arXiv subjects

Paul Lartaud

Publications and source records attributed to Paul Lartaud.

4 recordsLinked to original sources

arXiv2026

Diffeomorphic registration distances for Bayesian calibration of infinite-dimensional computer models

The simulation of physical phenomena with computer models relies on the estimation of physical and/or numerical parameters calibrated to fit experimental data. The approximations within the computer model and the errors in the measurements lead to uncertainties in the calibrated parameters. Bayesian calibration offers a well-studied framework to provide reliable uncertainty quantification on the calibrated parameters. When dealing with complex computer codes whose outputs are infinite-dimensional, Bayesian calibration may be extended by providing a relevant distance in the output space. In this paper, Bayesian calibration is performed using distances from the large deformation diffeomorphic metric matching (LDDMM) framework. LDDMM distances can provide a suitable metric for infinite-dimensional shapes such as scalar fields (i.e. images) or function graphs. This metric can be interpreted as the minimal energy deformation required to transform one shape into another. As such, it provides a readily interpretable metric for Bayesian calibration. On top of this, the representation of the diffeomorphism group as an exponential transformation of an RKHS is compatible with Bayesian inference and allows to define a predictive posterior distribution on the infinite-dimensional space shape.

stat.ME↗

arXiv2025

Sequential design for surrogate modeling in Bayesian inverse problems

Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace complex computer codes. Some sequential design strategies can be understood within the Stepwise Uncertainty Reduction (SUR) framework. In the SUR framework, each new design point is chosen by minimizing the expectation of a metric of uncertainty with respect to the yet unknown new data point. These methods offer an accessible framework for sequential experiment design, including almost sure convergence for common uncertainty functionals. This paper introduces two strategies. The first one, entitled Constraint Set Query (CSQ) is adapted from D-optimal designs where the search space is constrained in a ball for the Mahalanobis distance around the maximum a posteriori. The second, known as the IP-SUR (Inverse Problem SUR) strategy, uses a weighted-integrated mean squared prediction error as the uncertainty metric and is derived from SUR methods. It is tractable for Gaussian process surrogates with continuous sample paths. It comes with a theoretical guarantee for the almost sure convergence of the uncertainty functional. The premises of this work are highlighted in various test cases, in which these two strategies are compared to other sequential designs.

stat.ME↗

arXiv2024

Uncertainty quantification in neutron and gamma time correlation measurements

Neutron noise analysis is a predominant technique for fissile matter identification with passive methods. Quantifying the uncertainties associated with the estimated nuclear parameters is crucial for decision-making. A conservative uncertainty quantification procedure is possible by solving a Bayesian inverse problem with the help of statistical surrogate models but generally leads to large uncertainties due to the surrogate models' errors. In this work, we develop two methods for robust uncertainty quantification in neutron and gamma noise analysis based on the resolution of Bayesian inverse problems. We show that the uncertainties can be reduced by including information on gamma correlations. The investigation of a joint analysis of the neutron and gamma observations is also conducted with the help of active learning strategies to fine-tune surrogate models. We test our methods on a model of the SILENE reactor core, using simulated and real-world measurements.

stat.AP↗

arXiv2022

Multi-output Gaussian processes for inverse uncertainty quantification in neutron noise analysis

In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile material. This technique known as neutron noise analysis has applications in nuclear safeguards or waste identification. It provides a non-destructive examination method for an unknown fissile material. This is an example of an inverse problem where the cause is inferred from observations of the consequences. However, neutron correlation measurements are often noisy because of the stochastic nature of the underlying processes. This makes the resolution of the inverse problem more complex since the measurements are strongly dependent on the material characteristics. A minor change in the material properties can lead to very different outputs. Such an inverse problem is said to be ill-posed. For an ill-posed inverse problem the inverse uncertainty quantification is crucial. Indeed, seemingly low noise in the data can lead to strong uncertainties in the estimation of the material properties. Moreover, the analytical framework commonly used to describe neutron correlations relies on strong physical assumptions and is thus inherently biased. This paper addresses dual goals. Firstly, surrogate models are used to improve neutron correlations predictions and quantify the errors on those predictions. Then, the inverse uncertainty quantification is performed to include the impact of measurement error alongside the residual model bias.

stat.CO↗