I will review the recent algorithmic advances in this field and show how these significantly reduce the computational effort for precise and accurate determinations. This opens up the way to tackle challenging and interesting new problems, as will be illustrated by a highly non-trivial computation.

Speaker: Dr Mattia Dalla Brida (Universita' di Milano-Bicocca & INFN)
• 10
Numerical Stochastic Perturbation Theory in $\varphi^4$ Theory

Numerical stochastic perturbation theory (NSPT) is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard NSPT is based on the Langevin equation. In this contribution, we investigate in $\varphi^4$ theory some alternative methods. In particular, we present a study of the recently proposed Instantaneous Stochastic Perturbation Theory, as well as a formulation of numerical stochastic perturbation theory based on Generalised Hybrid Molecular Dynamics algorithms.

Speaker: Marco Garofalo (Higgs Centre for Theoretical Physics, The University of Edinburgh)
• 10:45 AM
Coffee break
• 11
Nonperturbative anisotropy calibration in lattice QCD at strong coupling

We propose a simple criterion for the nonperturbative renormalization of the anisotropy coupling in lattice QCD with massless staggered fermions, in the strong coupling limit. We compute numerically and to high precision the renormalised anisotropy, and the analogue of Karsch’s coefficients, using diagrammatic Monte Carlo algorithms and multi-histogram reweighting. We observe a large nonperturbative correction to the mean field anisotropy, and we analyse the implications of such a correction on the continuous time limits of the phase diagram of lattice QCD at strong coupling, and of the baryon mass.

Speaker: Helvio Jose Caleiro Vairinhos (Fisica Teorica e Met. Mat.-Inst. Nacional de Invest. Cientif.-Un)
• 12
Algebraic Multigrid: Theory and Practice

This talk gives an overview of recent progress made in the design and analysis of algebraic multigrid methods. The focus is on the setup algorithm that automatically constructs the multilevel hierarchy used in the solve phase. A sharp two-grid theory is introduced and then used to derive various quality measures of the coarse spaces constructed by the setup algorithm, based on the ideas of compatible relaxation, a related identity that assumes the use of the so-called ideal interpolation operator, and an optimal form of classical algebraic multigrid interpolation that gives the best possible two-grid convergence rate. Various numerical results are presented to illustrate these theoretical results. As a test problem, we focus on a finite volume discretization of a scalar diffusion problem with highly varying (discontinuous) diffusion coefficient.

Speaker: Dr James Brannick
• 12:30 PM
Lunch
• 13
GPU Computing to the Exascale and Beyond

With the demise of Denard scaling, it is well known that we cannot go faster for greater throughput, rather we have to go wider. However, with the imminent demise of Moore's Law, there lies continued challenges in reaching and exceeding the Exascale. We discuss how and why GPU computing provides a solution to take computational science to this next level. We consider some of the software and algorithm challenges that the Exascale will bring. Lastly, we take a dive into the newly-launched Volta GPU architecture, the architecture that will drive the next-generation CORAL Supercomputers.

Speaker: Dr Kate Clark (NVIDIA)
• 14
HMC, high level structures and architecture support in Grid

I will present the strategies we developed in Grid for the HMC sector, in order to support a variety of behaviours without code replication. I will also discuss the current status of the architecture support in view of the upcoming machines.

Speaker: Guido Cossu (The University of Edinburgh)
• 15
Analyzing AMA data on 48^3 × 96 lattices

As an example for analyzing data on RBC-UKQCD's 48^3 x 96 ensemble with physical pions, I investigate correlations between propagator sources placed on the same configuration and discuss options for analyzing this data set to extract the Bs-meson decay constant. The data are generated taking advantage of all-mode averaging (AMA) to reduce the numerical costs.

Speaker: Oliver Witsel
• 4:10 PM
Coffee break
• 4:45 PM
Visit to the Old University
• Thursday, June 29
• 16
Scaling Multigrid to the Exascale

Owing to its success in removing the critical slowing down of Dirac linear systems, adaptive multigrid is now a standard solver in the arsenal of tools that the lattice field theorist expects. In this work we report on the latest progress in improving the strong scaling of adaptive multigrid algorithms when running on GPU-accelerated architectures using the QUDA library. Techniques include Schwarz preconditioning, pipelined solvers, precision truncation and RDMA-enabled MPI. Furthermore, we report on progress on optimizing the adaptive setup process in order to increase its applicability to Hybrid Monte Carlo. Finally we discuss the challenges in scaling multigrid to the Exascale-generation of supercomputers.

Speaker: Dr Kate Clark (NVIDIA)
• 17
Novel Approaches for Staggered Multigrid Algorithms

Critical slowing down in the fermion sector is a leading obstacle facing the approach to the continuum in lattice gauge theory simulations. Adaptive multigrid ($\alpha$-MG) methods offer a solution to the resulting superlinear growth in the cost of iterative Krylov solves. Ongoing research has suggested that previously developed $\alpha$-MG methods, such as the successful formulation for Wilson-clover fermions, cannot be applied in a black-box fashion to other discretizations. In this talk I will expand on subtle issues offered by the staggered discretization. I will also discuss novel approaches that may sidestep these issues.

Speaker: Evan Weinberg
• 10:45 AM
Coffee break
• 18
An Eigensolver for the Hermitian Dirac Operator with Multigrid Acceleration

In this talk we present a Davidson type eigensolver combined with the DD-$\alpha$AMG multigrid solver library. The basic Davidson method is adjusted to our multigrid method and the structure of the hermitian Dirac operator in a way that both methods benefit from each other.

We compare the resulting eigensolver with a Chebychev filtered Arnoldi method (PARPACK) and the multi purpose eigensolver library PRIMME based on a variety of scaling and performance studies.

Speaker: Mr Artur Strebel (University of Wuppertal)
• 19
Local Adaptive Refinement on Lattice Gauge Fields

Adaptive Mesh Reﬁnement (AMR) has been widely used in computational ﬂuid dynamics, shock hydrodynamics, astrophysics, turbulence modeling and combustion to improve the performance of algorithms running large, complex problems. The results are often impressive. However, for various reasons which will be discussed, traditional AMR is not directly applicable to lattice QCD. This talk proposes a new numerical method, Local Adaptive Reﬁnement (LAR), for lattice QCD.
LAR is strongly motivated by AMR, and is designed to work with the aggregation-based algebraic multigrid framework of lattice QCD. The premise behind all adaptive reﬁnement methods is that certain numerical problems have solutions that exhibit local variations, which can be examined more fully at higher resolution (more closely spaced grid or lattice points) than the base level of
resolution used for the simulation. As a result, problems that would normally require very high resolution over a large domain (which is very computationally expensive) could instead be solved at lower resolution over the large domain, with automated local reﬁnement to higher resolution as needed. The scale and nature of the problems commonly found at the leading edge of today’s lattice QCD work suggest that the field could be a beneﬁt from adaptive reﬁnement. Among the topics that will be discussed are the need for an algebraic variable-based approach to reﬁnement, as opposed to a geometric grid-based approach, methods of determining the regions in which reﬁnement should occur, and ways to implement LAR in a parallel machine environment.

Speaker: Mr Edward White, Jr.
• 12:15 PM
End of the workshop