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High-fidelity numerical simulations such as Computational Fluid Dynamics (CFD) have been proven effective in analysing haemodynamics, offering insight into many vascular conditions. However, these methods often face challenges of high computational cost and long processing times. Data-driven approaches such as Reduced Order Modeling (ROM) and Machine Learning (ML) are increasingly being explored alongside CFD to advance biomechanical research and application. This study presents an integration of Proper Orthogonal Decomposition (POD)-based ROM with neural network-based ML models to predict Wall Shear Stress (WSS) in patient-specific vascular pathologies. CFD was used to generate WSS data, followed by POD to construct the ROM. The ML models were trained to predict the ROM coefficients from the inlet flowrate waveform, which can be routinely collected in the clinic. Two ML models were explored: a simpler flowrate-coefficients mapping model and a more advanced autoregressive model. Both models were tested against two case studies: flow in Peripheral Arterial Disease (PAD) and flow in Aortic Dissection (AD). Despite the limited training data sets (three flowrate waveforms for the PAD case and two for the AD case), the models were able to predict the haemodynamic indices, with the flowrate-coefficients mapping model outperforming the autoregressive model in both case studies. The accuracy is higher in the PAD case study, with reduced accuracy in the more complex case study of AD. Additionally, the computational cost analysis reveals a significant reduction in computational demands, with speed-up ratios on the order of $10^4$ for both case studies. This approach shows an effective integration of ROM and ML techniques for fast and reliable evaluations of haemodynamic properties that contribute to vascular conditions, setting the stage for clinical translation.