arXiv subjects

Josselin Garnier

Publications and source records attributed to Josselin Garnier.

At least 19 recordsLinked to original sources

arXiv2026

Passive Imaging with Ambient Noise Under Wave Speed Mismatch: Mathematical Analysis and Wave Speed Estimation

It is known that waves generated by ambient noise sources and recorded by passive receivers can be used to image the reflectivities of an unknown medium. However, reconstructing the reflectivity of the medium from partial boundary measurements remains a challenging problem, particularly when the background wave speed is unknown. In this paper, we investigate passive correlation-based imaging in the daylight configuration, where uncontrolled noise sources illuminate the medium and only ambient fields are recorded by a sensor array. We first analyze daylight migration for a point reflector embedded in a homogeneous background. By introducing a searching wave speed into the migration functional, we derive an explicit characterization of the deterministic shift and defocusing effects induced by wave-speed mismatch. We show that the maximum of the envelope of the resulting functional provides a reliable estimator of the true wave speed. We then extend the analysis to a random medium with correlation length smaller than the wavelength. Leveraging the shift formula obtained in the homogeneous case, we introduce a virtual guide star that remains fixed under migration with different searching speeds. This property enables an effective wave-speed estimation strategy based on spatial averaging around the virtual guide star. For both homogeneous and random media, we establish resolution analyses for the proposed wave-speed estimators. Numerical experiments are conducted to validate the theoretical result.

eess.SP↗

arXiv2026

Multi-fidelity Monte Carlo estimation of floor response spectra under combined seismic and structural parameter uncertainties

Floor response spectra (FRS) are essential tools for the design of non-structural elements (such as equipment or components). Given the various physical phenomena influencing FRS, high-fidelity (HF) mechanical models of the primary structure may be required to estimate them. Since numerical simulations based on such models are generally computationally expensive, this paper proposes using a multi-fidelity Monte Carlo (MFMC) approach for the efficient estimation of FRS. The method relies on using observations from a fast low-fidelity (LF) model as control variables. If the absolute value of the correlation between LF and HF samples is close to 1, this approach reduces both variance and estimation error compared to a standard Monte Carlo estimate based solely on HF data samples. Through a case study involving the reactor building of the Kashiwazaki-Kariwa nuclear power plant, we demonstrate the suitability of this method for FRS estimation. It effectively reduces variance and estimation error, even when using a LF model as simple as a single-degree-of-freedom system. We also show that the method accounts for modeling uncertainties while maintaining comparable performance. Its ease of use makes it a valuable tool for practitioners.

physics.data-an↗

arXiv2026

Asymptotics-guided learning and symbolic regression for dispersive resonances

We study resonance prediction in dispersive media, formulated as nonlinear spectral problems for volume integral operators. The main idea is to use asymptotic analysis not only as a baseline approximation, but also as a guide for constructing predictive correction models. We learn the residual between asymptotic and reference resonances using features suggested by the subwavelength expansion, including the logarithmic scales specific to two dimensions. The resulting corrections substantially improve single-resonator and dimer predictions, and symbolic regression produces compact formulas for the learned residual. The results show that asymptotic analysis can be used not only to approximate resonances, but also to design the feature space in which data-driven corrections become accurate, low-dimensional, and interpretable.

math.NA↗

arXiv2026

Reduced-order modeling for electromagnetic inverse problems: a layered medium benchmark

We study reduced-order modeling for inverse problems in layered media, focusing on the recovery of impedance profiles from time-domain measurements. Using the Goupillaud structure, we formulate the forward problem as a discrete dynamical system and introduce a ROM-based objective defined at the level of reduced operators. Through numerical experiments on a 5-layer medium under various structured perturbations, we compare the ROM-based objective with a classical data misfit. The results show that the ROM-based inversion provides a more favorable reconstruction in the clean setting and in certain structured perturbation regimes, while remaining consistently competitive with the classical approach across all cases considered.

math.NA↗

arXiv2026

Spatio-temporal equilibrium thermodynamics of guided optical waves at positive and negative temperatures

Optical thermalization has been recently studied in the 2D spatial evolution of (quasi-)monochromatic light waves propagating in multimode waveguides. Here, we investigate the spatio-temporal equilibrium properties of optical waves through the analysis of the (2+1)D Bose-Einstein thermal distribution and the corresponding classical Rayleigh-Jeans approximation. Numerical simulations of the nonlinear Schrödinger equation (NLSE) demonstrate relaxation toward the spatio-temporal Rayleigh-Jeans equilibrium state, as described by the corresponding wave turbulence kinetic equation. Remarkable adiabatic cooling phenomena stemming from the high-frequency tails of the Rayleigh-Jeans distribution are discussed and the consequent limitations of the classical approximation are highlighted. To overcome these issues, we make use of a quantum version of the NLSE whose associated kinetic equation describes relaxation toward the spatio-temporal Bose-Einstein equilibrium distribution. The analysis of thermodynamic properties reveals a strong dependence on the dispersion regime. In the anomalous dispersion regime, the system relaxes to positive-temperatures equilibrium states: as the number of modes of the waveguide increases, the fundamental spatial mode becomes macroscopically populated, while its temporal spectrum undergoes significant narrowing, ultimately leading to complete (2+1)D spatio-temporal condensation in the thermodynamic limit. In the normal dispersion regime, the system evolves toward negative-temperature equilibrium states characterized by an inverted spatial modal population. In this regime, we predict a phase transition to Bose-Einstein condensation at negative temperatures, which occurs by increasing the temperature above a negative critical value. Our work opens new avenues for future research and lay the groundwork for the development of spatiotemporal optical thermodynamics.

physics.optics↗

arXiv2026

Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics

Designing sampling algorithms for multimodal targets that remain stable under refinement of the finite-dimensional approximation of an underlying function-space problem is a central challenge. Annealed Langevin dynamics (ALD) is a natural alternative to classical Langevin in this context, since it is often observed to improve exploration across modes. Yet a gap remains between its empirical success and existing theory: under which conditions can ALD be guaranteed to remain stable across dimensions? In this paper, we bridge this gap by providing a uniform-in-dimension analysis of continuous-time ALD for Gaussian-mixture targets. Along an explicit annealing path obtained by gradually removing Gaussian smoothing from the target, we identify spectral conditions linking the smoothing covariance to the component covariances under which ALD achieves a prescribed accuracy in Kullback-Leibler divergence within a dimension-uniform time horizon. We then establish stability in a perturbative regime with imperfect initialization and approximate scores. Under a misspecified-mixture score model, we show that preconditioning ALD with an operator whose spectrum decays sufficiently fast prevents error terms from accumulating across coordinates and thereby preserves dimension-uniform control.

math.NA↗

arXiv2026

Multi-fidelity Gaussian process regression for noisy outputs and non-nested experimental designs: a comparison between the recursive and non-recursive formulations

This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based on the expectation-maximization algorithm, which exploits the structure of the recursive model. In particular, we derive closed-form update formulas when the scaling factor is modeled as a parametric linear predictor. This approach is compared with the fully coupled likelihood maximization of the classical non-recursive formulation introduced by Kennedy and O'Hagan. A series of benchmark experiments, covering applications of increasing complexity, highlights the performance of both approaches. The results demonstrate that the proposed recursive strategy significantly reduces training time, especially when large low-fidelity datasets are available, while maintaining competitive predictive accuracy and uncertainty estimation.

stat.AP↗

arXiv2026

Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures

Obtaining stable diffusion-based samplers in high- and infinite-dimensional settings is challenging because errors can accumulate across high-frequency coordinates and make the dynamics unstable under refinement of the finite-dimensional approximation of the underlying function-space problem. Discretization is a typical source of such errors, and preconditioning with a suitable spectral decay is one way to control their accumulation. In this paper, we study this problem for preconditioned annealed Langevin dynamics (ALD) applied to Gaussian mixtures. We first show that Euler-Maruyama (EM) discretization, by treating the stiff linear part of the annealed score with a forward Euler step, imposes a stability constraint coupling the preconditioner with the annealed covariance scale. Together with the conditions ensuring dimension-uniform control of the annealed dynamics, this constraint forces the initial smoothed law to remain uniformly close to the target across dimensions. We then consider an exponential-integrator scheme that integrates the stiff linear part of the annealed score exactly. Under explicit spectral summability conditions coupling the smoothing covariance, the component covariance spectra, and the preconditioner, we prove a dimension-uniform Kullback-Leibler (KL) bound for this scheme. This bound can be made arbitrarily small, uniformly in dimension, by allowing enough time for annealing and then refining the time mesh accordingly. Importantly, these conditions allow regimes in which the KL divergence between the target and the initial smoothed law diverges with dimension, showing that the restrictions imposed by EM are scheme-dependent rather than intrinsic to ALD.

stat.ML↗

arXiv2026

Taking advantage of multiple scattering for Optical Reflection Tomography

Optical Diffraction Tomography (ODT) is a powerful non-invasive imaging technique widely used in biological and medical applications. While significant progress has been made in transmission configuration, reflection ODT remains challenging due to the ill-posed nature of the inverse problem. We present a novel optimization algorithm for 3D refractive index (RI) reconstruction in reflection-mode microscopy. Our method takes advantage of the multiply-scattered waves that are reflected by uncontrolled background structures and that illuminate the foreground RI from behind. It tackles the ill-posed nature of the problem using weighted time loss, positivity constraints and Total Variation regularization. We have validated our method with data generated by detailed 2D and 3D simulations, demonstrating its performance under weak scattering conditions and with simplified forward models used in the optimization routine for computational efficiency. In addition, we highlight the need for multi-wavelength analysis and the use of regularization to ensure the reconstruction of the low spatial frequencies of the foreground RI.

physics.optics↗

arXiv2026

On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods

Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic-looking but incorrect details, undermining their reliability, especially when ground truth data is unavailable. We develop a theoretical framework showing that such hallucinations are not merely artifacts of particular models, but can arise from the ill-posed nature of the inverse problem itself. We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that depend only on the forward model. Building on this theory, we introduce algorithms to: (1) estimate the minimum hallucination magnitude achievable by any reconstruction model for a given input; (2) assess the faithfulness of reconstructed details by a given reconstruction model. Experiments across three imaging tasks demonstrate that our approach applies broadly, including to modern generative models, and provides a principled way to quantify and evaluate AI hallucinations.

stat.ML↗

arXiv2026

Multifidelity Gaussian process regression for solving nonlinear partial differential equations

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work, as the available information is inherently multifidelity, we propose a kernel learning approach based on cokriging, leveraging empirical information from multifidelity simulations. In the first step, we fit a differentiable non-stationary kernel to an empirical kernel obtained from low-fidelity simulations. In the second step, we derive a high-fidelity kernel with estimated hyperparameters, and construct a corresponding high-fidelity mean using the multifidelity framework. These components can then be used within a Gaussian process framework for solving PDEs. Finally, we demonstrate the performance of the proposed physics-informed method on the Burgers' equation.

stat.ML↗

arXiv2026

Quantitative synthetic aperture radar inversion

We study an inverse scattering problem for monostatic synthetic aperture radar (SAR): Estimate the wave speed in a heterogeneous, isotropic and nonmagnetic medium probed by waves emitted and measured by a moving antenna. The forward map, from the wave speed to the measurements, is derived from Maxwell's equations. It is a nonlinear map that accounts for multiple scattering and it is very oscillatory at high frequencies. This makes the standard, nonlinear least squares data fitting formulation of the inverse problem difficult to solve. We introduce an alternative, two-step approach: The first step computes the nonlinear map from the measurements to an approximation of the electric field inside the unknown medium aka, the internal wave. This is done for each antenna location in a non-iterative manner. The internal wave fits the data by construction, but it does not solve Maxwell's equations. The second step uses optimization to minimize the discrepancy between the internal wave and the solution of Maxwell's equations, for all antenna locations. The optimization is iterative. The first step defines an imaging function whose computational cost is comparable to that of standard SAR imaging, but it gives a better estimate of the support of targets. Further iterations improve the quantitative estimation of the wave speed. We assess the performance of the method with numerical simulations and compare the results with those of standard inversion.

math.NA↗

arXiv2026

Uncertainty Quantification in Coupled Multiphysics Systems via Gaussian Process Surrogates: Application to Fuel Assembly Bow

Predicting fuel assembly bow in pressurized water reactors requires solving tightly coupled fluid-structure interaction problems, whose direct simulations can be computationally prohibitive, making large-scale uncertainty quantification (UQ) very challenging. This work introduces a general mathematical framework for coupling Gaussian process (GP) surrogate models representing distinct physical solvers, aimed at enabling rigorous UQ in coupled multiphysics systems. A theoretical analysis establishes that the predictive variance of the coupled GP system remains bounded under mild regularity and stability assumptions, ensuring that uncertainty does not grow uncontrollably through the iterative coupling process. The methodology is then applied to the coupled hydraulic-structural simulation of fuel assembly bow, enabling global sensitivity analysis and full UQ at a fraction of the computational cost of direct code coupling. The results demonstrate accurate uncertainty propagation and stable predictions, establishing a solid mathematical basis for surrogate-based coupling in large-scale multiphysics simulations.

stat.AP↗

arXiv2026

Spatio-temporal thermalization and adiabatic cooling of guided light waves

We propose and theoretically characterize three-dimensional spatio-temporal thermalization of a continuous-wave classical light beam propagating along a multi-mode optical waveguide. By combining a non-equilibrium kinetic approach based on the wave turbulence theory and numerical simulations of the field equations, we anticipate that thermalizing scattering events are dramatically accelerated by the combination of strong transverse confinement with the continuous nature of the temporal degrees of freedom. In connection with the blackbody catastrophe, the thermalization of the classical field in the continuous temporal direction provides an intrinsic mechanism for adiabatic cooling and, then, spatial beam condensation. Our results open new avenues in the direction of a simultaneous spatial and temporal beam cleaning.

physics.optics↗

arXiv2025

Robust a posteriori estimation of probit-lognormal seismic fragility curves via sequential design of experiments and constrained reference prior

A seismic fragility curve expresses the probability of failure of a structure conditional to an intensity measure (IM) derived from seismic signals. When only limited data is available, the practitioner often refers to the probit-lognormal model coupled with maximum likelihood estimation (MLE) to obtain estimates of these curves. This means that only a binary indicator of the state (BIS) of the structure is known, namely a failure or non-failure state indicator, when it is subjected to a seismic signal with an intensity measure IM. In this context, the objective of this work is to propose a method for optimally estimating such curves by obtaining the most precise estimate possible with the minimum of data. The novelty of our work is twofold. First, we present and show how to mitigate the likelihood degeneracy problem which is ubiquitous with small data sets and hampers frequentist approaches such as MLE. Second, we propose a novel strategy for sequential design of experiments (DoE) that selects seismic signals from a large database of synthetic or real signals via their IM values, to be applied to structures to evaluate the corresponding BISs. This strategy relies on a criterion based on information theory in a Bayesian framework. It therefore aims to sequentially designate the IM value such that the pair (IM, BIS) has on average, with respect to the BIS of the structure, the greatest impact on the posterior distribution of the fragility curve. The methodology is applied to a case study from the nuclear industry. The results demonstrate its ability to efficiently and robustly estimate the fragility curve, and to avoid degeneracy even with a limited amount of data, i.e., less than 100. Furthermore, we demonstrate that the estimates quickly reach the model bias induced by the probit-lognormal modeling. Eventually, two criteria are suggested to help the user stop the DoE algorithm.

stat.AP↗

arXiv2025

Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems

Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite-dimensional function spaces - where such problems are naturally formulated - is crucial to ensure stability and convergence as the discretization of the underlying problem is refined. In this paper, we contribute to this line of work by analyzing a widely used sampler for linear inverse problems: Langevin dynamics driven by score-based generative models (SGMs) acting as priors, formulated directly in function space. Building on the theoretical framework for SGMs in Hilbert spaces, we give a rigorous definition of this sampler in the infinite-dimensional setting and derive, for the first time, error estimates that explicitly depend on the approximation error of the score. As a consequence, we obtain sufficient conditions for global convergence in Kullback-Leibler divergence on the underlying function space. Preventing numerical instabilities requires preconditioning of the Langevin algorithm and we prove the existence and the form of an optimal preconditioner. The preconditioner depends on both the score error and the forward operator and guarantees a uniform convergence rate across all posterior modes. Our analysis applies to both Gaussian and a general class of non-Gaussian priors. Finally, we present examples that illustrate and validate our theoretical findings.

stat.ML↗

arXiv2025

A control variate method based on polynomial approximation of Brownian path

We present a novel control variate technique for enhancing the efficiency of Monte Carlo (MC) estimation of expectations involving solutions to stochastic differential equations (SDEs). Our method integrates a primary fine-time-step discretization of the SDE with a control variate derived from a secondary coarse-time-step discretization driven by a piecewise parabolic approximation of Brownian motion. This approximation is conditioned on the same fine-scale Brownian increments, enabling strong coupling between the estimators. The expectation of the control variate is computed via an independent MC simulation using the coarse approximation. We characterize the minimized quadratic error decay as a function of the computational budget and the weak and strong orders of the primary and secondary discretization schemes. We demonstrate the method's effectiveness through numerical experiments on representative SDEs.

math.PR↗

arXiv2025

Bayesian Calibration for Prediction in a Multi-Output Transposition Context

Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental observations are necessary to calibrate certain simulator parameters for the prediction. In this work, we use a multi-output simulator to predict all its outputs, including those that have never been experimentally observed. This situation is referred to as the transposition context. To accurately quantify the discrepancy between model outputs and real data in this context, conventional methods cannot be applied, and the Bayesian calibration must be augmented by incorporating a joint model error across all outputs. To achieve this, the proposed method is to consider additional numerical input parameters within a hierarchical Bayesian model, which includes hyperparameters for the prior distribution of the calibration variables. This approach is applied on a computer code with three outputs that models the Taylor cylinder impact test with a small number of observations. The outputs are considered as the observed variables one at a time, to work with three different transposition situations. The proposed method is compared with other approaches that embed model errors to demonstrate the significance of the hierarchical formulation.

stat.ME↗