Bayesian inversion provides a comprehensive probabilistic framework for parameter estimation and Uncertainty Quan- tification (UQ) in inverse problems governed by partial differential equations (PDE) [1]. However, large-scale problems (i.e., problems involving many parameters and fine discretizations) remain challenging due to the often high computa- tional cost associated to the high-fidelity solvers. This work addresses the computational bottleneck in inverse problems governed by complex physical equations, motivated by applications involving heterogeneous material properties [2]. The forward problem in this context typically requires the solution of large-scale PDE, making standard Markov Chain Monte Carlo (MCMC) methods computationally prohibitive due to the need for thousands of iterative model evalua- tions [1]. To overcome this limitation, projection-based Reduced-Order Modeling (ROM) techniques are employed to construct low-dimensional surrogates of the high-fidelity numerical solver. The resulting reduced models significantly decrease the computational cost of forward evaluations while preserving the dominant numerical and physical features of the original system. By integrating ROM surrogate within MCMC sampling, the proposed framework enables effi- cient exploration of the posterior distribution and reliable UQ for the inferred parameters. These results highlight the potential of ROM to make Bayesian inversion with large-scale PDE tractable in computational mechanics and enineer- ing. References [1] Andrew M Stuart. Inverse problems: a bayesian perspective. Acta numerica, 19:451–559, 2010. [2] Olga Ortega-Gelabert, Sergio Zlotnik, Juan Carlos Afonso, and Pedro Díez. Fast stokes flow simulations for geophysical-geodynamic inverse problems and sensitivity analyses based on reduced order modeling. Journal of Geophysical Research: Solid Earth, 125(3), 2020.