9 papers
Bayesian Calibration with Functional Outputs Using Elastic Partial Matching
Paul Casteras, Julien Bect, Josselin Garnier +1
Calibrating a simulation model involves estimating its parameters by comparing model outputs with experimental data, so that simulation results faithfully reproduce the experimenta…
Multi-fidelity Monte Carlo estimation of floor response spectra under combined seismic and structural parameter uncertainties
Nils Baillie, Baptiste Kerleguer, Cyril Feau +2
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,…
Asymptotics-guided learning and symbolic regression for dispersive resonances
Konstantinos Alexopoulos, Josselin Garnier
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…
Reduced-order modeling for electromagnetic inverse problems: a layered medium benchmark
Konstantinos Alexopoulos, Josselin Garnier
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,…
Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures
Lorenzo Baldassari, Josselin Garnier, Knut Solna +1
Obtaining stable diffusion-based samplers in high- and infinite-dimensional settings is challenging because errors can accumulate across high-frequency coordinates and make the dyn…
On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods
David Iagaru, Nina M. Gottschling, Anders C. Hansen +1
Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic…
Multifidelity Gaussian process regression for solving nonlinear partial differential equations
Fatima-Zahrae El-Boukkouri, Josselin Garnier, Olivier Roustant
Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these met…
Multi-fidelity Gaussian process regression for noisy outputs and non-nested experimental designs: a comparison between the recursive and non-recursive formulations
Nils Baillie, Baptiste Kerleguer, Cyril Feau +1
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-fidel…
Bayesian Calibration for Prediction in a Multi-Output Transposition Context
Charlie Sire, Josselin Garnier, Cédric Durantin +3
Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental o…