Reduced-Order Modeling Framework for Bayesian Inversion of Large-Scale Problems
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Bayesian approaches to inverse problems provide a robust framework for uncertainty quantification(UQ) ; however, their application to large-scale problems (i.e., problems involving many parameters and fine discretization) remain challenging due to the often high computational cost associated to the high-fidelity solvers. This challenge is particularly acute in inverse problems governed by complex PDEs, where high-fidelity numerical models require extensive computational resources that become prohibitive during the iterative inference process. To address this bottleneck, this study investigates Reduced-Order Modeling (ROM) techniques to accelerate Bayesian inversion in physics-based modeling contexts . The proposed methodology constructs reduced models from high-fidelity simulations to generate efficient surrogates that capture the essential dynamics of the full-order system. These surrogates are then integrated into the Bayesian framework, facilitating rapid likelihood evaluation and efficient sampling of the posterior distribution. We find that the proposed methodology substantially reduces the computational burden of Bayesian inversion while maintaining accuracy in parameter estimation and UQ. These results demonstrate the effectiveness of ROM-based strategies for enabling Bayesian inference of the high fidelity inversions arising in computational mechanics.