Conveners
Algorithms and artificial intelligence
- Gurtej Kanwar (University of Edinburgh)
Algorithms and artificial intelligence
- Lorenzo Barca (DESY)
Algorithms and artificial intelligence
- Simran Singh (HISKP, University of Bonn)
Algorithms and artificial intelligence
- Ho Hsiao (Center for Computational Sciences, University of Tsukuba)
Algorithms and artificial intelligence
- Johann Ostmeyer (University of Bonn)
Algorithms and artificial intelligence
- Yusuke Namekawa (Fukuyama University)
Algorithms and artificial intelligence
- Roman Gruber
We present recent progress in combining a two-level sampling algorithm with distillation techniques to compute fermionic observables. The method relies on expressing the quark propagator as a series of domain-local contributions, each depending only on the gauge links in a restricted region, which can then be estimated independently with a two-level sampling strategy. This enables an...
The numerical sign problem remains one of the central challenges in first-principles simulations. The Worldvolume Hybrid Monte Carlo (WV-HMC) has recently emerged as a reliable and computationally efficient algorithm, and, crucially, avoids the ergodicity issues inherent in Lefschetz-thimble approaches. In this talk, after outlining the key ideas behind WV-HMC, I will present its extension to...
We apply the Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] to the two-dimensional doped Hubbard model, a system structurally similar to finite-density QCD. This model is known to suffer from a severe sign problem at low temperatures and away from half filling (doped), which renders traditional Determinantal Quantum Monte Carlo (DQMC) approaches ineffective. We demonstrate...
Unnormalized probability distributions are fundamental in modelling complex physical systems, especially in lattice field theory. Traditionally, Markov Chain Monte Carlo (MCMC) methods used to study these systems often exhibit slow convergence, critical slowing down, and poor mixing, resulting in highly correlated samples. Machine learningโbased sampling approaches, such as normalising flows...
In recent years, flow-based samplers have emerged as a promising alternative to traditional sampling methods in lattice gauge theory. In this talk, we will introduce a class of flow-based samplers known as Stochastic Normalizing Flows (SNFs), which combine neural networks with non-equilibrium Monte Carlo algorithms. We will show that SNFs exhibit excellent scaling with the volume in lattice...
Abstract:
We present a multilevel generative sampler for lattice field theories that combines local upsampling with normalizing flows (NFs). At each level, new sites are first sampled independently from Gaussian mixture models and then refined with NFs to introduce correlations, while the coarse sites remain embedded in the finer lattice. Our results show that hierarchical generative sampling...
Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. This approach has close ties to trivializing maps and numerical stochastic perturbation theory, in which field transformations are defined by integrating flow fields that exactly solve a local transport problem. In this talk, I will discuss a new Monte Carlo...
The main contribution to the cost of Lattice QCD calculations typically comes from solving the Dirac equation. Using preconditioners such as multigrid, this computational cost can be reduced significantly. We introduce a novel gauge-equivariant neural network architecture for preconditioning the Dirac equation. We study the behavior of this preconditioner as a function of topological charge...
In many modern machine learning applications, models are often trained
to near zero "training loss" (in other words, to interpolate the
training data), while also having far more training parameters than the
"number of data points". This appears to violate traditional
rules-of-thumb for avoiding overfitting, and considerable work has thus
been devoted to gain a better understanding of...
Gauge fixing is an essential step in lattice QCD calculations, particularly when studying gauge-dependent observables. Traditional iterative algorithms for gauge fixing are computationally expensive and often suffer from critical slowing down near fixed points, as well as scaling bottlenecks on large lattices. We present a novel machine learning framework for lattice gauge fixing, in which...
Investigating the critical endpoint of the finite-temperature QCD phase transition requires higher-order cumulants of the chiral condensate. These, in turn, involve traces of inverse Dirac operator powers $\text{Tr}\,M^{-n}$ ($n=1,2,3,4$). Because direct computation with the Conjugate Gradient method is computationally expensive, we adopted a machine-learning strategy using gradient-boosted...
Domain-wall fermions provide a good lattice realization of chiral fermions by introducing an additional fifth dimension. Achieving improved chiral symmetry typically necessitates increasing the extent of this dimension at the expense of significantly higher computational cost. We propose a machine-learning-based parameter-optimization approach that emulates the effect of a longer fifth...
In this talk, we discuss tests of the Hybrid Monte Carlo algorithm using four dimensional pure SU(3) gauge theory when the conjugate momenta are not chosen as random Gaussian variables of uniform variance for each lattice site, but instead are represented as different normal modes across the lattice volume, with variable variance. Generically, this involves simulating in a fixed gauge. One...
We present a new Monte Carlo sampling method to calculate the rate at which probability flows out of a meta-stable regime in a complex system. In field theory, this method could be used to calculate false vacuum decay rates. The original probability distribution of the system is multiplied by a simple re-weighting function which guarantees that the system transitions between the meta-stable...
We demonstrate, for the first time, that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard modelโa central framework for understanding the electronic structure of graphene and related materials. Conventional approaches such as Hybrid Monte Carlo often encounter ergodicity breakdowns near the time-continuum limit, introducing systematic biases. By...
Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures, with a focus on enhancing stability and efficiency. We further present the scaling...
A while ago, the generalised density-of-states method was proposed to address the sign problem that arises in systems with a complex action. More recently, with the advent of normalising flows and their ability to model complicated target densities, a flow-based density-of-states approach was developed. This method has been shown to successfully reconstruct the partition function of 0D, 1D,...
We study the lattice Schwinger model by combining the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with $\theta=\pi$ are known to exhibit first-order phase transitions for the values of the fermion mass above a critical value,...
This work is motivated by the limitations of conventional Euclidean Monte Carlo methods, particularly the sign problem, which hinder the exploration of physically rich regimes such as nonzero chemical potential, topological terms, and real time dynamics. To address this challenge, we present a Hamiltonian-based variational approach for numerical simulations of quantum mechanical systems. We...
We introduce an all-mode extension of the Higher-Order Tensor Renormalization Group (HOTRG) by using a squeezer transformation at the coarse-graining step. This all-mode framework eliminates systematic errors, leaving only statistical uncertainties, enabling direct comparison with exact results. We demonstrate the method on the two- and three-dimensional Ising models, obtaining results in...
We present a method based on the bootstrap to determine $p$-values from Monte Carlo data, in particular those generated in a lattice QCD calculation, where we make no assumptions about the underlying distribution. By generating samples from the underlying data, we are able to naturally incorporate the effects of autocorrelations and non-normally-distributed samples, both of which skew the...
A new method to approximate Euclidean correlation functions by exponential sums is introduces. The truncated Hankel correlator (THC) method builds a Hankel matrix from the full correlator data available and truncates the eigenspectrum of said Hankel matrix. It proceeds by applying the Prony generalised eigenvalue method to the thus obtained low-rank approximation. A large number of algebraic...
Computing derivatives of observables with respect to parameters of the theory is a powerful tool in lattice QCD, as it allows the study of physical effects not directly accessible in the original Monte Carlo simulation. Prominent examples of this include the impact of the up-down quark mass difference and electromagnetic corrections. In this talk, I will present a new approach based on...
Recent advances such as multigrid and deflation have significantly accelerated Dirac operator solves in lattice QCD. However, the substantial setup costs of these methods have impeded their application in the repeated Dirac inversions required for HMC ensemble generation. Building on earlier work at Columbia University, which showed that renormalization-group (RG) blocked coarse lattices with...
We present a new temperature estimator for lattice gauge theories. This estimator is based on the gradient and Hessian of the Euclidean action. It draws inspiration from geometric methods in statistical mechanics. This approach provides a gauge-invariant and momentum-free way to check thermodynamic consistency in Monte Carlo simulations. Unlike traditional methods, which control temperature...
Preliminary results are presented for an implementation of the overlap Dirac operator in lattice QCD based on the diagonal Kenney-Laub (KL) rational approximation to the matrix sign function. Both the Wilson and Brillouin Dirac operators are tested as kernels. As in any other rational approximation, the diagonal KL iterates of order (n,n) can be decomposed into partial fractions with n poles,...
Ensemble generation remains a central challenge in lattice field theory simulations, as traditional MCMC algorithms suffer from long autocorrelation times. Recent advances in generative modeling, including diffusion models, offer accelerated approaches for sampling complicated probability distributions. In this work, we present a diffusion-based framework for sampling ${\rm SU}(N)$ degrees of...
Real time evolution in QFT poses a severe sign problem, which may be alleviated via a complex Langevin approach.
However, so far simulation results consistently fail to converge with a large real-time extent. A kernel in a complex Langevin equation is known to influence the appearance of the boundary terms and integration cycles, and thus kernel choice can improve the range of real-time...
Complex langevin for theories with a sign problem effectively sample from a real-valued probability distribution that is a priori unknown and notoriously hard to predict. In generative AI, diffusion models can learn distributions from data. In this contribution, we investigate their ability to capture the distributions sampled by a complex Langevin process, comparing score-based and...
Approaching the continuum limit in a lattice field theory is an important but computationally difficult problem. Here, on the one side, most traditional Monte Carlo methods suffer from critical slowing down. On the other side, generative models find it increasingly difficult to learn the map from a simpler to the targeted theory.
To tackle this problem, we construct a generative model using...
