Publications

Preprint

Optimal Design of Experiments for Computer Code Calibration

Date: June 24, 2024
Published on: HAL

Abstract:
This work addresses the problem of Bayesian calibration of an expensive computer code, assuming no model discrepancy. In a calibration context where both measurement acquisition and code evaluations are costly, achieving accurate parameter estimation while minimizing experimental and computational costs is crucial.

We propose a hybrid design strategy for selecting both physical and numerical experiments to approximate the posterior density of calibration parameters. First, an initial Gaussian process emulator is built and used to compute an optimal criterion for physical experiment design. After selecting the physical design, we combine physical observations with available computer code outputs to sequentially add new points to the numerical design, improving the emulator for calibration purposes.

Three new criteria are introduced for physical experiment design—based on either posterior density or code variation—and two new criteria for numerical experiment design inspired by the Sequential Uncertainty Reduction (SUR) framework. A performance study and comparison with state-of-the-art methods are conducted on two benchmark test cases and a realistic application involving the calibration of a harmonic oscillator.

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PhD Thesis Manuscript

Design of Experiments for Expensive Computer Code Calibration

Date: June 25, 2025
Published on: HAL

Abstract:
This thesis focuses on the Bayesian calibration of expensive computer codes—with scalar, vector, or functional outputs—using a limited number of physical measurements. A computer code is considered expensive when its evaluation requires significant computational time. In such contexts, Bayesian inference on its parameters requires the use of a surrogate model, typically a Gaussian process emulator.

We propose a two-stage strategy combining the optimal selection of physical experiments (for field measurements) and numerical experiments (for emulator construction). The first stage involves building an initial Gaussian process emulator, which is then used to compute optimality criteria for physical experimental design.

Two families of criteria are introduced:
1. Bayesian criteria based on the posterior distribution of calibration parameters, incorporating uncertainties from physical and numerical observations as well as model parameters.
2. A code variation–based criterion, which combines model sensitivity with the space-filling properties of the design, offering reduced computational cost for optimization.

Four optimization algorithms are explored: simulated annealing, a greedy algorithm, a genetic algorithm, and Simultaneous Perturbation Stochastic Approximation (SPSA). After cog physical data, the emulator is refined via sequential design of numerical experiments, guided by acquisition criteria that progressively reduce calibration uncertainty. Two calibration-oriented acquisition criteria are proposed: the sum of posterior variances of calibration parameters, and the prediction error of physical observations.

The final emulator is used to approximate the posterior density of the parameters via Markov Chain Monte Carlo (MCMC) sampling combined with kernel-based nonparametric estimation.

The methodology is validated on scalar-output analytical functions, compared with state-of-the-art approaches, and then extended to vector- and function-valued computer codes. Finally, it is applied to the Bayesian calibration of a numerical simulator dedicated to geological CO₂ storage, using synthetic data.