Determining the Windkessel (WK) parameters of coupled 1D–0D models for blood flow from patient-specific blood pressure measurements is an inverse problem, being crucial for reliable simulations. However, traditional calibration schemes may require repeated costly numerical simulations within optimization loops, limiting their applicability in real-time settings. Recently, the use of optimized 0D surrogate models in a Bayesian framework for uncertainty-aware calibration demonstrated the benefit of replacing costly simulations [1]. However, the limited expressiveness of 0D models motivates the development of alternative surrogate approaches for hemodynamic inverse problems. In this talk, we propose a purely data-driven calibration framework based on a neural network (NN) surrogate that replaces the coupled 1D-0D model during parameter inference. A fully connected feedforward neural network is trained on high-fidelity simulation data generated by a dimensionally reduced 1D–0D blood flow model of a systemic arterial network, with the global WK parameters varied within a reference range. The NN learns the mapping from time, spatial position along the left brachial artery, and global WK parameters (total peripheral resistance R and total compliance C) to arterial blood pressure. Trained without physics-informed regularization, the surrogate accurately emulates pressure pulse waves over the full spatio-temporal and parametric domain at negligible computational cost. For calibrating the model to a measured pulse wave, the surrogate model is extended by "dummy" neurons representing the unknown WK parameters, the measurement location, and a temporal phase shift. By retraining only these neurons, the method is able to solve the inverse problem entirely within the NN framework, bypassing external optimization loops as in [2]. Numerical experiments with synthetic measurement data demonstrate accurate and robust parameter estimation, even under noise, uncertainty in sensor location, and temporal misalignment between model and data [3]. This highlights the potential in the field of real-time digital twins of the cardiovascular state.