Related papers: Deformations of Boltzmann Distributions
This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…
The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for…
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…
Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In…
The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve…
The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same…
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the…
A new lattice Boltzmann (LB) model is introduced, based on a regularization of the pre-collision distribution functions in terms of the local density, velocity, and momentum flux tensor. The model dramatically improves the precision and…
Normalizing flows are an established approach for modelling complex probability densities through invertible transformations from a base distribution. However, the accuracy with which the target distribution can be captured by the…
Stochastic normalizing flows are a class of deep generative models that combine normalizing flows with Monte Carlo updates and can be used in lattice field theory to sample from Boltzmann distributions. In this proceeding, we outline the…
The Boltzmann distribution (the most probable distribution) is one of the most important concepts used in physics, chemistry and biology. Suppose we put the system initially in one of the less probable state then the system will find the…
Consider a random polynomial $P_n$ of degree $n$ whose roots are independent random variables sampled according to some probability distribution $\mu_0$ on the complex plane $\mathbb C$. It is natural to conjecture that, for a fixed $t\in…
The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered.…
In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied…
Lattice-Boltzmann methods are established mesoscopic numerical schemes for fluid flow, that recover the evolution of macroscopic quantities (viz., velocity and pressure fields) evolving under macroscopic target equations. The approximated…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
In the frame of the Boltzmann equation, wall-bounded flows of rarefied gases require the implementation of boundary conditions at the kinetic level. Such boundary conditions induce a discontinuity in the distribution function with respect…
Flow-based generative models have been employed for sampling the Boltzmann distribution, but their application to high-dimensional systems is hindered by the significant computational cost of obtaining the Jacobian of the flow. To overcome…