hep-th

arXiv:2501.12116v1 Announce Type: new Abstract: We present a machine learning framework to facilitate the solution of nonlinear multiscale differential equations and, especially, inverse problems using Physics-Informed Neural Networks (PINNs). This framework is based on what is called multihead (MH) training, which involves training the network to learn a general space of all solutions for a given set of equations with certain variability, rather than learning a specific solution of the system. This setup is used with a second novel technique that we call Unimodular Regularization (UR) of the latent space of solutions. We show that the multihead approach, combined with the regularization, significantly improves the efficiency of PINNs by facilitating the transfer learning process thereby enabling the finding of solutions for nonlinear, coupled, and multiscale differential equations.

arXiv:2501.11454v1 Announce Type: cross Abstract: The Sachdev-Ye-Kitaev (SYK) model, known for its strong quantum correlations and chaotic behavior, serves as a key platform for quantum gravity studies. However, variationally preparing thermal states on near-term quantum processors for large systems (N>12, where N is the number of Majorana fermions) presents a significant challenge due to the rapid growth in the complexity of parameterized quantum circuits. This paper addresses this challenge by integrating reinforcement learning (RL) with convolutional neural networks, employing an iterative approach to optimize the quantum circuit and its parameters. The refinement process is guided by a composite reward signal derived from entropy and the expectation values of the SYK Hamiltonian. This approach reduces the number of CNOT gates by two orders of magnitude for systems N>10 compared to traditional methods like first-order Trotterization. We demonstrate the effectiveness of the RL framework in both noiseless and noisy quantum hardware environments, maintaining high accuracy in thermal state preparation. This work contributes to the advancement of a scalable, RL-based framework with applications for computations of thermal out-of-time-order correlators in quantum many-body systems and quantum gravity studies on near-term quantum hardware.

arXiv:2501.07123v1 Announce Type: cross Abstract: Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a key ingredient to describe physical observables measured in high-energy physics processes that involve hadron production, and predict their values at different energy. Fragmentation functions can not be calculated in theory and have to be determined instead from data. Traditional approaches rely on global fits of experimental data using a pre-assumed functional form inspired from phenomenological models to learn its parameters. This novel approach uses a ML technique, namely symbolic regression, to learn an analytical model from measured charged hadron multiplicities. The function learned by symbolic regression resembles the Lund string function and describes the data well, thus representing a potential candidate for use in global FFs fits. This study represents an approach to follow in such QCD-related phenomenology studies and more generally in sciences.

arXiv:2403.02237v2 Announce Type: replace-cross Abstract: We present our investigation of the study of two variable hypergeometric series, namely Appell $F_{1}$ and $F_{3}$ series, and obtain a comprehensive list of its analytic continuations enough to cover the whole real $(x,y)$ plane, except on their singular loci. We also derive analytic continuations of their 3-variable generalization, the Lauricella $F_{D}^{(3)}$ series and the Lauricella-Saran $F_{S}^{(3)}$ series, leveraging the analytic continuations of $F_{1}$ and $F_{3}$, which ensures that the whole real $(x,y,z)$ space is covered, except on the singular loci of these functions. While these studies are motivated by the frequent occurrence of these multivariable hypergeometric functions in Feynman integral evaluation, they can also be used whenever they appear in other branches of mathematical physics. To facilitate their practical use, we provide four packages: $\texttt{AppellF1.wl}$, $\texttt{AppellF3.wl}$, $\texttt{LauricellaFD.wl}$, and $\texttt{LauricellaSaranFS.wl}$ in $\textit{MATHEMATICA}$. These packages are applicable for generic as well as non-generic values of parameters, keeping in mind their utilities in the evaluation of the Feynman integrals. We explicitly present various physical applications of these packages in the context of Feynman integral evaluation and compare the results using other packages such as $\texttt{FIESTA}$. Upon applying the appropriate conventions for numerical evaluation, we find that the results obtained from our packages are consistent. Various $\textit{Mathematica}$ notebooks demonstrating different numerical results are also provided along with this paper.

arXiv:2501.00093v1 Announce Type: cross Abstract: Constructing the landscape of vacua of higher-dimensional theories of gravity by directly solving the low-energy (semi-)classical equations of motion is notoriously difficult. In this work, we investigate the feasibility of Machine Learning techniques as tools for solving the equations of motion for general warped gravity compactifications. As a proof-of-concept we use Neural Networks to solve the Einstein PDEs on non-trivial three manifolds obtained by filling one or more cusps of hyperbolic manifolds. While in three dimensions an Einstein metric is also locally hyperbolic, the generality and scalability of Machine Learning methods, the availability of explicit families of hyperbolic manifolds in higher dimensions, and the universality of the filling procedure strongly suggest that the methods and code developed in this work can be of broader applicability. Specifically, they can be used to tackle both the geometric problem of numerically constructing novel higher-dimensional negatively curved Einstein metrics, as well as the physical problem of constructing four-dimensional de Sitter compactifications of M-theory on the same manifolds.

arXiv:2404.18247v3 Announce Type: replace-cross Abstract: We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields. For a certain solution subspace, we demonstrate partial integrability by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. Subsequently, we study the integrability of these two-dimensional models from a complementary one-dimensional point of view, framed in terms of Liouville integrability. In this endeavour, we employ various machine learning techniques to systematise our search for numerical Lax pair matrices for these models, as well as conserved currents expressed as functions of phase space variables.

arXiv:2406.12916v3 Announce Type: replace Abstract: An important challenge in machine learning is to predict the initial conditions under which a given neural network will be trainable. We present a method for predicting the trainable regime in parameter space for deep feedforward neural networks (DNNs) based on reconstructing the input from subsequent activation layers via a cascade of single-layer auxiliary networks. We show that a single epoch of training of the shallow cascade networks is sufficient to predict the trainability of the deep feedforward network on a range of datasets (MNIST, CIFAR10, FashionMNIST, and white noise), thereby providing a significant reduction in overall training time. We achieve this by computing the relative entropy between reconstructed images and the original inputs, and show that this probe of information loss is sensitive to the phase behaviour of the network. We further demonstrate that this method generalizes to residual neural networks (ResNets) and convolutional neural networks (CNNs). Moreover, our method illustrates the network's decision making process by displaying the changes performed on the input data at each layer, which we demonstrate for both a DNN trained on MNIST and the vgg16 CNN trained on the ImageNet dataset. Our results provide a technique for significantly accelerating the training of large neural networks.