arXiv subjects

Antoine Venaille

Publications and source records attributed to Antoine Venaille.

At least 19 recordsLinked to original sources

arXiv2026

Correlation flow governs learning at criticality

The initialization of deep neural networks determines whether information and gradients can propagate across depth, yet a unified theory connecting these properties to learning dynamics remains elusive. Combining mean-field theory and random matrix theory, we establish a direct link between correlation propagation and the Neural Tangent Kernel (NTK) that governs learning in the sequential limit of infinitely wide, infinitely deep networks. Correlation propagation to infinite depth is possible only at a single, critical point in the weight-bias variance plane. At this point, we leverage the algebraic decay of the end-to-end Jacobian with depth to prove that the NTK becomes exactly proportional to the output correlation at infinite depth, tying together information propagation and learning dynamics. We further show that orthogonal initialization suppresses the leading finite-size corrections present under Gaussian initialization, clarifying the respective roles of the two initialization ensembles in this limit. These theoretical predictions are validated quantitatively on finite-width, finite-depth networks. Together, these results demonstrate that orthogonal initialization and criticality are required to control the asymptotic dynamics of deep learning.

cs.LG↗

arXiv2026

Enhanced Gulf Stream Path Variability Under Intensified Stratification

Increased upper-ocean stratification is an unavoidable consequence of global warming and will strongly impact the structure of ocean currents. Using a high-resolution ocean model, we show that intensification of stratification leads to the loss of coherence of the Gulf Stream Extension, replacing its steady eastward path with vigorous, chaotic meanders. This regime shift persists independently of changes in the Atlantic Meridional Overturning Circulation and surface wind forcing. Enhanced meandering under intensified stratification also proves to be a robust feature across both idealized and realistic ocean models that resolve mesoscale eddies, but is not captured by coarse-resolution models that parameterize eddies. The presented findings therefore highlight the need for improved representations of oceanic turbulence in climate projections.

physics.ao-ph↗

arXiv2025

A new initialisation to Control Gradients in Sinusoidal Neural network

Proper initialisation strategy is of primary importance to mitigate gradient explosion or vanishing when training neural networks. Yet, the impact of initialisation parameters still lacks a precise theoretical understanding for several well-established architectures. Here, we propose a new initialisation for networks with sinusoidal activation functions such as \texttt{SIREN}, focusing on gradients control, their scaling with network depth, their impact on training and on generalization. To achieve this, we identify a closed-form expression for the initialisation of the parameters, differing from the original \texttt{SIREN} scheme. This expression is derived from fixed points obtained through the convergence of pre-activation distribution and the variance of Jacobian sequences. Controlling both gradients and targeting vanishing pre-activation helps preventing the emergence of inappropriate frequencies during estimation, thereby improving generalization. We further show that this initialisation strongly influences training dynamics through the Neural Tangent Kernel framework (NTK). Finally, we benchmark \texttt{SIREN} with the proposed initialisation against the original scheme and other baselines on function fitting and image reconstruction. The new initialisation consistently outperforms state-of-the-art methods across a wide range of reconstruction tasks, including those involving physics-informed neural networks.

cs.LG↗

arXiv2025

A core-sensitive mixed $f$/$g$ mode of the Sun predicted by wave topology and hydrodynamical simulation

Helioseismology has revolutionized our understanding of the Sun by analyzing its global oscillation modes. However, the solar core remains elusive, limiting a full understanding of its evolution. In this work, we study a previously unnoticed global oscillation mode of the Sun using a fully compressible, hydrodynamical simulation of the solar interior, and assess that it is a mixed $f$/$g$ mode with a period of about one hour. This is the first global stellar hydrodynamics simulation that successfuly couple compressible and gravity modes. To understand this coupling, we invoke a recent theory on the nature of $f$-modes seen through the prism of wave topology, characterizing their ability to propagate deep into stellar interiors. We demonstrate that the mixed $f$/$g$ mode is highly sensitive to the core's rotation rate, providing a new promising pathway to explore the Sun's core.

astro-ph.SR↗

arXiv2025

The Impact of Stratification on Surface-Intensified Eastward Jets in Turbulent Gyres

This study examines the role of stratification in the formation and persistence of eastward jets (like the Gulf Stream and Kuroshio currents). Using a wind-driven, two-layer quasi-geostrophic model in a double-gyre configuration, we construct a phase diagram to classify flow regimes. The parameter space is defined by a criticality parameter $ ξ$, which controls the emergence of baroclinic instability, and the ratio of layer depths $ δ$, which describes the surface intensification of stratification. Eastward jets detaching from the western boundary are observed when $ δ\ll 1 $ and $ ξ\sim 1 $, representing a regime transition from a vortex-dominated western boundary current to a zonostrophic regime characterized by multiple eastward jets. Remarkably, these surface-intensified patterns emerge without considering bottom friction. The emergence of the coherent eastward jet is further addressed with complementary 1.5-layer simulations and explained through both linear stability analysis and turbulence phenomenology. In particular, we show that coherent eastward jets emerge when the western boundary layer is stable, and find that the asymmetry in the baroclinic instability of eastward and westward flows plays a central role in the persistence of eastward jets, while contributing to the disintegration of westward jets.

physics.flu-dyn↗

arXiv2025

Deep learning in the abyss: a stratified Physics Informed Neural Network for data assimilation

The reconstruction of deep ocean currents is a major challenge in data assimilation due to the scarcity of interior data. In this work, we present a proof of concept for deep ocean flow reconstruction using a Physics-Informed Neural Network (PINN), a machine learning approach that offers an alternative to traditional data assimilation methods. We introduce an efficient algorithm called StrAssPINN (for Stratified Assimilation PINNs), which assigns a separate network to each layer of the ocean model while allowing them to interact during training. The neural network takes spatiotemporal coordinates as input and predicts the velocity field at those points. Using a SIREN architecture (a multilayer perceptron with sine activation functions), which has proven effective in various contexts, the network is trained using both available observational data and dynamical priors enforced at several collocation points. We apply this method to pseudo-observed ocean data generated from a 3-layer quasi-geostrophic model, where the pseudo-observations include surface-level data akin to SWOT observations of sea surface height, interior data similar to ARGO floats, and a limited number of deep ARGO-like measurements in the lower layers. Our approach successfully reconstructs ocean flows in both the interior and surface layers, demonstrating a strong ability to resolve key ocean mesoscale features, including vortex rings, eastward jets associated with potential vorticity fronts, and smoother Rossby waves. This work serves as a prelude to applying StrAssPINN to real-world observational data.

physics.ao-ph↗

arXiv2025

Disentangling discrete and continuous spectra of tidally forced internal waves in shear flow

Generation of internal waves driven by barotropic tides over seafloor topography is a central issue in developing mixing and wave drag parameterizations for ocean circulation models. Traditional analytical approaches estimate the energy conversion rate from barotropic tides to internal waves using a modal expansion of the wave field. However, this framework becomes inadequate if a background shear flow is present, as singular solutions associated with critical levels emerge. To uncover the distinct roles of regular eigenmodes and singular solutions in tidal energy conversion, this study analytically investigates wave generation over a localized small topography in the presence of shear flow without Coriolis force. Applying horizontal Fourier and temporal Laplace transforms, we identify regions in the topographic wavenumber and forcing frequency space where unbounded energy growth occurs. These regions coincide with the spectrum of an operator governing free wave propagation and consist of discrete and continuous parts, which correspond to regular eigenmodes and singular solutions, respectively. Asymptotic evaluation of the Fourier integral reveals that the far-field response comprises standing wave trains linked to the discrete spectrum and evolving wave packets associated with the continuous spectrum. While the velocity amplitudes of the wave packets decay, their vertical velocity gradients grow during propagation, potentially leading to wave breaking. Finally, we derive a formula for the net barotropic-to-baroclinic energy conversion rate, extending the classical one by incorporating the contributions from both the discrete and continuous spectra.

physics.flu-dyn↗

arXiv2024

Bulk-Edge Correspondence Recovered in Incompressible Geophysical Flows

Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes in parameter space. In continuous media, violation of this correspondence has been reported when some of the frequency wavebands are unbounded, resulting in weak topological protection of chiral edge states. Here, we propose a strategy to reestablish strong bulk-edge correspondence in incompressible rotating stratified flows, taking advantage of a natural cutoff frequency provided by density stratification. The key idea involves the introduction of an auxiliary field to handle the divergence-free constraint. This approach highlights the resilience of internal coastal Kelvin waves near vertical walls under varying boundary conditions.

cond-mat.other↗

arXiv2024

Gyre Turbulence

The exploration of a two-dimensional wind-driven ocean model with no-slip boundaries reveals the existence of a turbulent asymptotic regime where energy dissipation becomes independent of fluid viscosity. This asymptotic flow represents an out-of-equilibrium state, characterized by a vigorous two-dimensional vortex gas superimposed onto a western-intensified gyre. The properties of the vortex gas are elucidated through scaling analysis for detached Prandtl boundary layers, providing a rationalization for the observed anomalous dissipation. The asymptotic regime demonstrates that boundary instabilities alone can be strong enough to evacuate wind-injected energy from the large-scale oceanic circulation.

physics.flu-dyn↗

arXiv2023

Recovering Quasi-Biennial Oscillations from Chaos

The Quasi-Biennial Oscillation (QBO) is understood to result from wave-mean-flow interactions, but the reasons for its relative stability remain a subject of ongoing debate. In addition, consensus has yet to be reached regarding the respective roles of different equatorial wave types in shaping the QBO's characteristics. Here we employ Holton-Lindzen-Plumb's quasilinear model to shed light on the robustness of periodic behavior in the presence of multiple wave forcings. A comprehensive examination of the various dynamical regimes in this model reveals that increased vertical wave propagation at higher altitudes favors periodicity. In the case of single standing wave forcing, enhanced vertical propagation is controlled by the wave attenuation length scale. The occurrence of non-periodic states at high forcing amplitudes is explained by the excitation of high vertical unstable modes. Increasing the attenuation length scale prevents the emergence of such modes. When multiple wave forcing is considered, the mean flow generated by a dominant primary wave facilitates greater vertical propagation of a perturbation wave. Raising the altitude where most of the wave damping occurs favors periodicity by preventing the development of secondary jets responsible for the aperiodic behavior. This mechanism underscores the potential role of internal gravity waves in supporting the periodicity of a QBO primarily driven by planetary waves.

physics.ao-ph↗

arXiv2022

From ray tracing to waves of topological origin in continuous media

Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of topological origin. It has been realized over the last decades that such waves of topological origin can be predicted by computing a single topological invariant, the first Chern number, in a dual bulk wave problem that is much simpler to solve than the original wave equation involving spatially varying coefficients. The correspondence between the simple bulk problem and the more complicated interface problem is usually justified by invoking an abstract index theorem. Here, by applying ray tracing machinery to the paradigmatic example of equatorial shallow water waves, we propose a physical interpretation of this correspondence. We first compute ray trajectories in a phase space given by position and wavenumber of the wave packet, using Wigner-Weyl transforms. We then apply a quantization condition to describe the spectral properties of the original wave operator. We show that the Chern number emerges naturally from this quantization relation.

physics.flu-dyn↗

arXiv2022

Topological modes in stellar oscillations

Stellar oscillations can be of topological origin. We reveal this deep and so-far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an hermitian problem to derive the expression of the stellar $\mathrm{\textit{acoustic-buoyant}}$ frequency $S$ of non-radial adiabatic pulsations. A topological analysis then connects the changes of sign of the acoustic-buoyant frequency to the existence of Lamb-like waves within the star. These topological modes cross the frequency gap and behave as gravity modes at low harmonic degree $\ell$ and as pressure modes at high $\ell$. $S$ is found to change sign at least once in the bulk of most stellar objects, making topological modes ubiquitous across the Hertzsprung-Russel diagram. Some topological modes are also expected to be trapped in regions where the internal structure varies strongly locally.

astro-ph.SR↗

arXiv2022

Unidirectional modes induced by nontraditional Coriolis force in stratified fluids

Using topology, we unveil the existence of new unidirectional modes in compressible rotating stratified fluids. We relate their emergence to the breaking of time-reversal symmetry by rotation and vertical mirror symmetry by stratification and gravity. We stress the role of the Coriolis force's nontraditional part, induced by a rotation field tangent to the surface. In contrast with horizontally trapped equatorial waves induced by the traditional component of Coriolis force perpendicular to the surface, we find vertically trapped modes that are trapped along interfaces between regions with distinct stratification properties. We show that such modes are generalized atmospheric Lamb waves whose direction of propagation can be selected by the nontraditional component of the Coriolis force.

physics.flu-dyn↗

arXiv2022

How do CPT-like symmetries shape the stability of geophysical flows?

We examine the role discrete symmetries, time-reversal and mirror symmetries, play in the context of geophysical waves and instabilities. By looking at three special cases from the two-layer quasi-geostrophic model as well as developing a general framework for translating real-space transformations to Fourier-space we are able to: 1) show that baroclinic instability is an example of spontaneous parity-time symmetry breaking; 2) show that pure parity symmetry for a fluid system is exactly analogous to charge-conjugation-parity symmetry in a condensed matter system; and 3) show that when a pure parity symmetry is broken, this is associated with the suppression of wave propagation. Further, in the latter case, instability can arise without a corresponding symmetry breaking. This study highlights the role of symmetry breaking behind the dynamics of geophysical waves and instabilities.

physics.ao-ph↗

arXiv2021

Wave topology brought to the coast

Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an unidirectional mode filling a frequency gap between different wave bands. The existence of such Kelvin waves is robust to changes in the boundary shape and in changes of the underlying model for the coast. This suggests a topological interpretation that has yet up to now remained elusive. Here we rectify the situation, by taking advantage of a reformulation of the shallow water dynamics that highlights an analogy with the celebrated Haldane model in condensed matter physics. For any profile of bottom topography, the number of modes that transit from one wave band to another in the dispersion relation is predicted by computing a first Chern number describing the topology of complex eigenmodes in a dual, simpler wave problem.

physics.flu-dyn↗

arXiv2021

Manifestation of Berry curvature in geophysical ray tracing

Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named Berry curvature, describing the local geometry of wave polarization relations and known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atoms physics. Here, we use a variational method with a vectorial Wentzel-Kramers-Brillouin (WKB) ansatz to derive ray tracing equations in geophysical waves and reveal the contribution of Berry curvature. We detail the case of shallow water wave packets and propose a new interpretation to the equatorial oscillation and the bending of rays in mid-latitude area. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincaré wave packets. This work enlightens the role of wave polarization's geometry in various geophysical and astrophysical fluid waves, beyond the shallow water model.

physics.flu-dyn↗

arXiv2020

From the geometry of Foucault pendulum to the topology of planetary waves

The physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and astrophysical waves. We deal in particular with the case of planetary equatorial waves, which highlights the key interplay between rotation and sphericity of the planet, to explain the emergence of waves which propagate their energy only towards the East. These minimal ingredients are precisely those put forward in the geometric interpretation of the Foucault pendulum. We discuss this classic example of mechanics to introduce the concepts of holonomy and vector bundle which we then use to calculate the topological properties of equatorial shallow water waves.

physics.geo-ph↗

arXiv2020

Quasigeostrophy against the wall

Coasts are obstructions to the classical derivation of continuously stratified quasigeostrophic equations, due to possible resonances between slow internal coastally trapped Kelvin waves and anticyclones. [Deremble et al Ocean Modelling 2017] proposed a coupled model between a quasigeostrophic interior and boundary layer Kelvin wave dynamics. We revisit the derivation of this model, paying particular attention to conservation laws. We find that quasigeostrophic energy is conserved despite the existence of Kelvin wave shocks in the boundary layer. The effect of those shocks is to change the global distribution of potential vorticity, and, consequently the interior flow structure. In that respect, we show that there is an active control of the boundary region on the interior flow.

physics.flu-dyn↗