When lattice QCD is formulated in sectors of fixed quark numbers, the canonical fermion determinants can be expressed explicitely in terms of transfer matrices defined at fixed time. This in turn provides a complete factorization of the fermion determinants in temporal direction. In this talk I describe this factorization for Wilson-type fermions and present explicit constructions of the...

By employing new extended multilevel hierarchy construction principles, AMG can be applied to many new types of problems. The extended principles include general rules for choosing relaxation, constructing the coarse-level variables, the coarse-to-fine interpolation, and coarse-level equations, and a quantitative performance predictor of the multi-level cycle convergence rate, called the mock...

We discuss the challenges of extending convergence results of classical Krylov subspace methods to their block counterparts and propose a new approach to this analysis. Block KSMs such as block GMRES are generalizations of classical KSMs, and are meant to iteratively solve linear systems with multiple right-hand sides (a.k.a. a block right-hand side) all-at-once rather than individually....

The calculation of disconnected diagram contributions to physical signals is

a computationally expensive task in Lattice QCD. To extract the physical

signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix,

must be stochastically estimated. Because the variance of the stochastic es-

timator is typically large, variance reduction techniques must be...

Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on fine lattices suffer from critical slowdown, the rapid growth of autocorrelations in the Markov chain with decreasing lattice spacing a. This causes a strong...

We summarize our results for the $\eta$ and $\eta^\prime$ masses and

their four independent decay constants at the physical point as well as

their anomalous gluonic matrix elements $a_{\eta^{(\prime)}}$.

The computation employs twenty-one $N_f=2+1$ Coordinated Lattice

Simulations (CLS) ensembles with non-perturbatively improved Wilson

fermions at four different lattice spacings and...

I will discuss the use of machine learning methods to accelerate algorithms for gauge field generation, in particular via flow models.

ecently 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. The training is done using some form of gradient descent so gradient estimation is necessery. In my talk I will...

Some selected questions:Critical slowing down with $a\to 0$.

- Rounding issues on large volumes.

- Multiscale approaches to increase signal over noise

- Benefits of (approximate eigenvectors) and how to obtain these

- Approaches to excited state contributions: multi-state fits, GEVP, smearing.

- efficient stochastic estimation of traces, all-to-all propagators, perambulators

These are...

The following questions emerged from an e-mail discussion with Gustavo Ramirez:

1) Deflation (with approximate projection) as a multigrid method seems tricky to be ported to GPU architectures in an efficient way.

2) Can one understand why ? Is that solely due to the poor scalability of the 'little Dirac operator' ?

3) Isn't that then a general problem for multigrid methods on GPU ?...

A precise knowledge of nucleon axial formfactors is needed for the new generation of terrestrial neutrino experiments. This is particularly challenging due to increased contamination, in this sector, from excitations, in particular from $N\pi$ scattering states. Transitions from a $N$ to a $N\pi$, mediated by an axial current are also interesting themselves, as these can be related to neutrino...