arXiv subjects

Pavel Petrov

Publications and source records attributed to Pavel Petrov.

16 recordsLinked to original sources

arXiv2026

NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures

Physics-Informed Neural Networks (PINNs) build neural representations of time-dependent PDE solutions, naturally incorporating physics knowledge and observational data, which makes them well suited to both forward and inverse PDE problems. PINNs, however, are known to suffer from spectral bias and lack of causality. Neuro-Spectral Architectures (NeuSA), a recently proposed alternative to PINNs, mitigate both issues, but their numerical integration becomes unstable for stiff differential equations arising in many relevant physical problems. This study proposes Neuro-Spectral Exponential Time Differencing Architectures (NEXT), which combines the spectral representation of the PDE solution in NeuSA with high-order exponential integrators. Within this approach, the linear stiff part of the vector field induced by the PDE is integrated exactly through matrix exponentials, while the possibly nonlinear remainder is modeled by a neural network. The effectiveness of NEXT is verified through benchmark experiments on a set of stiff PDEs, in which NEXT is stable and accurate while NeuSA diverges numerically. It is also shown that NEXT can be applied to inverse problems, where the model has to learn unknown parameters or boundary conditions from sparse data. All code used in this work is publicly available at: https://github.com/marcioh2m/next.git .

cs.LG↗

arXiv2026

A perfectly matched layer approach for the spectral split-step Padé method

The split-step-Padé (SSP) method is widely used to model wave phenomena in various applications, including radio physics, optics and acoustics. In this method, the propagator of the one-way counterpart of the Helmholtz equation is computed through its Padé approximant and a finite-difference discretization of the transverse operator. This work develops and validates numerically a spectral counterpart of the SSP method. A key challenge in practical applications is inverting the transverse operator in the presence of perfectly matched layers (PMLs), which are commonly used to truncate the computational domain. Such inversion can be accomplished using Krylov subspace methods, which converge rapidly, provided that a suitable preconditioner is used. We also study the analytical properties of the spectral SSP marching scheme under periodicity conditions in the transverse variable. We validate the newly developed spectral SSP method numerically in two realistic test scenarios from radio physics and underwater acoustics.

math.NA↗

arXiv2026

Covariant scalar-tensor theories beyond second derivatives

We propose a covariant, gauge-independent construction of foliation-based scalar-tensor theories, yielding diffeomorphism-invariant operators involving only gradients on the hypersurfaces where the scalar field is constant, assumed to be spacelike. This defines a basis of independent invariants up to four derivatives of $ϕ$, including the first nontrivial parity-odd pseudoscalar at this order, with a straightforward extension to higher derivatives. Our framework goes beyond degenerate higher-order scalar-tensor (DHOST) theories and provides a nonlinear extension of U-DHOST (where $\nabla_μϕ$ is supposed to be timelike) directly in covariant form, without using unitary gauge as a starting point or imposing degeneracy a priori. After minimal coupling to gravity, we analyze the theory through its Hamiltonian constraint structure and linear cosmological perturbations about an FLRW background, and show that it propagates three physical degrees of freedom.

hep-th↗

arXiv2026

Bounds on Gravitational Wave Production from Unitarity in an Early NEC-Violating Model

We study a cosmological scenario featuring an early phase of null energy condition (NEC) violation. Within this framework, we show that perturbative unitarity bounds place strong constraints on both the amplitude and the spectral tilt of primordial gravitational waves. Our analysis is largely insensitive to the detailed realization of the transition between the NEC-violating phase and subsequent cosmological phases, allowing our results to be extended to a broader class of models. Finally, the perturbative unitarity approach employed here is applicable to a wide range of cosmological scenarios.

hep-th↗

arXiv2025

Abelian and non-Abelian mimetic black holes

We investigate black hole solutions in the mimetic extension of the Einstein-Yang-Mills system, in which the Yang-Mills term is constrained to be constant. In the Abelian U(1) case, we find a static spherically symmetric solution that includes the Schwarzschild and Reissner-Nordstrom black holes as special cases. Moreover, we identify a stealth Schwarzschild solution with an electric hair. We show that it is impossible to have magnetic hair in the U(1) gauge case, while, in contrast, the non-Abelian SU(2) stealth solutions can sustain both electric and magnetic hair. Unlike the conventional SU(2) Einstein-Yang-Mills black hole, which requires a unit magnetic parameter to exhibit nontrivial non-Abelian contributions, the stealth mimetic SU(2) solution admits genuinely non-Abelian configurations with arbitrary integer magnetic parameter.

gr-qc↗

arXiv2025

Neuro-Spectral Architectures for Causal Physics-Informed Networks

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

cs.LG↗

arXiv2025

A Spectral Split-Step Padé Method for Guided Wave Propagation

In this study, a Fourier-based, split-step Padé (SSP) method for solving the parabolic wave equation with applications in guided wave propagation in ocean acoustics is presented. Traditional SSP implementations rely in finite-difference discretizations of the depth-dependent differential operator. This approach limits accuracy in coarse discretizations as well as computational efficiency in dense discretizations since it does not significantly benefit from parallelization. In contrast, our proposed method replaces finite differences with a spectral representation using the discrete sine transform (DST). This enables an exact treatment of the vertical operator under homogeneous boundary conditions. For non-constant sound speed, we use a Neumann series expansion to treat inhomogeneities as perturbations. Numerical experiments demonstrate the method's accuracy in range-independent media and rage-dependent scenarios, including propagation in deep ocean with Munk profile and in the presence of a parametrized synoptic eddy. Compared to finite-difference SSP methods, the Fourier-based approach achieves higher accuracy with fewer depth discretization points and avoids the resolution bottleneck associated with sharp field features, making it well-suited for large-scale, high-frequency wave propagation problems in ocean environments.

math.NA↗

arXiv2025

Linear Higher-Order Maxwell-Einstein-Scalar Theories

In the context of the Higher-Order Maxwell-Einstein-Scalar (HOMES) theories, which are invariant under spacetime diffeomorphisms and $U(1)$ gauge symmetry, we study two broad subclasses: the first is up to linear in $R_{μναβ}$, $\nabla_μ\nabla_νϕ$, $\nabla_ρ{F}_{μν}$ and up to quadratic in the vector field strength tensor $F_{μν}$; the second is up to linear in $\nabla_μ\nabla_νϕ$, contains no second derivatives of vector field and metric, but allows for arbitrary functions/powers of $F_{μν}$. Under these assumptions, we systematically derive the most general form of the action that leads to second-order (or lower) equations of motion. We prove that, among 41 possible terms in the first subclass, only four independent higher-derivative terms are allowed: the kinetic gravity braiding term $G_3(ϕ,X)\Boxϕ$ in the scalar sector with $X = -\nabla_μϕ\nabla^μϕ/ 2$; the Horndeski non-minimal coupling term $w_0(ϕ)R_{βδαγ}\tilde{F}^{αβ} \tilde{F}^{γδ}$ in the vector field sector, where $\tilde{F}^{μν}$ is the Hodge dual of $F_{μν}$; and two interaction terms between the scalar and vector field sectors: $[w_1(ϕ,X) g_{ρσ} + w_2(ϕ,X) \nabla_ρϕ\nabla_σϕ] \nabla_β\nabla_αϕ\, \tilde{F}^{αρ} \tilde{F}^{βσ}$. For the second subclass, which admits 11 possible terms, three of these four, excluding the Horndeski non-minimal coupling term proportional to $w_0(ϕ)$, are allowed. These independent terms serve as the building blocks of each subclass of HOMES. Remarkably, there is no higher-derivative parity-violating term in either subclass. Finally, we propose a new generalization of higher-derivative interaction terms for the case of a charged complex scalar field.

hep-th↗

arXiv2025

Genesis--Starobinsky inflation can explain the ACT data

We propose a novel non-singular cosmological scenario within the framework of Horndeski gravity, consisting of three successive stages: (i) a Genesis phase, in which the Universe slowly expands from an asymptotically flat spacetime; (ii) a brief transition stage restoring General Relativity; and (iii) a Starobinsky inflationary phase. This construction is fully consistent within a viable parameter space: it remains weakly coupled, free from ghost and gradient instabilities, with luminal tensor and subluminal scalar perturbations throughout the entire evolution. Importantly, the Genesis phase induces characteristic corrections to the Starobinsky potential, which cannot be captured by simple $\sum_i c_i R^i$-type modifications. These corrections robustly enhance the scalar spectral index, thereby improving the agreement of Starobinsky inflation with recent CMB measurements, in particular the data from the Atacama Cosmology Telescope (ACT).

gr-qc↗

arXiv2025

Square Root Operators and the Well-Posedness of Pseudodifferential Parabolic Models of Wave Phenomena

Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a known function. We discuss a rigorous definition of such operator square roots and show well-posedness of the pseudodifferential parabolic equation by using the theory of strongly continuous semigroups. This provides a justification for a family of widely-used numerical methods for wavefield simulations in various areas of physics.

physics.ao-ph↗

arXiv2025

Can Horndeski Genesis be Nonpathological?

We present a minimal setup within the framework of Horndeski gravity that can describe a nonpathological Genesis scenario. Our setup allows for a fully stable transition to the kination epoch, during which General Relativity (GR) is restored. This Genesis scenario circumvents the no-go theorem at the cost of encountering the risk of strong coupling in the past. Interestingly, our scenario admits two different regimes for the background solution for Hubble parameter at the Genesis stage: power-law behavior and manifestly non-power-law behavior. We explicitly show that, in both regimes, our model remains within unitarity bounds. In most cases, the tensor spectrum is blue-tilted. Then, we adopt a mechanism with a spectator field that allows for a red-tilted scalar power spectrum. We also suggest a deformation of the model that enables us to achieve sufficiently small values for the r ratio. Finally, we discuss the geodesic (in)completeness of the current model.

hep-th↗

arXiv2020

An adaptive algorithm for embedding information into compressed JPEG images using the QIM method

The widespread use of JPEG images makes them good covers for secret messages storing and transmitting. This paper proposes a new algorithm for embedding information in JPEG images based on the steganographic QIM method. The main problem of such embedding is the vulnerability to statistical steganalysis. To solve this problem, it is proposed to use a variable quantization step, which is adaptively selected for each block of the JPEG cover image. Experimental results show that the proposed approach successfully increases the security of embedding.

cs.MM↗

arXiv2018

Galileon-like vector fields

We construct simple Lagrangians of vector fields which involve second derivatives, but nevertheless lead to second order field equations. These vector fields are, therefore, analogs of generalized Galileons. Our construction is given first in Minkowski space, and then generalizied to include dynamical gravity. We present examples of backgrounds that are stable and ghost-free despite the absence of gauge invariance. Some of these backgrounds violate the Null Energy Condition.

hep-th↗

arXiv2017

Topological Data Analysis of Clostridioides difficile Infection and Fecal Microbiota Transplantation

Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a single index, and is able to capture higher order features beyond the usual clustering techniques. There are three descriptive statistics of persistent homology, namely barcode, persistence diagram and more recently, persistence landscape. Persistence landscape is useful for statistical inference as it belongs to a space of $p-$integrable functions, a separable Banach space. We apply tools in both computational topology and statistics to DNA sequences taken from Clostridioides difficile infected patients treated with an experimental fecal microbiota transplantation. Our statistical and topological data analysis are able to detect interesting patterns among patients and donors. It also provides visualization of DNA sequences in the form of clusters and loops.

q-bio.QM↗

arXiv2010

Electron star birth: A continuous phase transition at nonzero density

We show that charged black holes in Anti-de Sitter spacetime can undergo a third order phase transition at a critical temperature in the presence of charged fermions. In the low temperature phase, a fraction of the charge is carried by a fermion fluid located a finite distance from the black hole. In the zero temperature limit the black hole is no longer present and all charge is sourced by the fermions. The solutions exhibit the low temperature entropy density scaling s~T^{2/z} anticipated from the emergent IR criticality of recently discussed electron stars.

hep-th↗

arXiv2009

Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory

We use the real-time finite-temperature AdS/CFT correspondence to compute the effect of general R^2 corrections to the gravitational action in AdS space on the shear viscosity of the dual gauge theory. The R^2 terms in AdS_5 are determined by the central charges of the CFT. We present an example of a four-dimensional gauge theory in which the conjectured lower bound of 1/(4π) on the viscosity-to-entropy ratio is violated for finite N.

hep-th↗