In this work, we address damage detection problems which arise in Structural Health Monitoring (SHM) [1], specifically 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, the process of solving them can be computationally demanding due to the high cost of repeatedly simulating the underlying mathematical model, known as the forward model. The forward model must be simulated repeatedly in an iterative approach to estimate the unknown quantities of interest. 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. In this work, we compare various reduced order modeling methods to facilitate the inference of unknown damage parameters in FMLs, advancing SHM capabilities for these advanced materials [2]. REFERENCES [1] C. R. Farrar and K. Worden, An introduction to structural health monitoring. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1851 (2006): 303–315. [2] Carmen Gräßle and Saddam Hijazi, Schäden in Faser-Metall-Laminaten erkennen: Methoden der Datenassimilation in der Anwendung. Mitteilungen der Deutschen Mathematiker-Vereinigung, vol. 32, no. 4, 2024, pp. 216-222.