arXiv subjects

Alexandrine Gesret

Publications and source records attributed to Alexandrine Gesret.

4 recordsLinked to original sources

arXiv2026

Covariance-Informed Subspace: an Adaptive Gradient-Free Input Dimension Reduction Method for Bayesian Inference

This paper addresses the challenge of dimension reduction (DR) in Bayesian inference of high-resolution two-or three-dimensional fields, where a priori parametrizations require a large number of terms. The underlying idea is common to state-of-the-art methods in which the parameter space is decomposed into two subspaces, one informed by the likelihood and one constrained by the prior. DR techniques generally use gradient information from the log-likelihood to derive the corresponding subspaces. However, the gradient may be unavailable or expensive to compute accurately, for instance in the case of simulation-based inference. Inspired by approaches based on likelihood-informed subspaces, we develop a new DR method tailored for settings where gradient computation is not feasible. More specifically, we propose a gradient-free indicator for determining whether a direction is informed by the data. This indicator is derived from the posterior-to-prior covariance ratio introduced in Spantini et al. (2015). We show that, in the linear Gaussian case, this indicator combined with an approximate likelihood leads to a better posterior approximation. The method is then extended to nonlinear cases, and strategies to approximate the posterior covariance are detailed. We demonstrate the effectiveness of this DR through two high-dimensional inference problems arising from groundwater and atmospheric applications.

math.NA↗

arXiv2025

A new 1D $V_p$ and $V_s$ velocity model of the western Rift of Corinth, Greece, using a fully non-linear tomography algorithm

The objective of this study is to propose a new updated accurate 1-D $V_p$ and $V_s$ velocity model of the western Rift of Corinth for precise absolute earthquake locations. The methodology used to obtain this new model associates two fully non-linear algorithms, a complete exploration of the $V_p$ and $V_s$ model space combined with a grid search method for earthquake locations to minimize the P and S arrival time residuals. We calculated the misfit function for approximately 2.10 6 velocity models. For the best model (minimum misfit) we observed a global decrease of 30 % for both the P and S residuals with respect to the commonly used velocity model. The main features of this new model compared to other studies is a significant decrease of $V_p$ and $V_s$ velocities from surface down to a depth of approximately 3 km and a variable $V_p/V_s$ ratio decreasing from 1.86 at the surface to 1.78 at a depth of 8 km. The major influence on the locations of events is a global decrease of focal depths that range from a few hundred metres for deep events to more than one kilometre for shallow earthquakes.

physics.geo-ph↗

arXiv2025

Change of Measure for Bayesian Field Inversion with Hierarchical Hyperparameters Sampling

This paper proposes an effective treatment of hyperparameters in the Bayesian inference of a scalar field from indirect observations. Obtaining the joint posterior distribution of the field and its hyperparameters is challenging. The infinite dimensionality of the field requires a finite parametrization that usually involves hyperparameters to reflect the limited prior knowledge. In the present work, we consider a Karhunen-Lo{è}ve(KL) decomposition for the random field and hyperparameters to account for the lack of prior knowledge of its autocovariance function. The hyperparameters must be inferred. To efficiently sample jointly the KL coordinates of the field and the autocovariance hyperparameters, we introduce a change of measure to reformulate the joint posterior distribution into a hierarchical Bayesian form. The likelihood depends only onthe field's coordinates in a fixed KL basis, with a prior conditioned on the hyperparameters. We exploit this structure to derive an efficient Markov Chain Monte Carlo (MCMC) sampling scheme based on an adapted Metropolis-Hasting algorithm. We rely on surrogate models (Polynomial Chaos expansions) of the forward model predictions to further accelerate the MCMC sampling. A first application to a transient diffusionproblem shows that our method is consistent with other approaches based on a change of coordinates (Sraj et al., 2016). A second application to a seismic traveltime tomography highlights the importance of inferring the hyperparameters. A third application to a 2D anisotropic groundwater flow problem illustrates the method on a more complex geometry.

math.NA↗

arXiv2024

Neural machine translation of seismic waves for petrophysical inversion

Effective structural assessment of urban infrastructure is essential for sustainable land use and resilience to climate change and natural hazards. Seismic wave methods are widely applied in these areas for subsurface characterization and monitoring, yet they often rely on time-consuming inversion techniques that fall short in delivering comprehensive geological, hydrogeological, and geomechanical descriptions. Here, we explore the effectiveness of a passive seismic approach coupled with artificial intelligence (AI) for monitoring geological structures and hydrogeological conditions in the context of sinkhole hazard assessment. We introduce a deterministic petrophysical inversion technique based on a language model that decodes seismic wave velocity measurements to infer soil petrophysical and mechanical parameters as textual descriptions. Results successfully delineate 3D subsurface structures with their respective soil nature and mechanical characteristics, while accurately predicting daily water table levels. Validation demonstrates high accuracy, with a normalized root mean square error of 8%, closely rivaling with conventional stochastic seismic inversion methods, while delivering broader insights into subsurface conditions 2,000 times faster. These findings underscore the potential of advanced AI techniques to significantly enhance subsurface characterization across diverse scales, supporting decision-making for natural hazard mitigation.

physics.geo-ph↗