Sequential Bayesian identification using multi-fidelity Gaussian process surrogates: Application to an inverse transient thermal problem

A sequential Bayesian inversion algorithm is proposed for the estimation of unknown parameters in complex physical models, particularly when dealing with expensive simulations, a frequent challenge in industrial applications. The approach aims to accurately infer the posterior distribution of the parameters, ensuring that it is concentrated as possible around the true values while minimizing the number of direct model evaluations. To achieve this, a multi-fidelity meta-modeling strategy is employed within a reduced-order space, leveraging recursive Gaussian Process Regression to approximate the projection functions efficiently. The meta-model and the projection matrix are iteratively refined in a sequential way, by incorporating new training data selected based on the evolving posterior distribution, ensuring that only the most informative simulations are performed. This approach enables precise parameter estimation while controlling computational costs. Numerical and experimental case studies on the thermal modeling of a single-layer wall illustrates the method’s effectiveness in identifying thermal properties from four functional outputs. A comparative analysis with a fixed-cost identification strategy highlights the robustness of the proposed sequential method, demonstrating robust parameter estimates across iterations and a progressive reduction of uncertainty. By adaptively targeting the most valuable simulations, this algorithm efficiently balances computational cost and estimation accuracy, making it particularly well-suited for industrial applications involving expensive simulation codes.