Structural Health Monitoring (SHM) assesses the integrity of structures through in-situ sensor measurements [1]. However, its widespread adoption is often hindered by the high density of sensors required [2]. This talk introduces the concept of signature-informed modeling, which jointly constructs a reduced-order model (ROM) and observables specialized to capture the essential spatial and temporal information needed to identify parameters of interest. In this context, a signature is defined as a low-dimensional representation of the parameters, time-history aware, and invariant to nuisances such as measurement noise and some extent of model bias. This approach aims to reduce the number of required sensors to a minimum given the available knowledge on the system, while increasing the robustness of the parameter identification under varying operational conditions. A machine learning pipeline is designed to learn and decode such a signature from an available physics-based model and measured/synthetic datasets. The framework leverages ROM techniques (Proper Orthogonal Decomposition, Least Squares Petrov-Galerkin [3]), data assimilation (Parameterized-Background Data-Weak method [4], Unscented Kalman Filter), and invariant representation learning [5]. Numerical results are presented on 1D and 2D academic mechanical systems to compare the proposed approach with popular parameter inference techniques widely used in SHM applications. [1] Farrar, C. R., Worden, K., An introduction to Structural Health Monitoring, Philosophical Trans-actions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365(1851), pp.303–315, 2007. [2] Steinweg, D. M., Hornung, M., Cost and Benefit of Scheduled Structural Health Monitoring forCommercial Aircraft, Proceedings of the 32nd Congress of the International Council of the Aero-nautical Sciences (ICAS 2021), Shanghai, China, 2021. [3] Carlberg, K., Bou-Mosleh, C., Farhat, C., Efficient non-linear model reduction via a least-squaresPetrov–Galerkin projection and compressive tensor approximations, International Journal for Nu-merical Methods in Engineering, 86(2), pp. 155–181, 2011. [4] Maday, Y., Taddei, T., Adaptive PBDW approach to state estimation: noisy observations; user-defined update spaces, SIAM Journal on Scientific Computing, 41(4), pp. B669–B693, 2019. [5] Le-Khac, P. H., Healy, G., Smeaton, A. F., Contrastive representation learning: A framework andreview, IEEE Access, 8, pp. 193907–193934, 2020.