Conveners
Algorithms and artificial intelligence: LT2
- Scott Lawrence (Los Alamos National Laboratory)
Algorithms and artificial intelligence: LT2
- Antonio Rago (QTC & IMADA, University of Southern Denmark)
Algorithms and artificial intelligence: LT2
- Akio Tomiya (TWCU)
Algorithms and artificial intelligence: LT2
- Walter Wilcox (Baylor University)
Algorithms and artificial intelligence: LT2
- Gurtej Kanwar (University of Bern)
Algorithms and artificial intelligence: LT2
- Gert Aarts (Swansea University)
Algorithms and artificial intelligence: LT2
- Andreas Athenodorou (The Cyprus Institute)
Algorithms and artificial intelligence: LT2
- Lorenz von Smekal (Justus Liebig University Giessen, Helmholtz Forschungsakademie Hessen fรผr FAIR)
Algorithms and artificial intelligence: LT2
- James Osborn (ANL)
We present our preliminary results on the machine learning estimation of $\text{Tr} \, M^{-n}$ from other observables with the gradient boosting decision tree regression, where $M$ is the Dirac operator. Ordinarily, $\text{Tr} \, M^{-n}$ is obtained by linear CG solver for stochastic sources which needs considerable computational cost. Hence, we explore the possibility of cost reduction on the...
Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational cost. Adopting the methods of the minimally-decomposed TRG and its Triad prescriptions, we construct a Triad representation of the 4D ATRG by decomposing the...
In this talk, we will discuss transformers that preserve gauge symmetry and their applications. Gauge symmetry is crucial in lattice QCD. There has been significant progress in accelerating lattice calculations using machine learning, particularly neural networks. Meanwhile, in the field of machine learning, transformers such as GPT have rapidly advanced and transformed society. Transformers...
The expressive power of neural networks in modeling complex distributions is desirable to bypass topological freezing and critical slowing down in simulations of lattice field theory. Some approaches suffer from problems with topology, which may lead to some classes of configurations not being generated. In this talk, I will present a novel generative approach inspired by a model previously...
The Heatbath Algorithm is popular for sampling local lattice field theories. However, exact updates or sampling from the local density are challenging due to the continuous nature of the variables. Rejection methods can have low acceptance rates if the proposal is not correctly chosen, which is a non-trivial task. In this talk, I will propose a new and simple method for making proposals at...
The study of Quantum Chromodynamics (QCD) at non-zero baryonic density from first principles is notoriously hard due to the infamous sign problem. One way to potentially by-pass the sign problem is the complex Langevin approach, which is based on a complexification of the underlying field manifold. While this method does not suffer from a sign problem, it is plagued by its own set of...
The complex Langevin (CL) method shows significant potential in addressing the numerical sign problem. Nonetheless, it often produces incorrect results when used without any stabilization techniques. Leveraging insights from previous research that links Lefschetz thimbles and CL, we explore a strategy to regularize the CL method to address this issue of incorrect convergence. Specifically, we...
Diffusion models are currently the leading generative AI approach used for image generation in e.g. DALL-E and Stable Diffusion. In this talk we relate diffusion models to stochastic quantisation in field theory and employ it to generate configurations for scalar fields on a two-dimensional lattice. We end with some speculations on possible applications.
The probability distribution effectively sampled by a complex Langevin process for theories with a sign problem is not known a priori and notoriously hard to understand. Diffusion models, a class of generative AI, can learn distributions from data. In this contribution, we explore the ability of diffusion models to learn the distributions created by a complex Langevin process.
We present spectral functions extracted from Euclidean-time correlation functions by using sparse modeling. Sparse modeling is a method that solves inverse problems by considering only the sparseness of the solution we seek, without a default model. To check applicability of the method, we firstly test it with mock data which imitate charmonium correlation functions on a fine lattice. We show...
In lattice QCD studies, physical observables like the chiral
condensate or baryon number density are computed as the trace of a
combination of products of the inverse fermion matrix, typically
estimated stochastically using the random noise method. The accuracy of
this method depends on the number of random sources used; ideally, an
infinite number of sources would yield true physical...
In lattice QCD, the precision of results is often hampered by the inherent uncertainty of stochastic methods. Recently, control variates methods have emerged as a promising solution for such noise. Traditional control variates have been used to mitigate this issue, but they rely on educated guesses, which can be limiting. In this talk, I will introduce a neural network approach to parametrize...
Parton Distribution Functions (PDFs) describe universal properties of bound states and allow to calculate scattering amplitudes in processes with large momentum transfer. Calculating PDFs involves the evaluation of correlators with a Wilson line in lightcone-direction. In contrast to Monte Carlo methods in euclidean spacetime, these correlation functions can be directly calculated in the...
The tensor renormalization group (TRG) method is a powerful tool for studying lattice field theories and quantum many-body systems that is free from the sign problem. In this talk, I discuss two of the recent developments toward the TRG study of lattice QCD. The first is the proposal for incorporating multiple fermion flavors for 2D Abelian gauge theory, using the Grassmann tensor network. The...
We propose a method for the construction of the initial tensor representation and its dependence on the tensor renormalization group (TRG). The TRG method is a numerical calculation technique that utilizes tensor network representations of physical quantities to investigate physical properties without encountering the sign problem.
To apply the TRG method, it is essential to make a typical...
Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications, including lattice field theory and quantum chemistry.
However, the inherent noise present in Noisy Intermediate-Scale Quantum (NISQ) devices poses a significant...
Field-Transformed Hybrid Monte-Carlo (FTHMC) algorithm potentially mitigates the issue of critical slowing down by combining HMC with a field transformation, originally proposed by Luscher and motivated
as trivializing the theory.ย For the transformation, we use an invertible discrete smearing step modelled on the Wilson flow and applied it to the system with Iwasaki gauge fields and 2+1...
Hybrid Monte Carlo (HMC) simulations often suffer from long autocorrelation times, severely reducing their efficiency. In this talk two of the main sources of autocorrelations are identified and eliminated. The first source is the sampling of the canonical momenta from a sub-optimal normal distribution, the second is a badly chosen trajectory length. Analytic solutions to both problems are...
Many quantum field theories, including (potentially) the Standard Model, have metastable false vacuum states. Usually, false vacuum decay rates are calculated using the semi-classical approximation. We present a method for calculating false vacuum decay rates using lattice Monte Carlo simulations. As a proof-of-concept, we test the method using one-dimensional quantum mechanics. This method...
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such investigations. Here we apply concepts from random matrix theory to describe stochastic weight matrix dynamics, using the framework of Dyson Brownian motion. We derive...
Normalizing flows have recently arisen as a potential tool for aiding in sampling lattice field theories. In this talk I will give an overview of our groups' recent progress in applying normalizing flows to 4-dimensional nonabelian gauge theories, as well as current efforts to scale normalizing flows towards modern lattice field theory calculations.
Normalizing Flows (NFs) are a class of deep generative models recently proposed as a promising alternative to traditional Markov Chain Monte Carlo methods in lattice field theory calculations. By combining NF layers with out-of-equilibrium stochastic updates, we obtain Stochastic Normalizing Flows (SNFs), an intriguing class of machine learning algorithms that can be explained in terms of...
Non-equilibrium Monte Carlo simulations based on Jarzynski's equality are a well-understood method to compute differences in free energy and also to sample from a target probability distribution without the need to thermalize the system under study. In each evolution, the system starts from a given base distribution at equilibrium and it is gradually driven out-of-equilibrium while evolving...
In this talk, we give a progress report on exploring the method of normalizing
flows for generating gauge configurations. We discuss how to use the singular
value decomposition (SVD) to construct gauge-invariant quantities, which can be
employed to build gauge equivariant transformations of SU($n$) gauge links.
We discuss this algorithm's efficiency compared to Wilson loops' spectral flow.
We present a novel class of Hessian-free force-gradient integrators [[arXiv:2403.10370]][1]. Unlike traditional force-gradient integrators, the Hessian-free variants do not require the analytical expression of the force-gradient term, which includes the Hessian of the potential. Instead, this term is approximated through an additional force evaluation.
We examine the order conditions and...
When approaching the continuum, conventional update algorithms in lattice QCD and other topologically non-trivial theories experience a particularly severe form of critical slowing down that is caused by high action barriers separating the different topological sectors. Previous tests in different theories have shown that Metadynamics can be used to overcome these barriers and reduce the...
MCMC simulations of topologically non-trivial gauge theories such as QCD are plagued by long autocorrelation times, due to systems spending exponentially longer time stuck in a single topological sector at finer lattice spacings, which are necessary for high precision studies. This phenomenon is known as topological freezing, and several algorithms have been suggested to amend it throughout...
We will extend previous work on tuning HMC parameters using gradient information to include Hasenbusch mass ratios. The inclusion of mass ratios adds many more parameters that need to be tuned, and also allows for lots of variations in the choice of integrator pattern. We will investigate the effectiveness of automatically tuning a large number of HMC parameters and compare the optimally...
In this talk I will present the main results of our recent use of multilevel sampling to more efficiently reduce the error of glueball two-point functions in pure gauge theory. I will then discuss how multilevel can be combined with distillation techniques for quenched QCD simulations. In particular, I will present some preliminary results for disconnected contributions of two-pion correlation...
Typically, the conjugate gradient (CG) algorithm employs mixed precision and even-odd preconditioning to compute propagators for highly improved staggered quarks (HISQ). This approach suffers from critical slowing down as the light quark mass is decreased to its physical value. Multigrid is one alternative to combat critical slowing down, however, it involves setup costs which are not always...
We report results from the application of Fourier acceleration to $SU(3)$ lattice gauge theory using softly-fixed Landau gauge. Acceleration of the HMC algorithm is studied on a $16^4$ lattice volume with the Wilson gauge action and different values of $\beta$. Two types of boundary conditions with fixed boundary links are explored. The boundary links are fixed either to unit matrices or to...
A modification to the setup algorithm for the multigrid preconditioner of Wilson fermions is presented. A larger basis of test vectors than used in conventional multigrid is calculated by the smoother and is truncated by a singular value decomposition on the chiral components of the test vectors. The truncated basis is used to form the prolongation and restriction matrices of the multigrid...
Hamiltonian Simulations of non-abelian lattice gauge theories promise
new insights into multiple areas of QCD. To run numerical simulations,
the operators contained in the Kogut Susskind Hamiltonian need to be
discretised. While this is a mostly solved problem at strong couplings,
simulations in the weak coupling limit remain tricky. In this talk, we
report on our ongoing efforts to find...
We present the application of the Nested Sampling (NS) algorithm to lattice gauge theories. It allows to scan the $\beta$ dependence of any observable in a custom range of values, avoiding the need to run multiple simulations at different values of the coupling. As a concrete example, we consider the case of a pure gauge U(1) theory in 2+1 dimensions, a toy model for QCD showing confinement at...
We consider nested sampling as a generic integration technique over the space of lattice configurations and discuss its application to compute the density of states and the free energy. We show the benefits of this alternative sampling method for systems which suffer from ergodicity problems due to non-efficient tunneling, e.g. topological freezing. As a proof of principle, we apply nested...
Nested Sampling (NS) gives access to observables across a range of couplings and temperatures from one Monte Carlo simulation. This talk demonstrates an application of NS to the first-order confinement transition in 3+1D SU(3) gauge theory, highlighting practicalities of the implementation, such as how NS handles the suppressed tunneling between coexisting phases at the phase transition.
The extraction of interesting physics from lattice data is dependent on how precisely the expectation values of observables can be obtained.
I will in this talk present a method to utilize the smoothness of observables to improve the level of precision by calculating how the volume contracts or expands as the observable changes.
To do this, we will derive a formula to calculate the local...
A quantum mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of exponential (e.g. in volume) dimension, but low-dimensional projections can be efficiently explored by standard algorithms. Such approaches have been used to...
I describe a generalization of the Hybrid Monte Carlo (HMC) algorithm with molecular dynamics (MD) steps which use Nambuโs generalized Hamiltonian dynamics. Characterized by multiple Hamiltonian functions, this formalism allows me to include forces from non-local objects in the MD evolution while still preserving the target probability distribution. In this way, the local changes proposed by...
The Riemannian Manifold HMC (RMHMC) is designed to tackle critical slowing down by utilizing a rational function of the SU(3) gauge covariant laplace operator in place of the canonical mass term in the HMC algorithm. The RMHMC has been demonstrated to be effective at increasing the rate of change of long distance modes. We present the results of the recent studies done to tune the algorithm...
On the geometric convergence of HMC on Riemannian manifolds.
In this presentation we apply Harris' ergodic theorem on Markov chains to prove
the geometric convergence of Hamiltonian Monte Carlo: first on compact
Riemannian manifolds, and secondly on a large class of non-compact Riemannian
manifolds by introducing an extra Metropolis step in the radial direction. We
shall use $\phi^4$...
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for solving the sign problem. This method eliminates the ergodicity problem inherent in methods based on Lefschetz thimbles at low cost. In this talk, in preparation for its application to lattice QCD, we extend the WV-HMC method to the case where the configuration space is a group...
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is
a low-cost algorithm for solving the sign and the ergodicity problems simultaneously. We apply the WV-HMC method to the (1+2)-dim Hubbard model, which can be regarded as a prototype of QCD at finite density. We investigate the computational scaling and compare the results of observables with those obtained by a...
