Related papers: Generative Flow Networks in Covariant Loop Quantum…

Many score-based active learning methods have been successfully applied to graph-structured data, aiming to reduce the number of labels and achieve better performance of graph neural networks based on predefined score functions. However,…

We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the…

Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization…

A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. However, this choice of kinematics can easily lead to gravitational dynamics peaked on…

The Spin Foam approach to quantum gravity aims at providing a covariant path-integral formulation of canonical Loop Quantum Gravity. Since spin foam amplitudes are defined through discretisations of spacetime, understanding the continuum…

Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying…

A framework to learn a multi-modal distribution is proposed, denoted as the Conditional Quantum Generative Adversarial Network (C-qGAN). The neural network structure is strictly within a quantum circuit and, as a consequence, is shown to…

Granular flows govern many natural and industrial processes, yet their interior kinematics and mechanics remain largely unobservable, as experiments access only boundaries or free surfaces. Conventional numerical simulations are…

So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2)_k$ and examine their…

The goal of spin foam models is to provide a viable path integral formulation of quantum gravity. Because of background independence, their underlying framework has certain novel features that are not shared by path integral formulations of…

As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…

This article deals with approximating steady-state particle-resolved fluid flow around a fixed particle of interest under the influence of randomly distributed stationary particles in a dispersed multiphase setup using Convolutional Neural…

Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant…

We review the canonical analysis of the Palatini action without going to the time gauge as in the standard derivation of Loop Quantum Gravity. This allows to keep track of the Lorentz gauge symmetry and leads to a theory of Covariant Loop…

Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…

Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling…

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL(2,C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic…

Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…