Introductory remarks and overview of the topics of the workshop.
The logarithmic linear relaxation (LLR) method is a density of states method that can precisely determine thermodynamic properties of first order phase transitions, by analysing the micro-canonical structure of both the stable and meta-stable branches of the transition. This is method has become particularly interesting in the context of first order confinement transitions at finite...
Sampling methods based on the density of states provide a framework for determining properties of first-order phase transitions of gauge theories from first principles. These transitions are physically interesting, e.g. in the context of predicting a stochastic gravitational wave signal from early universe phase transitions. I will present results for $Sp(4)$ Yang-Mills theory around its...
The normalising-flow-based density of states approach has recently been shown to successfully reconstruct the partition function of (1+1)D scalar field theories, recovering the correct Lee–Yang zeros. In this talk, we extend this idea by applying gauge-equivariant normalizing flows to reconstruct the density of states in pure (1+1)D U(1) gauge theory with a $\theta$-term. In particular, we...
Since the density of states (DOS) is the foundation for our capacity to compute thermodynamic characteristics, sample complex energy landscapes, and describe rare-event behaviour, accurately calculating the DOS is a crucial challenge in many fields of computational physics. For applications like neutron spectrum analysis, surrogate modelling of reactor behaviour, and uncertainty quantification...
Many extensions of the Standard Model feature first-order phase transitions at the electroweak scale. These are particularly interesting since they may source gravitational waves, the spectrum of which is, in part, determined by the nucleation rate of bubbles. Computing this rate on the lattice requires us to determine the probability of the heavily suppressed critical bubble...
QCD at finite temperature and density is usually studied in the lattice
formalism with a grand canonical approach, where the properties of
the system are defined in terms of the baryochemical potential $\mu$.
Studies in the canonical formulation are less common. Here we present
first canonical results computed with physical quark masses. The simulations
have been performed on...
We present an application of machine-learned flows that reduces the variance in lattice QCD observables. This approach is effective when the desired observable or correlation function can be expressed as a derivative with respect to an action parameter. We demonstrate the computational advantage of this method for several quantities in pure-gauge SU(3) and QCD.
Lattice field theory allows for the direct computation of physical
quantities in strongly coupled theories. In particular, numerical
Monte Carlo simulations using Euclidean correlation functions give
direct access to the energy spectrum of the theory. However, the fast
degradation of the signal with the Euclidean time, known as the signal
to noise problem, significantly affects the...
The sphaleron rate is a key phenomenological quantity, relevant both for axion thermal production in the early Universe and for transport phenomena such as the Chiral Magnetic Effect.
I will begin by outlining the numerical strategy used to extract the sphaleron rate from lattice correlators, employing a regularized Backus–Gilbert reconstruction.
Then, I will present early results for...
Energy-based diffusion models can learn the unnormalised probability distribution from data. We apply this idea to a well-studied example in the context of lattice field theories with a sign problem, for which training data is generated using complex Langevin dynamics. We demonstrate that the learned distribution can subsequently be used to generate configurations using importance sampling....
Recent advances in deep generative modeling have enabled accelerated approaches to sampling complicated probability distributions. In this work, we develop symmetry-equivariant diffusion models to generate lattice field configurations. We build score networks that are equivariant to a range of group transformations and train them using an augmented score matching scheme. By reweighting...
In this talk, I present our results for the machine learning of a renormalization-group improved action for the O(3) non-linear sigma-model in d=2. After introducing the theoretical setup, I will discuss the convolutional neural networks used in this study. Using these networks, we trained a neural network to parameterize a fixed-point action, a classically perfect action. Its properties are...
In this talk I will discuss continuous normalizing flows for the sampling of the theory of quantum rotor. Using this toy model, we study the capability of continuous normalizing flows to sample across different topological sectors, and to help reduce noise in the computation of correlation functions.
A key challenge in designing discrete normalizing flows is to find expressive parametrized transformations that remain invertible and with tractable Jacobian determinant. Existing approaches face trade-offs: affine transformations are simple but limited, while splines are expressive but piecewise-continuous and bounded. We introduce a family of analytic bijections that are smooth, globally...
In lattice field theories with topological sectors, such as QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms struggle to sample the whole configuration space due to large action barriers separating distinct topological sectors. This manifests itself in the form of long autocorrelation times that diverge in the continuum limit and...
We discuss two applications of the Parallel Tempering on Boundary Conditions (PTBC) algorithm to fight topological freezing in the simulation of SU($N$) Yang--Mills theories on the lattice: the determination of the renormalized coupling in the Twisted Gradient Flow scheme and the scale setting via gradient flow. We show that the PTBC algorithm is much more efficient in decorrelating the...
In Lattice QCD, the problem of topological freezing refers to the increasingly long autocorrelation times of topological observables as the continuum limit is approached. In this talk, we present an analysis of a method known to mitigate this: parallel tempering on boundary conditions. This algorithm consists of simultaneously generating several Markov chains or “replicas”, each of these...
Markov Chain Monte Carlo (MCMC) is a powerful algorithmic framework for sampling from complex probability distributions. Standard MCMC methods struggle with high-dimensional distributions containing well-separated modes, becoming trapped in local regions. Parallel tempering (PT) addresses this by using intermediate annealing distributions to bridge a tractable reference (e.g., Gaussian) and an...
Jarzynski equality allows the determination of the free energy difference between the initial and final macrostate of the out-of-equilibrium evolution of a thermodynamic system. This notion has recently been applied to out-of-equilibrium Markov chain Monte Carlo simulations of lattice field theories. The main goal of this talk is to illustrate this methodology.
In particular, we employ this...
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...
We propose a novel algorithm for the solution of the Schrödinger equation of SU(N) lattice gauge theories. Physics-Informed Neural Networks (PINNs) are employed to find the coupling flow of the eigenstates, starting from the strong coupling limit and evolving adiabatically towards the continuum limit at $1/g \to \infty$. For each strong-coupling eigenstate, the trained network provides a...
Many complex systems are modular. Such systems can be represented as "component systems", i.e., sets of elementary components, such as proteins in cells or neurons in the brain. These systems are strongly constrained but the underlying functional design and architecture (for example the structure of gene-regulatory interactions in the cell) is not obvious a priori, and its detection is often a...
In this work, we focus on the development of algorithms to update the field configurations for lattice gauge theories. In particular, we have been interested in testing these methods using the CP$^{N-1}$ model, which reproduces the same physical properties contained in QCD, such as asymptotic freedom, confinement and mass gap. This model has the advantage of being simpler to simulate (requires...