arXiv subjects

Pablo Tejerina-Pérez

Publications and source records attributed to Pablo Tejerina-Pérez.

7 recordsLinked to original sources

arXiv2026

Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua

We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormalization group flows, including skipping flows between non-adjacent fixed points. Building on previous work based on Physics-Informed Neural Networks (PINNs), we extend the holographic inverse problem of reconstructing the bulk scalar potential from boundary thermodynamic data into this new regime. This setting presents a variety of conceptual and numerical challenges, such as near-degenerate states, large hierarchies of energy scales, and regions of the potential that are not directly probed by the input data. We develop a set of methodological advances that overcome these obstacles, thereby improving the established PINNs-based methodology and extending it to new physical regimes of interest that were previously out of reach. Applying the developed framework, we demonstrate accurate reconstruction of scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness. Our results extend the bridge between holography and machine learning, and suggest that data-driven approaches can provide new insights into the structure of strongly coupled systems.

hep-th↗

arXiv2026

Recovering Sharp Conductivity Features in the Finite-Data Calderón Problem with Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calderón inverse problem from limited boundary data. In this work, we revisit neural Calderón inversion by introducing multiscale boundary excitations based on randomized wavelet functions and investigating the role of Fourier-feature encoding (FFE) for representing sharp conductivity variations. We propose a physics-informed reconstruction framework that represents the unknown conductivity and the associated family of electric potentials with separate neural networks conditioned on the applied boundary excitations. The governing elliptic PDE is enforced through physics-informed residuals, while finite Dirichlet-to-Neumann (DtN) data are incorporated through boundary losses. Using synthetic data from a finite-difference forward solver, we evaluate the method on conductivity fields with inclusions, sharp interfaces, smooth profiles, and heterogeneous media. Results show that the framework recovers dominant conductivity structures from finite boundary measurements with relative errors between $3\%-12\%$ approximately. We show that FFE improves the reconstruction of localized sharp features, particularly for inclusions and interfaces, but are not universally optimal, with raw-coordinate networks performing competitively for smoother fields. These results highlight coordinate representations and boundary excitation design as key factors in neural Calderón inversion.

cs.LG↗

arXiv2026

A Bell Experiment in an Entangled Universe

We propose a possible quantum signature of the early Universe that could lead to observational imprints of the quantum nature of the inflationary period. Graviton production from the presence of a classical, coherent state of the inflaton scalar field results in entangled states in the gravitons' polarizations. At horizon crossing, interactions between the gravitons and (lower scale) inflatons, together with the gathering of ``which-path information'' from the cosmological horizon, perform the required Bell experiments leading to a definitive measure, which can be imprinted in the scalar correlation four-point function. This is because of a non-trivial effect due to the derivatives on two scalar fluctuations, and it provides a fingerprint that depends on the polarization of the graviton that Alice and/or Bob measured in their patch. We hint how this signature could be measured in the high-order correlation function of galaxies, in particular on the halo bias and the intrinsic alignment.

astro-ph.CO↗

arXiv2026

A Bell experiment during inflation: probing quantum entanglement in tensor fluctuations through correlations of primordial scalar curvature perturbations

We propose a method that provides an observational signature of the quantum origin of primordial fluctuations generated during inflation. The method gives a prescription for testing a Bell inequality constructed exclusively from the standard scalar and tensor perturbations of minimal single-field inflation. We consider an inflationary spacetime populated by pairs of gravitons entangled in their polarization states. Third-order interactions between two scalars and one graviton transfer polarization information to the scalar sector through the product of spatial derivatives of scalars with the tensor polarization factors. Rather than performing the full multidimensional momentum integrations, we isolate and compute the tensor polarization structure of the primordial scalar eight-point correlation function. This eight-point correlation function factorizes into the product of four scalar two-point functions associated with opposite (mirrored) momentum configurations in Fourier space. This factorization falls from the fact that the two gravitons are spatially well-separated within the cosmological horizon of inflation, replicating the setup of standard Bell experiments. Through these interactions, we track how non-local correlations between both gravitons from polarization entanglement are imprinted on the scalar sector. We show that, for specific configurations of the scalar momenta after the end of inflation (detailed in the text), this observable can be used to construct a Bell-violating quantity in a way that matches the well-known Clauser-Horne-Shimony-Holt inequality definition. In principle, this offers a route to probe the quantum nature of primordial fluctuations through observables accessible today.

astro-ph.CO↗

arXiv2025

Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space

Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here 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 \textit{multi-head} (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 multi-head approach, combined with Unimodular 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.

cs.LG↗

arXiv2024

An Entangled Universe

We propose a possible quantum signature of the early Universe that could lead to observational imprints of the quantum nature of the inflationary period. Graviton production in the presence of an inflaton scalar field results in entangled states in polarization. This is because of a non-trivial effect due to the derivatives on two scalar fluctuations and it provides a fingerprint that depends on the polarization of the graviton that Alice and/or Bob measured in their patch. At horizon crossing, interactions between the gravitons and inflatons perform the required Bell experiments leading to a definitive measure. We hint how this signature could be measure in the high-order correlation function of galaxies, in particular on the halo bias and the intrinsic alignment.

astro-ph.CO↗

arXiv2024

Gravitational Duals from Equations of State

Holography relates gravitational theories in five dimensions to four-dimensional quantum field theories in flat space. Under this map, the equation of state of the field theory is encoded in the black hole solutions of the gravitational theory. Solving the five-dimensional Einstein's equations to determine the equation of state is an algorithmic, direct problem. Determining the gravitational theory that gives rise to a prescribed equation of state is a much more challenging, inverse problem. We present a novel approach to solve this problem based on physics-informed neural networks. The resulting algorithm is not only data-driven but also informed by the physics of the Einstein's equations. We successfully apply it to theories with crossovers, first- and second-order phase transitions.

hep-th↗