The integration of in-silico models into clinical research has advanced our understanding of tissue and fluid behaviour in the human body, enabling disease progression prediction and treatment evaluation [1,2]. This mini-symposium will focus on recent developments in modelling and analysis of forward and inverse problems in biomedicine, focusing on the linkage between novel techniques based on surrogate reduced-order modeling with applications in the context of cardiovascular and cerebral mechanics. Forward problems address field prediction from known physiological parameters and boundary conditions, e.g., solving the Navier–Stokes equations in vascular segments or simulating the poroelastic dynamics driven by CSF–brain parenchyma interaction. These models pose computational challenges due to the complexity of geometries and of the multiphysics coupling, as well as to the need of patient-specific parameter tuning. Inverse problems aim to reconstruct unknown parameters or full states—such as pressure fields, material properties, or transport dynamics—from medical data typically characterized by limited availability and quality (presence of noise and measurement artefacts), using optimization, data assimilation and scientific machine learning (SciML) strategies. Examples include physics-informed neural networks, Kalman filters, auto-encoders, and variational methods. The symposium will highlight challenges and advances related to the application of these techniques in the context of vascular diseases (e.g., modeling of aneurysms and stenosis), CSF-related disorders (hydrocephalus, Alzheimer’s disease) and for soft tissues (e.g., liver, brain). Methodological contributions of interest include novel finite element schemes to address the coupled problems, data assimilation based on model order reduction, multiscale modelling, machine learning, surrogate and data-driven modelling and variational data assimilation. [1] Lombardi, D. Reduced order modelling for direct and inverse problems in haemodynamics, Editor(s): Francisco Chinesta, Elías Cueto, Yohan Payan, Jacques Ohayon. In Biomechanics of Living Organs, Reduced Order Models for the Biomechanics of Living Organs. 2023. [2] I. Fumagalli, S. Pagani, C. Vergara, L. Dede, A. D.A., M. Del Greco, A. Frontera, G. Luciani, G. Pontone, R. Scrofani, A. Quarteroni, The role of computational methods in cardiovascular medicine: a narrative review. Transl Pediatr. 13 (2024).