In this work, we employ model order reduction and data-assimilation techniques for the goal of solving inverse problems which often arise in the field of structural health monitoring (SHM). This work is conducted in the framework of the DFG project FOR3022, titled “Ultrasonic Monitoring of Fibre Metal Laminates Using Integrated Sensors.” Our focus is on detecting, characterizing, and localizing damage in structures using non-destructive evaluation (NDE) techniques. We concentrate on fiber metal laminates (FMLs)—a class of composite materials developed in the 1980s that combines the benefits of metals and composites, enabling lighter structures. However, this weight reduction introduces challenges to structural integrity and safety, as damages in FMLs are often not visible. This limitation highlights the value of mathematical approaches from data assimilation and inverse problem frameworks for effective damage identification in FMLs. From a mathematical perspective, the aforementioned damage detection problems are viewed through the lens of solving inverse problems. Solving such problems involves the use of simulated or observed data to infer unknown inputs, physical constants, or system parameters. However, solving such problems often requires high computational costs since each iterative update to estimate the unknown quantities of interest requires multiple simulations of the underlying forward model. To reduce this computational burden, Reduced Order Models (ROMs) offer a promising solution by acting as efficient surrogate models that accelerate forward model computations through leveraging structures and patterns present in the data. The mathematical problem of interest is the second order mechanical discrete system obtained upon the spatial discretization of the equation of motion. The problem is parametrized by the damage parameters and is reduced using the non-intrusive projection-based Operator Inference (OpInf) approach \cite{Peherstorfer}. We show the results of our approach for a damaged fiber metal laminate model \cite{Graessle,Hijazi}.